TSTP Solution File: GRP604-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:19:48 EDT 2022
% Result : Unsatisfiable 0.71s 1.01s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 09:47:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.01 ============================== Prover9 ===============================
% 0.71/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.01 Process 4097 was started by sandbox on n009.cluster.edu,
% 0.71/1.01 Tue Jun 14 09:47:08 2022
% 0.71/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3943_n009.cluster.edu".
% 0.71/1.01 ============================== end of head ===========================
% 0.71/1.01
% 0.71/1.01 ============================== INPUT =================================
% 0.71/1.01
% 0.71/1.01 % Reading from file /tmp/Prover9_3943_n009.cluster.edu
% 0.71/1.01
% 0.71/1.01 set(prolog_style_variables).
% 0.71/1.01 set(auto2).
% 0.71/1.01 % set(auto2) -> set(auto).
% 0.71/1.01 % set(auto) -> set(auto_inference).
% 0.71/1.01 % set(auto) -> set(auto_setup).
% 0.71/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.01 % set(auto) -> set(auto_limits).
% 0.71/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.01 % set(auto) -> set(auto_denials).
% 0.71/1.01 % set(auto) -> set(auto_process).
% 0.71/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.01 % set(auto2) -> assign(stats, some).
% 0.71/1.01 % set(auto2) -> clear(echo_input).
% 0.71/1.01 % set(auto2) -> set(quiet).
% 0.71/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.01 % set(auto2) -> clear(print_given).
% 0.71/1.01 assign(lrs_ticks,-1).
% 0.71/1.01 assign(sos_limit,10000).
% 0.71/1.01 assign(order,kbo).
% 0.71/1.01 set(lex_order_vars).
% 0.71/1.01 clear(print_given).
% 0.71/1.01
% 0.71/1.01 % formulas(sos). % not echoed (3 formulas)
% 0.71/1.01
% 0.71/1.01 ============================== end of input ==========================
% 0.71/1.01
% 0.71/1.01 % From the command line: assign(max_seconds, 300).
% 0.71/1.01
% 0.71/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.01
% 0.71/1.01 % Formulas that are not ordinary clauses:
% 0.71/1.01
% 0.71/1.01 ============================== end of process non-clausal formulas ===
% 0.71/1.01
% 0.71/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.01
% 0.71/1.01 ============================== PREDICATE ELIMINATION =================
% 0.71/1.01
% 0.71/1.01 ============================== end predicate elimination =============
% 0.71/1.01
% 0.71/1.01 Auto_denials:
% 0.71/1.01 % copying label prove_these_axioms_4 to answer in negative clause
% 0.71/1.01
% 0.71/1.01 Term ordering decisions:
% 0.71/1.01
% 0.71/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.71/1.01 Function symbol KB weights: a=1. b=1. double_divide=1. multiply=1. inverse=0.
% 0.71/1.01
% 0.71/1.01 ============================== end of process initial clauses ========
% 0.71/1.01
% 0.71/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.01
% 0.71/1.01 ============================== end of clauses for search =============
% 0.71/1.01
% 0.71/1.01 ============================== SEARCH ================================
% 0.71/1.01
% 0.71/1.01 % Starting search at 0.01 seconds.
% 0.71/1.01
% 0.71/1.01 ============================== PROOF =================================
% 0.71/1.01 % SZS status Unsatisfiable
% 0.71/1.01 % SZS output start Refutation
% 0.71/1.01
% 0.71/1.01 % Proof 1 at 0.05 (+ 0.01) seconds: prove_these_axioms_4.
% 0.71/1.01 % Length of proof is 48.
% 0.71/1.01 % Level of proof is 20.
% 0.71/1.01 % Maximum clause weight is 28.000.
% 0.71/1.01 % Given clauses 15.
% 0.71/1.01
% 0.71/1.01 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.71/1.01 2 inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.71/1.01 3 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.71/1.01 4 inverse(double_divide(b,a)) != inverse(double_divide(a,b)) # answer(prove_these_axioms_4). [copy(3),rewrite([1(3),1(7)])].
% 0.71/1.01 5 inverse(double_divide(A,inverse(double_divide(B,double_divide(A,double_divide(C,D)))))) = inverse(double_divide(inverse(double_divide(C,B)),D)). [para(2(a,1),2(a,1,1,1,1,2)),flip(a)].
% 0.71/1.01 6 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B. [para(5(a,1),2(a,1,1,1))].
% 0.71/1.01 7 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,inverse(double_divide(A,double_divide(C,D))))),B))) = D. [para(2(a,1),6(a,1,1,1,1,1))].
% 0.71/1.01 8 inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),D)),double_divide(E,D))) = inverse(double_divide(B,double_divide(E,double_divide(A,C)))). [para(5(a,1),6(a,1,1,1,1,1))].
% 0.71/1.01 11 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C. [para(6(a,1),6(a,1,1,1))].
% 0.71/1.01 14 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)). [para(11(a,1),6(a,1,1,1,1,1))].
% 0.71/1.01 17 inverse(double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),double_divide(C,double_divide(B,D)))) = D. [para(11(a,1),11(a,1,1,2,1))].
% 0.71/1.01 20 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(inverse(double_divide(C,D)),double_divide(C,E)),B))) = double_divide(E,double_divide(D,A)). [para(17(a,1),6(a,1,1,1,1,1))].
% 0.71/1.01 43 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(C,inverse(double_divide(D,double_divide(C,E))))))) = inverse(double_divide(D,double_divide(B,E))). [para(2(a,1),14(a,1,1,1)),flip(a)].
% 0.71/1.01 51 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C. [para(14(a,1),6(a,1))].
% 0.71/1.01 55 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(inverse(double_divide(C,D)),E)))) = inverse(double_divide(D,double_divide(B,double_divide(C,E)))). [para(6(a,1),14(a,1,1,1)),flip(a)].
% 0.71/1.01 61 inverse(double_divide(A,double_divide(B,double_divide(inverse(double_divide(C,D)),double_divide(C,A))))) = double_divide(inverse(double_divide(E,B)),double_divide(E,D)). [para(11(a,1),14(a,1,1,1))].
% 0.71/1.01 68 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,double_divide(D,E)),B))) = double_divide(E,double_divide(double_divide(inverse(double_divide(F,D)),double_divide(F,C)),A)). [para(17(a,1),14(a,2,1))].
% 0.71/1.01 76 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(inverse(double_divide(A,inverse(inverse(double_divide(inverse(double_divide(D,E)),double_divide(B,E)))))),C))) = D. [para(14(a,2),7(a,1,1,2,1,1,2,1))].
% 0.71/1.01 82 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(double_divide(inverse(double_divide(E,C)),double_divide(E,F)),double_divide(inverse(double_divide(F,D)),A)). [para(14(a,1),14(a,2,1))].
% 0.71/1.01 95 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))). [para(51(a,1),6(a,1,1,1,1,1,1))].
% 0.71/1.01 114 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,D)),inverse(double_divide(A,E)))),B))) = double_divide(C,inverse(double_divide(D,E))). [para(51(a,1),7(a,1,1,2,1,1,2,1,2))].
% 0.71/1.01 115 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)). [para(51(a,1),7(a,1,1,2,1,1,2,1)),rewrite([95(10)])].
% 0.71/1.01 128 inverse(inverse(double_divide(A,double_divide(B,A)))) = B. [back_rewrite(76),rewrite([95(15),115(10),115(6)])].
% 0.71/1.01 139 inverse(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),C))) = inverse(double_divide(A,B)). [para(51(a,1),128(a,1,1,1,2))].
% 0.71/1.01 140 inverse(inverse(A)) = A. [para(51(a,1),128(a,1,1,1))].
% 0.71/1.01 141 double_divide(double_divide(A,inverse(double_divide(B,C))),C) = inverse(double_divide(A,B)). [back_rewrite(139),rewrite([140(6)])].
% 0.71/1.01 150 double_divide(A,double_divide(B,A)) = B. [back_rewrite(128),rewrite([140(4)])].
% 0.71/1.01 181 inverse(double_divide(A,double_divide(B,inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,D)))))) = inverse(double_divide(A,double_divide(B,double_divide(inverse(double_divide(F,E)),double_divide(F,C))))). [para(14(a,2),8(a,2,1,2,2)),rewrite([8(12)]),flip(a)].
% 0.71/1.01 186 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(C,B))) = inverse(double_divide(D,double_divide(C,double_divide(E,double_divide(E,inverse(double_divide(D,A))))))). [para(51(a,1),8(a,1,1,1,1,1,1))].
% 0.71/1.01 189 double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D)))))) = inverse(double_divide(C,D)). [para(51(a,1),8(a,2,1,2)),rewrite([95(13)])].
% 0.71/1.01 196 inverse(double_divide(inverse(double_divide(A,B)),double_divide(double_divide(C,D),B))) = double_divide(inverse(C),double_divide(D,A)). [para(150(a,1),14(a,2,1,1))].
% 0.71/1.01 199 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = double_divide(C,B). [para(150(a,1),51(a,1,2,2,1))].
% 0.71/1.01 200 double_divide(double_divide(A,B),A) = B. [para(150(a,1),150(a,1,2))].
% 0.71/1.01 204 double_divide(double_divide(inverse(double_divide(A,B)),double_divide(A,C)),double_divide(inverse(double_divide(C,D)),E)) = double_divide(inverse(B),double_divide(D,E)). [back_rewrite(82),rewrite([196(6)]),flip(a)].
% 0.71/1.01 207 double_divide(A,double_divide(double_divide(inverse(double_divide(B,C)),double_divide(B,D)),E)) = double_divide(inverse(D),double_divide(double_divide(C,A),E)). [back_rewrite(68),rewrite([196(7)]),flip(a)].
% 0.71/1.01 209 inverse(double_divide(inverse(A),inverse(double_divide(B,C)))) = double_divide(A,double_divide(B,C)). [back_rewrite(20),rewrite([207(8),141(5)])].
% 0.71/1.01 221 inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(double_divide(inverse(double_divide(C,A)),D),B). [back_rewrite(55),rewrite([199(8)]),flip(a)].
% 0.71/1.01 222 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,C)))),D) = inverse(double_divide(B,double_divide(D,C))). [back_rewrite(43),rewrite([199(9)])].
% 0.71/1.01 225 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(114),rewrite([209(8),196(8),200(4)])].
% 0.71/1.01 246 inverse(double_divide(A,double_divide(B,inverse(double_divide(A,C))))) = inverse(double_divide(inverse(C),inverse(B))). [back_rewrite(186),rewrite([225(5),150(3),221(11),225(10),222(11)]),flip(a)].
% 0.71/1.01 249 double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,double_divide(A,D)))))),E) = inverse(double_divide(B,double_divide(E,inverse(double_divide(D,inverse(C)))))). [back_rewrite(181),rewrite([225(4),150(2),225(10),221(13),225(12)]),flip(a)].
% 0.71/1.01 263 double_divide(A,inverse(double_divide(B,double_divide(A,C)))) = inverse(double_divide(C,inverse(B))). [back_rewrite(61),rewrite([225(4),221(7),225(6),249(7),246(6),140(2),225(7)]),flip(a)].
% 0.71/1.01 278 inverse(double_divide(A,double_divide(B,double_divide(C,D)))) = double_divide(double_divide(C,inverse(double_divide(A,D))),B). [back_rewrite(221),rewrite([225(7)])].
% 0.71/1.01 285 inverse(double_divide(A,inverse(double_divide(B,C)))) = double_divide(inverse(C),double_divide(A,B)). [back_rewrite(204),rewrite([225(4),263(4),225(6),225(7),263(7),140(4),225(3)])].
% 0.71/1.01 288 inverse(double_divide(inverse(A),inverse(B))) = double_divide(A,B). [back_rewrite(199),rewrite([225(5),263(5)])].
% 0.71/1.01 292 inverse(double_divide(A,B)) = double_divide(inverse(B),inverse(A)). [back_rewrite(189),rewrite([225(5),285(4),278(6),150(3),150(5)]),flip(a)].
% 0.71/1.01 376 double_divide(A,B) = double_divide(B,A). [back_rewrite(288),rewrite([292(4),140(2),140(2)])].
% 0.71/1.01 390 $F # answer(prove_these_axioms_4). [back_rewrite(4),rewrite([376(3),292(4),376(5),292(9),376(10)]),xx(a)].
% 0.71/1.01
% 0.71/1.01 % SZS output end Refutation
% 0.71/1.01 ============================== end of proof ==========================
% 0.71/1.01
% 0.71/1.01 ============================== STATISTICS ============================
% 0.71/1.01
% 0.71/1.01 Given=15. Generated=575. Kept=388. proofs=1.
% 0.71/1.01 Usable=3. Sos=6. Demods=79. Limbo=98, Disabled=284. Hints=0.
% 0.71/1.01 Megabytes=0.43.
% 0.71/1.01 User_CPU=0.05, System_CPU=0.01, Wall_clock=0.
% 0.71/1.01
% 0.71/1.01 ============================== end of statistics =====================
% 0.71/1.01
% 0.71/1.01 ============================== end of search =========================
% 0.71/1.01
% 0.71/1.01 THEOREM PROVED
% 0.71/1.01 % SZS status Unsatisfiable
% 0.71/1.01
% 0.71/1.01 Exiting with 1 proof.
% 0.71/1.01
% 0.71/1.01 Process 4097 exit (max_proofs) Tue Jun 14 09:47:08 2022
% 0.71/1.01 Prover9 interrupted
%------------------------------------------------------------------------------