TSTP Solution File: GRP056-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP056-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 11:16:58 EDT 2022
% Result : Unsatisfiable 0.88s 1.15s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.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 : Mon Jun 13 21:21:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.88/1.15 ============================== Prover9 ===============================
% 0.88/1.15 Prover9 (32) version 2009-11A, November 2009.
% 0.88/1.15 Process 28847 was started by sandbox2 on n016.cluster.edu,
% 0.88/1.15 Mon Jun 13 21:21:00 2022
% 0.88/1.15 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28693_n016.cluster.edu".
% 0.88/1.15 ============================== end of head ===========================
% 0.88/1.15
% 0.88/1.15 ============================== INPUT =================================
% 0.88/1.15
% 0.88/1.15 % Reading from file /tmp/Prover9_28693_n016.cluster.edu
% 0.88/1.15
% 0.88/1.15 set(prolog_style_variables).
% 0.88/1.15 set(auto2).
% 0.88/1.15 % set(auto2) -> set(auto).
% 0.88/1.15 % set(auto) -> set(auto_inference).
% 0.88/1.15 % set(auto) -> set(auto_setup).
% 0.88/1.15 % set(auto_setup) -> set(predicate_elim).
% 0.88/1.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.88/1.15 % set(auto) -> set(auto_limits).
% 0.88/1.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.88/1.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.88/1.15 % set(auto) -> set(auto_denials).
% 0.88/1.15 % set(auto) -> set(auto_process).
% 0.88/1.15 % set(auto2) -> assign(new_constants, 1).
% 0.88/1.15 % set(auto2) -> assign(fold_denial_max, 3).
% 0.88/1.15 % set(auto2) -> assign(max_weight, "200.000").
% 0.88/1.15 % set(auto2) -> assign(max_hours, 1).
% 0.88/1.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.88/1.15 % set(auto2) -> assign(max_seconds, 0).
% 0.88/1.15 % set(auto2) -> assign(max_minutes, 5).
% 0.88/1.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.88/1.15 % set(auto2) -> set(sort_initial_sos).
% 0.88/1.15 % set(auto2) -> assign(sos_limit, -1).
% 0.88/1.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.88/1.15 % set(auto2) -> assign(max_megs, 400).
% 0.88/1.15 % set(auto2) -> assign(stats, some).
% 0.88/1.15 % set(auto2) -> clear(echo_input).
% 0.88/1.15 % set(auto2) -> set(quiet).
% 0.88/1.15 % set(auto2) -> clear(print_initial_clauses).
% 0.88/1.15 % set(auto2) -> clear(print_given).
% 0.88/1.15 assign(lrs_ticks,-1).
% 0.88/1.15 assign(sos_limit,10000).
% 0.88/1.15 assign(order,kbo).
% 0.88/1.15 set(lex_order_vars).
% 0.88/1.15 clear(print_given).
% 0.88/1.15
% 0.88/1.15 % formulas(sos). % not echoed (2 formulas)
% 0.88/1.15
% 0.88/1.15 ============================== end of input ==========================
% 0.88/1.15
% 0.88/1.15 % From the command line: assign(max_seconds, 300).
% 0.88/1.15
% 0.88/1.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.88/1.15
% 0.88/1.15 % Formulas that are not ordinary clauses:
% 0.88/1.15
% 0.88/1.15 ============================== end of process non-clausal formulas ===
% 0.88/1.15
% 0.88/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.88/1.15
% 0.88/1.15 ============================== PREDICATE ELIMINATION =================
% 0.88/1.15
% 0.88/1.15 ============================== end predicate elimination =============
% 0.88/1.15
% 0.88/1.15 Auto_denials:
% 0.88/1.15 % copying label prove_these_axioms to answer in negative clause
% 0.88/1.15
% 0.88/1.15 Term ordering decisions:
% 0.88/1.15
% 0.88/1.15 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.88/1.15 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.88/1.15
% 0.88/1.15 ============================== end of process initial clauses ========
% 0.88/1.15
% 0.88/1.15 ============================== CLAUSES FOR SEARCH ====================
% 0.88/1.15
% 0.88/1.15 ============================== end of clauses for search =============
% 0.88/1.15
% 0.88/1.15 ============================== SEARCH ================================
% 0.88/1.15
% 0.88/1.15 % Starting search at 0.01 seconds.
% 0.88/1.15
% 0.88/1.15 ============================== PROOF =================================
% 0.88/1.15 % SZS status Unsatisfiable
% 0.88/1.15 % SZS output start Refutation
% 0.88/1.15
% 0.88/1.15 % Proof 1 at 0.19 (+ 0.00) seconds: prove_these_axioms.
% 0.88/1.15 % Length of proof is 95.
% 0.88/1.15 % Level of proof is 31.
% 0.88/1.15 % Maximum clause weight is 135.000.
% 0.88/1.15 % Given clauses 40.
% 0.88/1.15
% 0.88/1.15 1 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.88/1.15 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].
% 0.88/1.15 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)].
% 0.88/1.15 4 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))). [para(1(a,1),1(a,1,1,1,1,1,2,1))].
% 0.88/1.15 5 multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(C)))),inverse(multiply(inverse(C),C))) = C. [para(1(a,1),1(a,1,1,1,1,1))].
% 0.88/1.15 6 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),multiply(inverse(C),C))))),B)),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = D. [para(1(a,1),1(a,1,1,1,2))].
% 0.88/1.15 10 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(C),C)))),C)))),multiply(A,inverse(C))) = B. [para(4(a,1),1(a,1))].
% 0.88/1.15 13 multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(inverse(multiply(inverse(D),D)))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(C),C)),D)))),multiply(E,inverse(D))). [para(1(a,1),4(a,1,1,1,1,1))].
% 0.88/1.15 17 multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))). [para(4(a,1),4(a,1))].
% 0.88/1.15 23 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D)))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = multiply(C,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(D),D)))),D))). [para(10(a,1),1(a,1,1,1,1,1,2,1))].
% 0.88/1.15 25 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(C),inverse(multiply(inverse(D),D)))),D)))))),multiply(A,inverse(inverse(multiply(inverse(multiply(B,inverse(D))),multiply(B,inverse(D)))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(B,inverse(D))),multiply(B,inverse(D))))),inverse(multiply(inverse(multiply(B,inverse(D))),multiply(B,inverse(D))))))) = multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(multiply(B,inverse(D))))). [para(10(a,1),4(a,2,1,1,2,1))].
% 0.88/1.15 35 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))). [para(10(a,1),17(a,1,1,1,2,1)),rewrite([10(21)])].
% 0.88/1.15 37 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))),C))) = B. [para(35(a,1),1(a,1,1,1)),rewrite([23(21)])].
% 0.88/1.15 40 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))). [para(1(a,1),35(a,1,2,2,1)),rewrite([1(22)])].
% 0.88/1.15 52 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(D)))),inverse(multiply(inverse(D),D)))),D))) = multiply(A,inverse(C)). [para(40(a,1),1(a,1,1,1,1,1,2,1)),rewrite([23(23)])].
% 0.88/1.15 53 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(C,inverse(D)))))),multiply(A,inverse(multiply(C,inverse(D)))))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))) = B. [para(40(a,1),1(a,1,2,1))].
% 0.88/1.15 65 multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),D)))),multiply(B,inverse(D)))),inverse(multiply(inverse(A),multiply(inverse(D),D))))),C)),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))) = multiply(inverse(D),D). [para(1(a,1),5(a,1,1,1,2,1,1,2))].
% 0.88/1.15 102 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(B),D)))),multiply(C,inverse(D)))),inverse(E)))),inverse(multiply(inverse(E),E)))),E))) = multiply(A,inverse(multiply(inverse(D),D))). [para(1(a,1),52(a,1,2,1,1,1,1,1,1,1))].
% 0.88/1.15 153 multiply(A,inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(C))))) = multiply(A,inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(C))))). [para(53(a,1),52(a,1,2,1,1,1,1,1,1,1)),rewrite([102(26)])].
% 0.88/1.15 160 multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),C)))),multiply(B,inverse(multiply(inverse(C),C)))))) = multiply(A,inverse(multiply(inverse(D),D))). [para(1(a,1),153(a,1,2,1,1,1)),rewrite([1(14)]),flip(a)].
% 0.88/1.15 187 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),D)))),multiply(B,inverse(D)))),inverse(multiply(inverse(E),multiply(inverse(D),D))))),C)))),multiply(A,inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D))))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))))) = multiply(inverse(multiply(F,inverse(E))),multiply(F,inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))). [para(6(a,1),4(a,2,1,1,2,1))].
% 0.88/1.15 188 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))))) = multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(E),B)))),multiply(D,inverse(B)))),inverse(multiply(inverse(C),multiply(inverse(B),B))))),E)),inverse(multiply(inverse(B),B)))). [para(6(a,1),4(a,2,1,1))].
% 0.88/1.15 196 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))))),B)))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),multiply(inverse(B),B)))) = multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))))). [para(6(a,1),10(a,1,1,1,2,1)),flip(a)].
% 0.88/1.15 236 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),C)))),multiply(B,inverse(multiply(inverse(C),C))))))),multiply(A,inverse(D)))),inverse(multiply(inverse(D),D))) = D. [para(160(a,2),1(a,1,1,1,1,1))].
% 0.88/1.15 239 multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(inverse(C),C))). [para(1(a,1),160(a,1,2,1,1,1)),rewrite([1(14)])].
% 0.88/1.15 240 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(F),F)))),multiply(E,inverse(multiply(inverse(F),F))))),C)))),multiply(D,inverse(C))). [para(160(a,1),4(a,1,1,1,1,1))].
% 0.88/1.15 248 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),C)))),multiply(A,inverse(C))) = inverse(multiply(inverse(C),C)). [para(160(a,2),4(a,1,1,1,1,1)),rewrite([236(30)]),flip(a)].
% 0.88/1.15 328 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(multiply(inverse(C),C)). [back_rewrite(240),rewrite([248(40)])].
% 0.88/1.15 333 multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(inverse(multiply(inverse(D),D)))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = inverse(multiply(inverse(D),D)). [back_rewrite(13),rewrite([248(37)])].
% 0.88/1.15 334 multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),D)))),multiply(B,inverse(D)))),inverse(multiply(inverse(A),multiply(inverse(D),D))))),C)),inverse(multiply(inverse(D),D)))) = inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D))). [back_rewrite(188),rewrite([328(34)]),flip(a)].
% 0.88/1.15 337 multiply(inverse(inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(A),A)))),inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(A),A)))) = multiply(inverse(A),A). [back_rewrite(65),rewrite([334(24)])].
% 0.88/1.15 342 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),B)))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),multiply(inverse(B),B)))) = multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))))). [back_rewrite(196),rewrite([337(16)])].
% 0.88/1.15 344 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),D)))),multiply(B,inverse(D)))),inverse(multiply(inverse(E),multiply(inverse(D),D))))),C)))),multiply(A,inverse(inverse(multiply(inverse(D),D)))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))) = multiply(inverse(multiply(F,inverse(E))),multiply(F,inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))). [back_rewrite(187),rewrite([337(36),337(43),337(47)])].
% 0.88/1.15 351 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = C. [para(239(a,1),1(a,1,1,1,1,1))].
% 0.88/1.15 354 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),D))) = B. [para(239(a,1),1(a,1))].
% 0.88/1.15 361 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(B),B)))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))) = multiply(inverse(multiply(C,inverse(multiply(inverse(D),D)))),multiply(C,inverse(B))). [para(239(a,1),4(a,2,1,1))].
% 0.88/1.15 377 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(D),D))))) = B. [para(239(a,1),37(a,1,2,1))].
% 0.88/1.15 384 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),multiply(inverse(C),C))))),C)),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = D. [para(239(a,1),6(a,1,1,1,1,1,1,1,1,1))].
% 0.88/1.15 386 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),multiply(inverse(C),C))))),inverse(multiply(inverse(E),E)))),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = D. [para(239(a,1),6(a,1,1,1))].
% 0.88/1.15 389 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),multiply(inverse(C),C))))),B)),inverse(multiply(inverse(E),E))) = D. [para(239(a,1),6(a,1))].
% 0.88/1.15 390 multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),D))). [para(239(a,1),239(a,1,2,1))].
% 0.88/1.15 391 multiply(inverse(A),A) = inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B))). [back_rewrite(334),rewrite([389(23)])].
% 0.88/1.15 392 multiply(inverse(A),A) = c_0. [new_symbol(391)].
% 0.88/1.15 393 inverse(c_0) = c_0. [back_rewrite(391),rewrite([392(2),392(3),392(5),392(5)]),flip(a)].
% 0.88/1.15 394 multiply(A,inverse(multiply(c_0,c_0))) = multiply(A,c_0). [back_rewrite(390),rewrite([392(2),393(2),393(2),392(3),393(3),392(7),393(7)])].
% 0.88/1.15 395 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),c_0)))),B)),c_0) = D. [back_rewrite(389),rewrite([392(12),392(19),393(19)])].
% 0.88/1.15 397 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(c_0,B)))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),c_0)))),c_0)),c_0) = C. [back_rewrite(386),rewrite([392(2),393(2),393(2),392(12),392(17),393(17),392(20),393(20),392(21),394(23)])].
% 0.88/1.15 398 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B)))),inverse(multiply(inverse(C),c_0)))),B)),c_0) = C. [back_rewrite(384),rewrite([392(2),393(2),392(10),392(17),393(17),392(18),394(20)])].
% 0.88/1.15 402 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(A,c_0))),c_0)),c_0))) = B. [back_rewrite(377),rewrite([392(3),393(3),393(3),392(7),393(7),393(7),392(8),393(8),394(10),392(10),393(10)])].
% 0.88/1.15 412 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0))),c_0) = multiply(inverse(multiply(C,c_0)),multiply(C,inverse(B))). [back_rewrite(361),rewrite([392(5),393(5),393(5),392(9),393(9),393(9),392(10),393(10),394(12),392(11),393(11)])].
% 0.88/1.15 415 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),c_0) = B. [back_rewrite(354),rewrite([392(11),393(11)])].
% 0.88/1.15 417 multiply(inverse(multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B)))),c_0) = B. [back_rewrite(351),rewrite([392(2),393(2),392(9),393(9)])].
% 0.88/1.15 421 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(C),D)))),multiply(B,inverse(D)))),inverse(multiply(inverse(E),c_0)))),C)))),multiply(A,c_0))),c_0) = multiply(inverse(multiply(F,inverse(E))),multiply(F,inverse(inverse(multiply(c_0,c_0))))). [back_rewrite(344),rewrite([392(12),392(21),393(21),393(21),392(25),393(25),393(25),392(26),393(26),394(28),392(30),393(30),392(31)])].
% 0.88/1.15 423 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(c_0,B)))),multiply(A,inverse(B)))),inverse(multiply(inverse(C),c_0))) = multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(inverse(multiply(c_0,c_0))))). [back_rewrite(342),rewrite([392(2),393(2),393(2),392(12),392(19),393(19),392(20)])].
% 0.88/1.15 429 multiply(c_0,c_0) = c_0. [back_rewrite(333),rewrite([392(12),393(12),393(12),415(12),392(2),393(2),392(3),393(3),393(3),392(4),393(4),394(6),392(5),393(5)])].
% 0.88/1.15 433 multiply(inverse(multiply(A,inverse(multiply(c_0,B)))),multiply(A,inverse(B))) = c_0. [back_rewrite(248),rewrite([392(2),393(2),392(10),393(10)])].
% 0.88/1.15 540 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(inverse(multiply(inverse(C),c_0)),D)))))),multiply(A,c_0))),c_0) = multiply(inverse(multiply(E,inverse(C))),multiply(E,inverse(multiply(B,inverse(D))))). [back_rewrite(25),rewrite([392(3),393(3),392(16),393(12),393(12),392(20),393(16),393(16),392(21),393(17),429(17),393(16)])].
% 0.88/1.15 547 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([392(4),392(5),392(7)]),xx(a)].
% 0.88/1.15 552 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(c_0,inverse(multiply(inverse(B),c_0))). [back_rewrite(423),rewrite([433(8),393(2),429(12),393(11),393(11)]),flip(a)].
% 0.88/1.15 554 multiply(inverse(multiply(c_0,inverse(A))),c_0) = multiply(c_0,inverse(multiply(inverse(A),c_0))). [back_rewrite(421),rewrite([552(22),395(20),429(12),393(11),393(11),552(12)])].
% 0.88/1.15 559 multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),c_0)),c_0)),c_0))) = A. [back_rewrite(397),rewrite([433(8),393(2),554(9),554(12)])].
% 0.88/1.15 567 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(B),c_0)),D)))),c_0)),c_0))). [back_rewrite(540),rewrite([552(13),554(16)]),flip(a)].
% 0.88/1.15 587 multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B))) = multiply(c_0,inverse(multiply(inverse(multiply(inverse(B),c_0)),c_0))). [back_rewrite(412),rewrite([552(6),554(9)]),flip(a)].
% 0.88/1.15 611 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(c_0,multiply(inverse(inverse(B)),inverse(C))). [para(392(a,1),40(a,1,1,1)),rewrite([393(2)]),flip(a)].
% 0.88/1.15 612 multiply(inverse(multiply(inverse(inverse(A)),inverse(B))),c_0) = multiply(c_0,multiply(inverse(inverse(B)),inverse(A))). [para(392(a,1),40(a,1,2)),rewrite([611(13)])].
% 0.88/1.15 617 multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),c_0)),C)))),c_0)),c_0))) = multiply(c_0,multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C))))). [back_rewrite(567),rewrite([611(8)]),flip(a)].
% 0.88/1.15 642 multiply(inverse(multiply(c_0,multiply(c_0,inverse(A)))),c_0) = A. [para(429(a,1),417(a,1,1,1,1,1)),rewrite([393(2)])].
% 0.88/1.15 643 multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),c_0)),c_0)),c_0) = A. [para(392(a,1),417(a,1,1,1,2))].
% 0.88/1.15 651 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B)))),inverse(C))),B)),c_0) = multiply(inverse(multiply(D,c_0)),multiply(D,inverse(C))). [para(417(a,1),398(a,1,1,1,1,1,2,1))].
% 0.88/1.15 653 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B)))),inverse(C))),B)),c_0) = multiply(c_0,multiply(c_0,inverse(C))). [para(642(a,1),398(a,1,1,1,1,1,2,1))].
% 0.88/1.15 655 multiply(inverse(multiply(inverse(inverse(A)),c_0)),c_0) = multiply(c_0,multiply(c_0,inverse(A))). [para(643(a,1),398(a,1,1,1,1,1,2,1)),rewrite([653(14)]),flip(a)].
% 0.88/1.15 658 multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B))) = multiply(c_0,multiply(c_0,inverse(B))). [back_rewrite(651),rewrite([653(14)]),flip(a)].
% 0.88/1.15 666 multiply(c_0,inverse(multiply(inverse(multiply(inverse(A),c_0)),c_0))) = multiply(c_0,multiply(c_0,inverse(A))). [back_rewrite(587),rewrite([658(6)]),flip(a)].
% 0.88/1.15 670 multiply(c_0,multiply(c_0,inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),c_0)),C)))))) = multiply(c_0,multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C))))). [back_rewrite(617),rewrite([666(16)])].
% 0.88/1.15 683 multiply(c_0,multiply(c_0,inverse(multiply(inverse(A),c_0)))) = A. [back_rewrite(559),rewrite([666(12)])].
% 0.88/1.15 692 multiply(inverse(multiply(inverse(A),c_0)),c_0) = multiply(c_0,A). [para(402(a,1),683(a,1,2)),rewrite([429(6)]),flip(a)].
% 0.88/1.15 693 multiply(c_0,inverse(multiply(c_0,multiply(c_0,A)))) = multiply(inverse(A),c_0). [para(402(a,1),554(a,1,1,1)),rewrite([429(8),692(10),692(12)]),flip(a)].
% 0.88/1.15 700 multiply(c_0,inverse(multiply(c_0,A))) = multiply(c_0,multiply(c_0,inverse(A))). [back_rewrite(666),rewrite([692(7)])].
% 0.88/1.15 701 multiply(c_0,multiply(c_0,inverse(A))) = multiply(c_0,inverse(A)). [back_rewrite(655),rewrite([692(7)]),flip(a)].
% 0.88/1.15 704 multiply(inverse(A),c_0) = multiply(c_0,inverse(A)). [back_rewrite(693),rewrite([700(7),700(6),701(6),701(5)]),flip(a)].
% 0.88/1.15 706 multiply(c_0,inverse(multiply(c_0,A))) = multiply(c_0,inverse(A)). [back_rewrite(700),rewrite([701(10)])].
% 0.88/1.15 709 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(683),rewrite([701(8)])].
% 0.88/1.15 720 multiply(c_0,inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),c_0)),C))))) = multiply(c_0,multiply(inverse(inverse(B)),inverse(multiply(A,inverse(C))))). [back_rewrite(670),rewrite([701(12)])].
% 0.88/1.15 724 multiply(c_0,inverse(inverse(A))) = A. [back_rewrite(642),rewrite([701(5),704(6),706(6)])].
% 0.88/1.15 727 multiply(c_0,A) = A. [back_rewrite(692),rewrite([704(6),709(6)]),flip(a)].
% 0.88/1.15 748 inverse(multiply(inverse(inverse(A)),inverse(B))) = multiply(inverse(inverse(B)),inverse(A)). [back_rewrite(612),rewrite([704(7),727(7),727(11)])].
% 0.88/1.15 750 inverse(multiply(inverse(A),c_0)) = multiply(inverse(inverse(A)),c_0). [back_rewrite(554),rewrite([727(3),727(10)]),flip(a)].
% 0.88/1.15 762 inverse(inverse(A)) = A. [back_rewrite(724),rewrite([727(4)])].
% 0.88/1.15 766 inverse(multiply(A,inverse(multiply(multiply(B,c_0),C)))) = multiply(B,inverse(multiply(A,inverse(C)))). [back_rewrite(720),rewrite([750(5),762(3),727(8),762(9),727(12)])].
% 0.88/1.15 777 multiply(A,c_0) = A. [back_rewrite(709),rewrite([750(5),762(3),727(4)])].
% 0.88/1.15 781 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(547),rewrite([727(3)]),xx(a)].
% 0.88/1.15 801 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(748),rewrite([762(2),762(5)])].
% 0.88/1.15 806 multiply(multiply(A,B),inverse(C)) = multiply(A,multiply(B,inverse(C))). [back_rewrite(766),rewrite([777(2),801(4),801(6)])].
% 0.88/1.15 823 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(762(a,1),806(a,1,2)),rewrite([762(4)])].
% 0.88/1.15 824 $F # answer(prove_these_axioms). [resolve(823,a,781,a)].
% 0.88/1.15
% 0.88/1.15 % SZS output end Refutation
% 0.88/1.15 ============================== end of proof ==========================
% 0.88/1.15
% 0.88/1.15 ============================== STATISTICS ============================
% 0.88/1.15
% 0.88/1.15 Given=40. Generated=1493. Kept=822. proofs=1.
% 0.88/1.15 Usable=11. Sos=8. Demods=18. Limbo=0, Disabled=804. Hints=0.
% 0.88/1.15 Megabytes=1.80.
% 0.88/1.15 User_CPU=0.19, System_CPU=0.00, Wall_clock=1.
% 0.88/1.15
% 0.88/1.15 ============================== end of statistics =====================
% 0.88/1.15
% 0.88/1.15 ============================== end of search =========================
% 0.88/1.15
% 0.88/1.15 THEOREM PROVED
% 0.88/1.15 % SZS status Unsatisfiable
% 0.88/1.15
% 0.88/1.15 Exiting with 1 proof.
% 0.88/1.15
% 0.88/1.15 Process 28847 exit (max_proofs) Mon Jun 13 21:21:01 2022
% 0.88/1.15 Prover9 interrupted
%------------------------------------------------------------------------------