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ex26.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6433 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex26.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex26.in
formulas(sos).
-p(x,y) | q(x,y,f(x,y)).
-r(y,z) | q(a,y,z).
r(y,z) | -q(a,y,z).
p(x,g(x)) | q(x,g(x),z).
-r(x,y) | -q(x,w,z).
end_of_list.
formulas(goals).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
-p(x,y) | q(x,y,f(x,y)). [assumption].
-r(x,y) | q(a,x,y). [assumption].
r(x,y) | -q(a,x,y). [assumption].
p(x,g(x)) | q(x,g(x),y). [assumption].
-r(x,y) | -q(x,z,u). [assumption].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating p/2
1 p(x,g(x)) | q(x,g(x),y). [assumption].
2 -p(x,y) | q(x,y,f(x,y)). [assumption].
Derived: q(x,g(x),y) | q(x,g(x),f(x,g(x))). [resolve(1,a,2,a)].
Eliminating r/2
3 r(x,y) | -q(a,x,y). [assumption].
4 -r(x,y) | q(a,x,y). [assumption].
5 -r(x,y) | -q(x,z,u). [assumption].
Derived: -q(x,y,z) | -q(a,x,u). [resolve(5,a,3,a)].
============================== end predicate elimination =============
Auto_denials: (non-Horn, no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ q ]).
Function symbol precedence: function_order([ a, f, g ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(binary_resolution). % (non-Horn)
% set(neg_ur_resolution). % (non-Horn, less than 100 clauses)
Auto_process settings:
% set(factor). % (non-Horn)
% set(unit_deletion). % (non-Horn)
kept: 6 q(x,g(x),y) | q(x,g(x),f(x,g(x))). [resolve(1,a,2,a)].
kept: 7 -q(x,y,z) | -q(a,x,u). [resolve(5,a,3,a)].
kept: 8 q(x,g(x),f(x,g(x))). [factor(6,a,b)].
kept: 9 -q(a,a,x). [factor(7,a,b)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
7 -q(x,y,z) | -q(a,x,u). [resolve(5,a,3,a)].
8 q(x,g(x),f(x,g(x))). [factor(6,a,b)].
9 -q(a,a,x). [factor(7,a,b)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.00 seconds.
given #1 (I,wt=8): 7 -q(x,y,z) | -q(a,x,u). [resolve(5,a,3,a)].
given #2 (I,wt=8): 8 q(x,g(x),f(x,g(x))). [factor(6,a,b)].
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 9.
% Level of proof is 4.
% Maximum clause weight is 13.000.
% Given clauses 2.
1 p(x,g(x)) | q(x,g(x),y). [assumption].
2 -p(x,y) | q(x,y,f(x,y)). [assumption].
3 r(x,y) | -q(a,x,y). [assumption].
5 -r(x,y) | -q(x,z,u). [assumption].
6 q(x,g(x),y) | q(x,g(x),f(x,g(x))). [resolve(1,a,2,a)].
7 -q(x,y,z) | -q(a,x,u). [resolve(5,a,3,a)].
8 q(x,g(x),f(x,g(x))). [factor(6,a,b)].
10 -q(g(a),x,y). [resolve(8,a,7,b)].
11 $F. [resolve(10,a,8,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=2. Generated=5. Kept=5. proofs=1.
Usable=2. Sos=1. Demods=0. Limbo=0, Disabled=8. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=1.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=3.
Megabytes=0.03.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6433 exit (max_proofs) Wed Jun 26 22:33:07 2019