TSTP Solution File: GRP425-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP425-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:19:02 EDT 2022
% Result : Unsatisfiable 0.74s 1.17s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP425-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 03:58:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.74/1.17 ============================== Prover9 ===============================
% 0.74/1.17 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.17 Process 26083 was started by sandbox on n011.cluster.edu,
% 0.74/1.17 Tue Jun 14 03:58:35 2022
% 0.74/1.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25930_n011.cluster.edu".
% 0.74/1.17 ============================== end of head ===========================
% 0.74/1.17
% 0.74/1.17 ============================== INPUT =================================
% 0.74/1.17
% 0.74/1.17 % Reading from file /tmp/Prover9_25930_n011.cluster.edu
% 0.74/1.17
% 0.74/1.17 set(prolog_style_variables).
% 0.74/1.17 set(auto2).
% 0.74/1.17 % set(auto2) -> set(auto).
% 0.74/1.17 % set(auto) -> set(auto_inference).
% 0.74/1.17 % set(auto) -> set(auto_setup).
% 0.74/1.17 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.17 % set(auto) -> set(auto_limits).
% 0.74/1.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.17 % set(auto) -> set(auto_denials).
% 0.74/1.17 % set(auto) -> set(auto_process).
% 0.74/1.17 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.17 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.17 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.17 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.17 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.17 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.17 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.17 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.17 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.17 % set(auto2) -> assign(stats, some).
% 0.74/1.17 % set(auto2) -> clear(echo_input).
% 0.74/1.17 % set(auto2) -> set(quiet).
% 0.74/1.17 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.17 % set(auto2) -> clear(print_given).
% 0.74/1.17 assign(lrs_ticks,-1).
% 0.74/1.17 assign(sos_limit,10000).
% 0.74/1.17 assign(order,kbo).
% 0.74/1.17 set(lex_order_vars).
% 0.74/1.17 clear(print_given).
% 0.74/1.17
% 0.74/1.17 % formulas(sos). % not echoed (2 formulas)
% 0.74/1.17
% 0.74/1.17 ============================== end of input ==========================
% 0.74/1.17
% 0.74/1.17 % From the command line: assign(max_seconds, 300).
% 0.74/1.17
% 0.74/1.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.17
% 0.74/1.17 % Formulas that are not ordinary clauses:
% 0.74/1.17
% 0.74/1.17 ============================== end of process non-clausal formulas ===
% 0.74/1.17
% 0.74/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.17
% 0.74/1.17 ============================== PREDICATE ELIMINATION =================
% 0.74/1.17
% 0.74/1.17 ============================== end predicate elimination =============
% 0.74/1.17
% 0.74/1.17 Auto_denials:
% 0.74/1.17 % copying label prove_these_axioms_2 to answer in negative clause
% 0.74/1.17
% 0.74/1.17 Term ordering decisions:
% 0.74/1.17
% 0.74/1.17 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 0.74/1.17 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 0.74/1.17
% 0.74/1.17 ============================== end of process initial clauses ========
% 0.74/1.17
% 0.74/1.17 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.17
% 0.74/1.17 ============================== end of clauses for search =============
% 0.74/1.17
% 0.74/1.17 ============================== SEARCH ================================
% 0.74/1.17
% 0.74/1.17 % Starting search at 0.01 seconds.
% 0.74/1.17
% 0.74/1.17 ============================== PROOF =================================
% 0.74/1.17 % SZS status Unsatisfiable
% 0.74/1.17 % SZS output start Refutation
% 0.74/1.17
% 0.74/1.17 % Proof 1 at 0.18 (+ 0.01) seconds: prove_these_axioms_2.
% 0.74/1.17 % Length of proof is 75.
% 0.74/1.17 % Level of proof is 27.
% 0.74/1.17 % Maximum clause weight is 135.000.
% 0.74/1.17 % Given clauses 29.
% 0.74/1.17
% 0.74/1.17 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].
% 0.74/1.17 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 0.74/1.17 3 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))].
% 0.74/1.17 4 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))].
% 0.74/1.17 5 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))].
% 0.74/1.17 9 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(C),C)))),C)))),multiply(A,inverse(C))) = B. [para(3(a,1),1(a,1))].
% 0.74/1.17 12 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),3(a,1,1,1,1,1))].
% 0.74/1.17 16 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(3(a,1),3(a,1))].
% 0.74/1.17 22 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(9(a,1),1(a,1,1,1,1,1,2,1))].
% 0.74/1.17 34 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(9(a,1),16(a,1,1,1,2,1)),rewrite([9(21)])].
% 0.74/1.17 36 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))),C))) = B. [para(34(a,1),1(a,1,1,1)),rewrite([22(21)])].
% 0.74/1.17 39 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))). [para(1(a,1),34(a,1,2,2,1)),rewrite([1(22)])].
% 0.74/1.17 51 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(39(a,1),1(a,1,1,1,1,1,2,1)),rewrite([22(23)])].
% 0.74/1.17 52 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(39(a,1),1(a,1,2,1))].
% 0.74/1.17 64 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),4(a,1,1,1,2,1,1,2))].
% 0.74/1.17 101 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),51(a,1,2,1,1,1,1,1,1,1))].
% 0.74/1.17 152 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(52(a,1),51(a,1,2,1,1,1,1,1,1,1)),rewrite([101(26)])].
% 0.74/1.17 159 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),152(a,1,2,1,1,1)),rewrite([1(14)]),flip(a)].
% 0.74/1.17 186 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(5(a,1),3(a,2,1,1,2,1))].
% 0.74/1.17 187 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(5(a,1),3(a,2,1,1))].
% 0.74/1.17 195 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(5(a,1),9(a,1,1,1,2,1)),flip(a)].
% 0.74/1.17 235 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(159(a,2),1(a,1,1,1,1,1))].
% 0.74/1.17 238 multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(inverse(C),C))). [para(1(a,1),159(a,1,2,1,1,1)),rewrite([1(14)])].
% 0.74/1.17 239 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(159(a,1),3(a,1,1,1,1,1))].
% 0.74/1.17 247 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),B)),C)))),multiply(A,inverse(C))) = inverse(multiply(inverse(C),C)). [para(159(a,2),3(a,1,1,1,1,1)),rewrite([235(30)]),flip(a)].
% 0.74/1.17 327 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(239),rewrite([247(40)])].
% 0.74/1.17 332 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(12),rewrite([247(37)])].
% 0.74/1.17 333 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(187),rewrite([327(34)]),flip(a)].
% 0.74/1.17 336 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(64),rewrite([333(24)])].
% 0.74/1.17 341 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(195),rewrite([336(16)])].
% 0.74/1.17 343 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(186),rewrite([336(36),336(43),336(47)])].
% 0.74/1.17 350 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = C. [para(238(a,1),1(a,1,1,1,1,1))].
% 0.74/1.17 353 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(D),D))) = B. [para(238(a,1),1(a,1))].
% 0.74/1.17 360 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(238(a,1),3(a,2,1,1))].
% 0.74/1.17 376 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(238(a,1),36(a,1,2,1))].
% 0.74/1.17 383 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(238(a,1),5(a,1,1,1,1,1,1,1,1,1))].
% 0.74/1.17 385 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(238(a,1),5(a,1,1,1))].
% 0.74/1.17 388 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(238(a,1),5(a,1))].
% 0.74/1.17 389 multiply(A,inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),D))). [para(238(a,1),238(a,1,2,1))].
% 0.74/1.17 390 multiply(inverse(A),A) = inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B))). [back_rewrite(333),rewrite([388(23)])].
% 0.74/1.17 391 multiply(inverse(A),A) = c_0. [new_symbol(390)].
% 0.74/1.17 392 inverse(c_0) = c_0. [back_rewrite(390),rewrite([391(2),391(3),391(5),391(5)]),flip(a)].
% 0.74/1.17 393 multiply(A,inverse(multiply(c_0,c_0))) = multiply(A,c_0). [back_rewrite(389),rewrite([391(2),392(2),392(2),391(3),392(3),391(7),392(7)])].
% 0.74/1.17 394 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(388),rewrite([391(12),391(19),392(19)])].
% 0.74/1.17 396 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(385),rewrite([391(2),392(2),392(2),391(12),391(17),392(17),391(20),392(20),391(21),393(23)])].
% 0.74/1.17 397 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(383),rewrite([391(2),392(2),391(10),391(17),392(17),391(18),393(20)])].
% 0.74/1.17 401 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),multiply(A,c_0))),c_0)),c_0))) = B. [back_rewrite(376),rewrite([391(3),392(3),392(3),391(7),392(7),392(7),391(8),392(8),393(10),391(10),392(10)])].
% 0.74/1.17 411 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(360),rewrite([391(5),392(5),392(5),391(9),392(9),392(9),391(10),392(10),393(12),391(11),392(11)])].
% 0.74/1.17 414 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),c_0) = B. [back_rewrite(353),rewrite([391(11),392(11)])].
% 0.74/1.17 416 multiply(inverse(multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B)))),c_0) = B. [back_rewrite(350),rewrite([391(2),392(2),391(9),392(9)])].
% 0.74/1.17 420 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(343),rewrite([391(12),391(21),392(21),392(21),391(25),392(25),392(25),391(26),392(26),393(28),391(30),392(30),391(31)])].
% 0.74/1.17 422 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(341),rewrite([391(2),392(2),392(2),391(12),391(19),392(19),391(20)])].
% 0.74/1.17 428 multiply(c_0,c_0) = c_0. [back_rewrite(332),rewrite([391(12),392(12),392(12),414(12),391(2),392(2),391(3),392(3),392(3),391(4),392(4),393(6),391(5),392(5)])].
% 0.74/1.17 432 multiply(inverse(multiply(A,inverse(multiply(c_0,B)))),multiply(A,inverse(B))) = c_0. [back_rewrite(247),rewrite([391(2),392(2),391(10),392(10)])].
% 0.74/1.17 546 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(2),rewrite([391(4)])].
% 0.74/1.17 551 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(c_0,inverse(multiply(inverse(B),c_0))). [back_rewrite(422),rewrite([432(8),392(2),428(12),392(11),392(11)]),flip(a)].
% 0.74/1.17 553 multiply(inverse(multiply(c_0,inverse(A))),c_0) = multiply(c_0,inverse(multiply(inverse(A),c_0))). [back_rewrite(420),rewrite([551(22),394(20),428(12),392(11),392(11),551(12)])].
% 0.74/1.17 558 multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),c_0)),c_0)),c_0))) = A. [back_rewrite(396),rewrite([432(8),392(2),553(9),553(12)])].
% 0.74/1.17 586 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(411),rewrite([551(6),553(9)]),flip(a)].
% 0.74/1.17 641 multiply(inverse(multiply(c_0,multiply(c_0,inverse(A)))),c_0) = A. [para(428(a,1),416(a,1,1,1,1,1)),rewrite([392(2)])].
% 0.74/1.17 642 multiply(inverse(multiply(inverse(multiply(inverse(inverse(A)),c_0)),c_0)),c_0) = A. [para(391(a,1),416(a,1,1,1,2))].
% 0.74/1.17 650 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(416(a,1),397(a,1,1,1,1,1,2,1))].
% 0.74/1.17 652 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(641(a,1),397(a,1,1,1,1,1,2,1))].
% 0.74/1.17 654 multiply(inverse(multiply(inverse(inverse(A)),c_0)),c_0) = multiply(c_0,multiply(c_0,inverse(A))). [para(642(a,1),397(a,1,1,1,1,1,2,1)),rewrite([652(14)]),flip(a)].
% 0.74/1.17 657 multiply(inverse(multiply(A,c_0)),multiply(A,inverse(B))) = multiply(c_0,multiply(c_0,inverse(B))). [back_rewrite(650),rewrite([652(14)]),flip(a)].
% 0.74/1.17 665 multiply(c_0,inverse(multiply(inverse(multiply(inverse(A),c_0)),c_0))) = multiply(c_0,multiply(c_0,inverse(A))). [back_rewrite(586),rewrite([657(6)]),flip(a)].
% 0.74/1.17 682 multiply(c_0,multiply(c_0,inverse(multiply(inverse(A),c_0)))) = A. [back_rewrite(558),rewrite([665(12)])].
% 0.74/1.17 691 multiply(inverse(multiply(inverse(A),c_0)),c_0) = multiply(c_0,A). [para(401(a,1),682(a,1,2)),rewrite([428(6)]),flip(a)].
% 0.74/1.17 692 multiply(c_0,inverse(multiply(c_0,multiply(c_0,A)))) = multiply(inverse(A),c_0). [para(401(a,1),553(a,1,1,1)),rewrite([428(8),691(10),691(12)]),flip(a)].
% 0.74/1.17 699 multiply(c_0,inverse(multiply(c_0,A))) = multiply(c_0,multiply(c_0,inverse(A))). [back_rewrite(665),rewrite([691(7)])].
% 0.74/1.17 700 multiply(c_0,multiply(c_0,inverse(A))) = multiply(c_0,inverse(A)). [back_rewrite(654),rewrite([691(7)]),flip(a)].
% 0.74/1.17 703 multiply(inverse(A),c_0) = multiply(c_0,inverse(A)). [back_rewrite(692),rewrite([699(7),699(6),700(6),700(5)]),flip(a)].
% 0.74/1.17 708 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(682),rewrite([700(8)])].
% 0.74/1.17 726 multiply(c_0,A) = A. [back_rewrite(691),rewrite([703(6),708(6)]),flip(a)].
% 0.74/1.17 727 $F # answer(prove_these_axioms_2). [resolve(726,a,546,a)].
% 0.74/1.17
% 0.74/1.17 % SZS output end Refutation
% 0.74/1.17 ============================== end of proof ==========================
% 0.74/1.17
% 0.74/1.17 ============================== STATISTICS ============================
% 0.74/1.17
% 0.74/1.17 Given=29. Generated=1269. Kept=726. proofs=1.
% 0.74/1.17 Usable=6. Sos=33. Demods=60. Limbo=23, Disabled=665. Hints=0.
% 0.74/1.17 Megabytes=1.73.
% 0.74/1.17 User_CPU=0.18, System_CPU=0.01, Wall_clock=0.
% 0.74/1.17
% 0.74/1.17 ============================== end of statistics =====================
% 0.74/1.17
% 0.74/1.17 ============================== end of search =========================
% 0.74/1.17
% 0.74/1.17 THEOREM PROVED
% 0.74/1.17 % SZS status Unsatisfiable
% 0.74/1.17
% 0.74/1.17 Exiting with 1 proof.
% 0.74/1.17
% 0.74/1.17 Process 26083 exit (max_proofs) Tue Jun 14 03:58:35 2022
% 0.74/1.17 Prover9 interrupted
%------------------------------------------------------------------------------