TSTP Solution File: GRP059-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP059-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 11:16:59 EDT 2022
% Result : Unsatisfiable 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP059-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:58:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.03 ============================== Prover9 ===============================
% 0.75/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.03 Process 417 was started by sandbox2 on n005.cluster.edu,
% 0.75/1.03 Mon Jun 13 11:58:39 2022
% 0.75/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32482_n005.cluster.edu".
% 0.75/1.03 ============================== end of head ===========================
% 0.75/1.03
% 0.75/1.03 ============================== INPUT =================================
% 0.75/1.03
% 0.75/1.03 % Reading from file /tmp/Prover9_32482_n005.cluster.edu
% 0.75/1.03
% 0.75/1.03 set(prolog_style_variables).
% 0.75/1.03 set(auto2).
% 0.75/1.03 % set(auto2) -> set(auto).
% 0.75/1.03 % set(auto) -> set(auto_inference).
% 0.75/1.03 % set(auto) -> set(auto_setup).
% 0.75/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.03 % set(auto) -> set(auto_limits).
% 0.75/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.03 % set(auto) -> set(auto_denials).
% 0.75/1.03 % set(auto) -> set(auto_process).
% 0.75/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.03 % set(auto2) -> assign(stats, some).
% 0.75/1.03 % set(auto2) -> clear(echo_input).
% 0.75/1.03 % set(auto2) -> set(quiet).
% 0.75/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.03 % set(auto2) -> clear(print_given).
% 0.75/1.03 assign(lrs_ticks,-1).
% 0.75/1.03 assign(sos_limit,10000).
% 0.75/1.03 assign(order,kbo).
% 0.75/1.03 set(lex_order_vars).
% 0.75/1.03 clear(print_given).
% 0.75/1.03
% 0.75/1.03 % formulas(sos). % not echoed (2 formulas)
% 0.75/1.03
% 0.75/1.03 ============================== end of input ==========================
% 0.75/1.03
% 0.75/1.03 % From the command line: assign(max_seconds, 300).
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.03
% 0.75/1.03 % Formulas that are not ordinary clauses:
% 0.75/1.03
% 0.75/1.03 ============================== end of process non-clausal formulas ===
% 0.75/1.03
% 0.75/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.03
% 0.75/1.03 ============================== PREDICATE ELIMINATION =================
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials:
% 0.75/1.03 % copying label prove_these_axioms to answer in negative clause
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03
% 0.75/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.75/1.03 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.00 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms.
% 0.75/1.03 % Length of proof is 68.
% 0.75/1.03 % Level of proof is 24.
% 0.75/1.03 % Maximum clause weight is 34.000.
% 0.75/1.03 % Given clauses 66.
% 0.75/1.03
% 0.75/1.03 1 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.03 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.75/1.03 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 0.75/1.03 4 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)). [para(1(a,1),1(a,1,1,1,1,1))].
% 0.75/1.03 8 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))),E)),F),inverse(F)),multiply(V6,inverse(V6)))) = E. [para(4(a,2),1(a,1,1,1,1,1,1,1))].
% 0.75/1.03 9 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D))))),E),F),multiply(V6,inverse(V6)))) = inverse(multiply(E,F)). [para(4(a,2),1(a,1,1,1,1,1,1))].
% 0.75/1.03 15 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(4(a,1),4(a,1))].
% 0.75/1.03 21 multiply(A,inverse(A)) = c_0. [new_symbol(15)].
% 0.75/1.03 32 inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0))),D),E),c_0)) = inverse(multiply(D,E)). [back_rewrite(9),rewrite([21(8),21(14)])].
% 0.75/1.03 33 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)),D)),E),inverse(E)),c_0)) = D. [back_rewrite(8),rewrite([21(8),21(16)])].
% 0.75/1.03 37 inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0)) = c_0. [back_rewrite(4),rewrite([21(8),21(11)])].
% 0.75/1.03 38 inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),c_0)) = C. [back_rewrite(1),rewrite([21(7)])].
% 0.75/1.03 39 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),B),inverse(B)),c_0)) = A. [back_rewrite(33),rewrite([37(9)])].
% 0.75/1.03 40 inverse(multiply(multiply(multiply(inverse(c_0),A),B),c_0)) = inverse(multiply(A,B)). [back_rewrite(32),rewrite([37(9)])].
% 0.75/1.03 46 inverse(multiply(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A))))),c_0)) = A. [para(21(a,1),39(a,1,1,1,1))].
% 0.75/1.03 49 inverse(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0)) = inverse(c_0). [para(21(a,1),46(a,1,1,1,2,1,1,1))].
% 0.75/1.03 51 multiply(multiply(multiply(c_0,inverse(inverse(inverse(c_0)))),c_0),inverse(c_0)) = c_0. [para(49(a,1),21(a,1,2))].
% 0.75/1.03 64 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(inverse(inverse(c_0)),A)). [para(21(a,1),40(a,1,1,1,1))].
% 0.75/1.03 65 inverse(multiply(A,inverse(multiply(inverse(c_0),A)))) = inverse(multiply(c_0,c_0)). [para(21(a,1),40(a,1,1,1)),flip(a)].
% 0.75/1.03 67 inverse(multiply(inverse(inverse(c_0)),inverse(inverse(inverse(multiply(c_0,A)))))) = A. [para(46(a,1),40(a,2)),rewrite([40(15),64(10)])].
% 0.75/1.03 70 inverse(multiply(inverse(inverse(c_0)),inverse(c_0))) = inverse(multiply(c_0,c_0)). [para(21(a,1),64(a,1,1,1)),flip(a)].
% 0.75/1.03 73 multiply(multiply(inverse(inverse(c_0)),inverse(c_0)),inverse(multiply(c_0,c_0))) = c_0. [para(70(a,1),21(a,1,2))].
% 0.75/1.03 85 inverse(multiply(inverse(c_0),c_0)) = c_0. [para(65(a,1),39(a,1,1,1,1,1)),rewrite([39(10)]),flip(a)].
% 0.75/1.03 90 multiply(multiply(inverse(c_0),c_0),c_0) = c_0. [para(85(a,1),21(a,1,2))].
% 0.75/1.03 100 inverse(multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)) = c_0. [para(51(a,1),37(a,1,1,1,1,2,1,1)),rewrite([40(17)])].
% 0.75/1.03 101 inverse(multiply(multiply(inverse(multiply(multiply(A,B),inverse(c_0))),A),B)) = c_0. [para(37(a,1),40(a,1)),flip(a)].
% 0.75/1.03 128 inverse(multiply(multiply(multiply(inverse(multiply(c_0,c_0)),A),B),c_0)) = inverse(multiply(inverse(c_0),multiply(A,B))). [para(65(a,1),38(a,1,1,1,1,1))].
% 0.75/1.03 136 inverse(multiply(multiply(multiply(inverse(multiply(c_0,A)),multiply(multiply(inverse(c_0),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0)),c_0),c_0)) = A. [para(100(a,1),39(a,1,1,1,2))].
% 0.75/1.03 140 inverse(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0)))))) = c_0. [para(100(a,1),38(a,1,1,1,1,1)),rewrite([21(4),64(11)])].
% 0.75/1.03 141 multiply(multiply(inverse(inverse(c_0)),multiply(c_0,inverse(inverse(inverse(c_0))))),c_0) = c_0. [para(140(a,1),21(a,1,2))].
% 0.75/1.03 145 inverse(multiply(multiply(inverse(c_0),A),inverse(A))) = c_0. [para(21(a,1),101(a,1,1,1,1,1,1)),rewrite([21(4)])].
% 0.75/1.03 152 inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(c_0)),inverse(c_0))),inverse(multiply(c_0,c_0)))) = c_0. [para(73(a,1),101(a,1,1,1,1,1,1)),rewrite([21(4)])].
% 0.75/1.03 156 inverse(multiply(multiply(multiply(c_0,inverse(multiply(multiply(A,B),inverse(c_0)))),A),c_0)) = B. [para(101(a,1),38(a,1,1,1,1,1))].
% 0.75/1.03 202 inverse(multiply(inverse(inverse(c_0)),A)) = inverse(A). [para(145(a,1),38(a,1,1,1,1,1)),rewrite([21(4),64(5)])].
% 0.75/1.03 205 inverse(multiply(c_0,c_0)) = c_0. [para(145(a,1),101(a,1,1,1,1)),rewrite([21(4)])].
% 0.75/1.03 220 inverse(inverse(c_0)) = c_0. [back_rewrite(70),rewrite([202(7),205(7)])].
% 0.75/1.03 222 inverse(multiply(c_0,inverse(inverse(inverse(multiply(c_0,A)))))) = A. [back_rewrite(67),rewrite([220(3)])].
% 0.75/1.03 223 inverse(multiply(multiply(c_0,A),c_0)) = inverse(multiply(c_0,A)). [back_rewrite(64),rewrite([220(8)])].
% 0.75/1.03 228 inverse(c_0) = c_0. [back_rewrite(152),rewrite([220(5),21(6),205(8),90(6)])].
% 0.75/1.03 229 inverse(multiply(multiply(multiply(c_0,A),B),c_0)) = inverse(multiply(c_0,multiply(A,B))). [back_rewrite(128),rewrite([205(4),228(8)])].
% 0.75/1.03 246 inverse(multiply(c_0,A)) = inverse(A). [back_rewrite(202),rewrite([228(2),228(2)])].
% 0.75/1.03 252 multiply(multiply(c_0,multiply(c_0,c_0)),c_0) = c_0. [back_rewrite(141),rewrite([228(2),228(2),228(4),228(4),228(4)])].
% 0.75/1.03 255 inverse(multiply(multiply(multiply(inverse(A),c_0),c_0),c_0)) = A. [back_rewrite(136),rewrite([246(3),228(3),228(5),228(5),228(5),252(8)])].
% 0.75/1.03 286 inverse(multiply(inverse(multiply(multiply(A,B),c_0)),A)) = B. [back_rewrite(156),rewrite([228(4),229(10),246(8)])].
% 0.75/1.03 324 inverse(multiply(multiply(c_0,A),c_0)) = inverse(A). [back_rewrite(223),rewrite([246(8)])].
% 0.75/1.03 325 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(222),rewrite([246(4),246(6)])].
% 0.75/1.03 344 inverse(multiply(multiply(multiply(inverse(A),B),inverse(B)),c_0)) = A. [back_rewrite(39),rewrite([246(3)])].
% 0.75/1.03 354 multiply(inverse(inverse(inverse(A))),A) = c_0. [para(325(a,1),21(a,1,2))].
% 0.75/1.03 355 multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),c_0) = c_0. [para(37(a,1),325(a,1,1,1,1)),rewrite([228(2),228(2),228(2)]),flip(a)].
% 0.75/1.03 357 multiply(c_0,A) = A. [para(246(a,1),325(a,1,1,1,1)),rewrite([325(4)]),flip(a)].
% 0.75/1.03 371 inverse(multiply(A,c_0)) = inverse(A). [back_rewrite(324),rewrite([357(2)])].
% 0.75/1.03 391 inverse(multiply(multiply(inverse(A),B),inverse(B))) = A. [back_rewrite(344),rewrite([371(7)])].
% 0.75/1.03 394 inverse(multiply(inverse(multiply(A,B)),A)) = B. [back_rewrite(286),rewrite([371(4)])].
% 0.75/1.03 395 inverse(inverse(A)) = A. [back_rewrite(255),rewrite([371(8),371(6),371(4)])].
% 0.75/1.03 406 multiply(inverse(A),A) = c_0. [back_rewrite(354),rewrite([395(2)])].
% 0.75/1.03 407 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([406(4),406(5),406(7),357(6)]),xx(a),xx(b)].
% 0.75/1.03 409 multiply(A,c_0) = A. [para(371(a,1),395(a,1,1)),rewrite([395(2)]),flip(a)].
% 0.75/1.03 416 multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C) = c_0. [back_rewrite(355),rewrite([409(8)])].
% 0.75/1.03 418 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(394(a,1),395(a,1,1)),flip(a)].
% 0.75/1.03 425 multiply(A,multiply(inverse(A),B)) = B. [para(391(a,1),418(a,1,1)),rewrite([395(5)])].
% 0.75/1.03 428 multiply(inverse(A),multiply(A,B)) = B. [para(395(a,1),425(a,1,2,1))].
% 0.75/1.03 429 multiply(multiply(A,B),inverse(B)) = A. [para(418(a,1),425(a,1,2))].
% 0.75/1.03 434 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(428(a,1),418(a,1,1,1)),flip(a)].
% 0.75/1.03 435 multiply(multiply(A,multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),C)),B) = c_0. [back_rewrite(416),rewrite([434(3),434(3)])].
% 0.75/1.03 446 multiply(multiply(inverse(A),multiply(multiply(A,B),C)),inverse(C)) = B. [para(435(a,1),428(a,1,2)),rewrite([434(8),434(7),434(7),434(5),395(3),395(3),395(4),409(8)])].
% 0.75/1.03 489 multiply(multiply(A,multiply(B,C)),inverse(C)) = multiply(A,B). [para(428(a,1),446(a,1,1,2,1)),rewrite([395(2)])].
% 0.75/1.03 495 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(489(a,1),429(a,1,1)),rewrite([395(3)])].
% 0.75/1.03 496 $F # answer(prove_these_axioms). [resolve(495,a,407,a)].
% 0.75/1.03
% 0.75/1.03 % SZS output end Refutation
% 0.75/1.03 ============================== end of proof ==========================
% 0.75/1.03
% 0.75/1.03 ============================== STATISTICS ============================
% 0.75/1.03
% 0.75/1.03 Given=66. Generated=1447. Kept=494. proofs=1.
% 0.75/1.03 Usable=21. Sos=30. Demods=53. Limbo=3, Disabled=441. Hints=0.
% 0.75/1.03 Megabytes=0.50.
% 0.75/1.03 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.75/1.03
% 0.75/1.03 ============================== end of statistics =====================
% 0.75/1.03
% 0.75/1.03 ============================== end of search =========================
% 0.75/1.03
% 0.75/1.03 THEOREM PROVED
% 0.75/1.03 % SZS status Unsatisfiable
% 0.75/1.03
% 0.75/1.03 Exiting with 1 proof.
% 0.75/1.03
% 0.75/1.03 Process 417 exit (max_proofs) Mon Jun 13 11:58:39 2022
% 0.75/1.03 Prover9 interrupted
%------------------------------------------------------------------------------