TSTP Solution File: GRP054-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP054-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 1.81s 2.10s
% Output : Refutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP054-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.16/0.36 % Computer : n019.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Mon Jun 13 21:05:54 EDT 2022
% 0.16/0.36 % CPUTime :
% 1.81/2.10 ============================== Prover9 ===============================
% 1.81/2.10 Prover9 (32) version 2009-11A, November 2009.
% 1.81/2.10 Process 19241 was started by sandbox on n019.cluster.edu,
% 1.81/2.10 Mon Jun 13 21:05:55 2022
% 1.81/2.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19087_n019.cluster.edu".
% 1.81/2.10 ============================== end of head ===========================
% 1.81/2.10
% 1.81/2.10 ============================== INPUT =================================
% 1.81/2.10
% 1.81/2.10 % Reading from file /tmp/Prover9_19087_n019.cluster.edu
% 1.81/2.10
% 1.81/2.10 set(prolog_style_variables).
% 1.81/2.10 set(auto2).
% 1.81/2.10 % set(auto2) -> set(auto).
% 1.81/2.10 % set(auto) -> set(auto_inference).
% 1.81/2.10 % set(auto) -> set(auto_setup).
% 1.81/2.10 % set(auto_setup) -> set(predicate_elim).
% 1.81/2.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.81/2.10 % set(auto) -> set(auto_limits).
% 1.81/2.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.81/2.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.81/2.10 % set(auto) -> set(auto_denials).
% 1.81/2.10 % set(auto) -> set(auto_process).
% 1.81/2.10 % set(auto2) -> assign(new_constants, 1).
% 1.81/2.10 % set(auto2) -> assign(fold_denial_max, 3).
% 1.81/2.10 % set(auto2) -> assign(max_weight, "200.000").
% 1.81/2.10 % set(auto2) -> assign(max_hours, 1).
% 1.81/2.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.81/2.10 % set(auto2) -> assign(max_seconds, 0).
% 1.81/2.10 % set(auto2) -> assign(max_minutes, 5).
% 1.81/2.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.81/2.10 % set(auto2) -> set(sort_initial_sos).
% 1.81/2.10 % set(auto2) -> assign(sos_limit, -1).
% 1.81/2.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.81/2.10 % set(auto2) -> assign(max_megs, 400).
% 1.81/2.10 % set(auto2) -> assign(stats, some).
% 1.81/2.10 % set(auto2) -> clear(echo_input).
% 1.81/2.10 % set(auto2) -> set(quiet).
% 1.81/2.10 % set(auto2) -> clear(print_initial_clauses).
% 1.81/2.10 % set(auto2) -> clear(print_given).
% 1.81/2.10 assign(lrs_ticks,-1).
% 1.81/2.10 assign(sos_limit,10000).
% 1.81/2.10 assign(order,kbo).
% 1.81/2.10 set(lex_order_vars).
% 1.81/2.10 clear(print_given).
% 1.81/2.10
% 1.81/2.10 % formulas(sos). % not echoed (2 formulas)
% 1.81/2.10
% 1.81/2.10 ============================== end of input ==========================
% 1.81/2.10
% 1.81/2.10 % From the command line: assign(max_seconds, 300).
% 1.81/2.10
% 1.81/2.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.81/2.10
% 1.81/2.10 % Formulas that are not ordinary clauses:
% 1.81/2.10
% 1.81/2.10 ============================== end of process non-clausal formulas ===
% 1.81/2.10
% 1.81/2.10 ============================== PROCESS INITIAL CLAUSES ===============
% 1.81/2.10
% 1.81/2.10 ============================== PREDICATE ELIMINATION =================
% 1.81/2.10
% 1.81/2.10 ============================== end predicate elimination =============
% 1.81/2.10
% 1.81/2.10 Auto_denials:
% 1.81/2.10 % copying label prove_these_axioms to answer in negative clause
% 1.81/2.10
% 1.81/2.10 Term ordering decisions:
% 1.81/2.10
% 1.81/2.10 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.81/2.10 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.81/2.10
% 1.81/2.10 ============================== end of process initial clauses ========
% 1.81/2.10
% 1.81/2.10 ============================== CLAUSES FOR SEARCH ====================
% 1.81/2.10
% 1.81/2.10 ============================== end of clauses for search =============
% 1.81/2.10
% 1.81/2.10 ============================== SEARCH ================================
% 1.81/2.10
% 1.81/2.10 % Starting search at 0.01 seconds.
% 1.81/2.10
% 1.81/2.10 ============================== PROOF =================================
% 1.81/2.10 % SZS status Unsatisfiable
% 1.81/2.10 % SZS output start Refutation
% 1.81/2.10
% 1.81/2.10 % Proof 1 at 1.05 (+ 0.01) seconds: prove_these_axioms.
% 1.81/2.10 % Length of proof is 111.
% 1.81/2.10 % Level of proof is 26.
% 1.81/2.10 % Maximum clause weight is 143.000.
% 1.81/2.10 % Given clauses 54.
% 1.81/2.10
% 1.81/2.10 1 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 1.81/2.10 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].
% 1.81/2.10 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)].
% 1.81/2.10 4 multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))). [para(1(a,1),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.81/2.10 5 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(C,E)),inverse(multiply(D,multiply(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(C,E)))))))))),multiply(A,multiply(inverse(multiply(C,inverse(multiply(inverse(D),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(C,E))))) = B. [para(1(a,1),1(a,1,1,1,1,2,1,2,1,2,1,1))].
% 1.81/2.10 6 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))))) = D. [para(4(a,1),1(a,1,1,2))].
% 1.81/2.10 7 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))) = B. [para(4(a,1),1(a,1,1))].
% 1.81/2.10 10 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = B. [para(4(a,2),1(a,1))].
% 1.81/2.10 13 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F)))) = inverse(multiply(inverse(multiply(V6,inverse(multiply(D,inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),multiply(V6,V7))). [para(4(a,1),4(a,1,2))].
% 1.81/2.10 22 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E)). [para(7(a,1),4(a,1,1,1,2,1,1)),rewrite([1(35)])].
% 1.81/2.10 28 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),B)) = D. [para(10(a,1),1(a,1,1,2))].
% 1.81/2.10 71 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(E),inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(D,F)),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(C,V6)),inverse(multiply(multiply(inverse(multiply(V7,inverse(multiply(E,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8)),multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(V7,inverse(multiply(E,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8))),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(C,V6)))))))))),multiply(A,multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(V7,inverse(multiply(E,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8))),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(C,V6))))) = B. [para(4(a,2),5(a,1,1,1,1,2,1,2,1,1,1,1,2,1,1))].
% 1.81/2.10 88 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(inverse(multiply(E,D)),multiply(E,B))). [para(28(a,1),1(a,1,1,1,1,2)),flip(a)].
% 1.81/2.10 177 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))) = B. [para(88(a,1),1(a,1,1,1,1)),rewrite([10(24)])].
% 1.81/2.10 211 multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C))))) = B. [para(88(a,1),10(a,1,1,1)),rewrite([10(25)])].
% 1.81/2.10 220 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(inverse(inverse(multiply(D,inverse(multiply(inverse(D),D)))))),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(multiply(F,inverse(multiply(B,inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(F,V6)),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))),multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))))))))) = inverse(multiply(inverse(multiply(V7,E)),multiply(V7,D))). [para(22(a,1),88(a,1,2,1,2,1,1))].
% 1.81/2.10 246 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D) = inverse(multiply(inverse(multiply(E,multiply(inverse(multiply(F,inverse(multiply(inverse(inverse(inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(F,V6),inverse(multiply(inverse(multiply(F,V6)),multiply(F,V6)))))))))),multiply(E,B))). [para(28(a,1),88(a,1,2))].
% 1.81/2.10 272 inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))). [para(88(a,1),88(a,1))].
% 1.81/2.10 331 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(D,inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(E,multiply(inverse(multiply(inverse(multiply(F,inverse(multiply(inverse(D),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),inverse(multiply(inverse(E),inverse(multiply(multiply(F,V6),inverse(multiply(inverse(multiply(F,V6)),multiply(F,V6))))))))),B))). [para(6(a,1),88(a,2,1,1)),rewrite([7(29)])].
% 1.81/2.10 332 inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),inverse(multiply(inverse(D),inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(inverse(multiply(C,inverse(multiply(inverse(C),C))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F))))) = D. [para(88(a,1),6(a,1,1,1,1,1,1)),rewrite([10(25),10(30),10(36)])].
% 1.81/2.10 345 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(272(a,1),1(a,1,1,1,1,2,1,1)),rewrite([1(17)])].
% 1.81/2.10 405 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)). [para(1(a,1),345(a,1,1)),flip(a)].
% 1.81/2.10 418 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(272(a,1),345(a,1,1))].
% 1.81/2.10 419 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))). [para(345(a,1),345(a,1,2))].
% 1.81/2.10 443 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(inverse(B),B)))))),multiply(A,C)) = multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),C)). [para(177(a,1),345(a,1,1)),flip(a)].
% 1.81/2.10 1723 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D). [para(10(a,1),405(a,2,2))].
% 1.81/2.10 2011 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = multiply(inverse(inverse(multiply(inverse(multiply(D,multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(F),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),inverse(multiply(inverse(B),inverse(multiply(multiply(E,V6),inverse(multiply(inverse(multiply(E,V6)),multiply(E,V6))))))))),inverse(multiply(inverse(multiply(V7,inverse(multiply(F,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8)))))),multiply(D,V9)))),inverse(multiply(V9,inverse(multiply(inverse(V9),V9))))). [para(13(a,2),211(a,1,1,1,1,1,1,2)),flip(a)].
% 1.81/2.10 2018 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(C,inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),multiply(B,D))))),multiply(A,E))),multiply(F,V6)) = multiply(inverse(multiply(V7,multiply(inverse(multiply(inverse(multiply(V8,inverse(multiply(inverse(C),inverse(multiply(V9,inverse(multiply(inverse(V9),V9)))))))),inverse(multiply(inverse(F),inverse(multiply(multiply(V8,V9),inverse(multiply(inverse(multiply(V8,V9)),multiply(V8,V9))))))))),E))),multiply(V7,V6)). [para(13(a,1),418(a,1,2,1,1)),rewrite([7(30)])].
% 1.81/2.10 2044 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),E)),F)),multiply(inverse(multiply(V6,E)),multiply(V6,inverse(multiply(inverse(multiply(V7,inverse(multiply(B,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8)))))) = multiply(inverse(multiply(V9,F)),multiply(V9,inverse(multiply(inverse(multiply(V10,inverse(multiply(D,inverse(multiply(V11,inverse(multiply(inverse(V11),V11)))))))),multiply(V10,V11))))). [para(13(a,1),419(a,2,2,2))].
% 1.81/2.10 2187 inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(B),inverse(multiply(A,inverse(multiply(inverse(A),A)))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))) = B. [para(1723(a,2),1(a,1,1,2))].
% 1.81/2.10 2188 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(C,inverse(multiply(inverse(B),inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),multiply(C,D))). [para(1(a,1),1723(a,1,1)),flip(a)].
% 1.81/2.10 2189 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [para(1723(a,2),3(b,1,1))].
% 1.81/2.10 2195 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D)))))),multiply(A,E)) = multiply(E,inverse(multiply(inverse(E),E))). [para(1723(a,2),4(a,1,1,1,2,1)),rewrite([1(28)])].
% 1.81/2.10 2203 multiply(inverse(A),A) = multiply(B,inverse(multiply(inverse(multiply(C,inverse(multiply(B,inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),multiply(C,D)))). [para(4(a,1),1723(a,1,2)),rewrite([1(13)]),flip(a)].
% 1.81/2.10 2208 inverse(inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(B,inverse(multiply(A,inverse(multiply(inverse(A),A)))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))))) = B. [para(1723(a,2),7(a,1,1,1,2))].
% 1.81/2.10 2211 multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(inverse(B)),inverse(multiply(A,inverse(multiply(inverse(A),A)))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))) = B. [para(1723(a,2),10(a,1,2))].
% 1.81/2.10 2213 multiply(inverse(A),A) = multiply(inverse(B),B). [para(10(a,1),1723(a,1,1,1)),rewrite([10(14)])].
% 1.81/2.10 2234 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(D),E)) = multiply(inverse(multiply(F,D)),multiply(F,E)). [para(1723(a,2),345(a,1,1,1))].
% 1.81/2.10 2235 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))) = multiply(inverse(multiply(F,B)),multiply(F,A)). [para(1723(a,2),345(a,1,2))].
% 1.81/2.10 2243 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),inverse(multiply(D,inverse(multiply(inverse(D),D)))))) = D. [para(1723(a,2),177(a,1,1,1,1,1))].
% 1.81/2.10 2276 multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),inverse(multiply(inverse(D),inverse(multiply(inverse(inverse(D)),inverse(D)))))) = D. [para(1723(a,2),211(a,1,1,1,1))].
% 1.81/2.10 2406 multiply(inverse(multiply(inverse(A),multiply(B,C))),multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,F)))) = multiply(V6,multiply(inverse(multiply(B,inverse(multiply(inverse(V6),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),A)). [para(1723(a,2),405(a,1,2))].
% 1.81/2.10 2408 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(multiply(C,inverse(multiply(inverse(C),C)))),multiply(inverse(multiply(B,inverse(multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V6)))))),D)). [para(1723(a,2),405(a,2,2,1,1,2,1))].
% 1.81/2.10 2419 multiply(inverse(A),A) = c_0. [new_symbol(2213)].
% 1.81/2.10 2420 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_unit_del(2189),rewrite([2419(4),2419(5),2419(9)]),xx(a)].
% 1.81/2.10 2427 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(multiply(C,inverse(c_0))),multiply(inverse(multiply(B,inverse(c_0))),D)). [back_rewrite(2408),rewrite([2419(7),2419(15)])].
% 1.81/2.10 2429 multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,inverse(c_0))))))),D)) = multiply(inverse(multiply(inverse(D),multiply(B,C))),c_0). [back_rewrite(2406),rewrite([2419(10),2419(9)]),flip(a)].
% 1.81/2.10 2494 multiply(inverse(inverse(c_0)),inverse(multiply(inverse(A),inverse(c_0)))) = A. [back_rewrite(2276),rewrite([2419(6),2419(8)])].
% 1.81/2.10 2514 inverse(multiply(inverse(inverse(c_0)),inverse(multiply(A,inverse(c_0))))) = A. [back_rewrite(2243),rewrite([2419(6),2419(5)])].
% 1.81/2.10 2516 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(2235),rewrite([2419(9)]),flip(a)].
% 1.81/2.10 2517 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(2234),rewrite([2419(6),2516(9)]),flip(a)].
% 1.81/2.10 2521 multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(c_0)))))),B)) = A. [back_rewrite(2211),rewrite([2419(5),2419(17),2517(13)])].
% 1.81/2.10 2522 inverse(inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)))) = A. [back_rewrite(2208),rewrite([2419(3),2419(15),2517(11)])].
% 1.81/2.10 2525 multiply(A,inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)))) = c_0. [back_rewrite(2203),rewrite([2419(2),2419(3),2516(11),2517(12)]),flip(a)].
% 1.81/2.10 2529 multiply(inverse(c_0),multiply(inverse(inverse(c_0)),A)) = multiply(A,inverse(c_0)). [back_rewrite(2195),rewrite([2419(6),2516(6),2517(7),2419(9)])].
% 1.81/2.10 2530 multiply(A,multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,inverse(c_0)))))),B))) = c_0. [back_rewrite(2188),rewrite([2419(2),2419(4),2516(12),2517(13)]),flip(a)].
% 1.81/2.10 2531 inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,inverse(c_0)))))),B))) = A. [back_rewrite(2187),rewrite([2419(4),2419(16),2517(12)])].
% 1.81/2.10 2636 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(c_0))))))),E)),F)),multiply(inverse(multiply(B,E)),c_0)) = multiply(inverse(multiply(D,F)),c_0). [back_rewrite(2044),rewrite([2419(3),2419(15),2419(27),2516(35),2517(36),2516(39),2522(36),2419(32),2516(40),2517(41),2516(44),2522(41)])].
% 1.81/2.10 2655 multiply(inverse(c_0),multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(c_0))))))),E)),F)) = multiply(inverse(multiply(inverse(c_0),multiply(B,E))),multiply(D,F)). [back_rewrite(2018),rewrite([2419(2),2516(10),2517(11),2516(16),2517(17),2522(15),2419(10),2419(22),2516(31),2517(32)]),flip(a)].
% 1.81/2.10 2661 multiply(inverse(inverse(multiply(inverse(c_0),multiply(A,B)))),inverse(multiply(B,inverse(c_0)))) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(C,inverse(c_0)))))),C)). [back_rewrite(2011),rewrite([2419(2),2516(10),2517(11),2419(14),2419(26),2419(32),2516(40),2517(41),2516(47),2517(48),2655(48),2525(26),2419(15),2419(19)]),flip(a)].
% 1.81/2.10 3049 multiply(A,multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(A),B)))),C)) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(c_0)))),C)). [back_rewrite(443),rewrite([2419(2),2516(8),2517(9),2516(13),2517(14)]),flip(a)].
% 1.81/2.10 3061 inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(A),B)))),inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(B,inverse(c_0))),inverse(c_0))))))),inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(D,inverse(c_0)))))),D))))) = C. [back_rewrite(332),rewrite([2516(4),2517(5),2419(10),2419(14),2419(19),2419(22),2419(22),2516(30),2517(31)])].
% 1.81/2.10 3062 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(c_0))))),inverse(multiply(C,inverse(c_0))))))),inverse(multiply(D,inverse(multiply(multiply(A,C),inverse(c_0)))))) = inverse(multiply(inverse(c_0),multiply(D,B))). [back_rewrite(331),rewrite([2419(2),2419(8),2419(19),2419(25),2419(37),2429(43),2516(34),2517(35),2517(39),2531(37)])].
% 1.81/2.10 3073 inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(A),multiply(B,C))))),D))) = multiply(inverse(multiply(B,inverse(multiply(inverse(inverse(inverse(multiply(D,inverse(c_0))))),inverse(multiply(C,inverse(c_0))))))),A). [back_rewrite(246),rewrite([2419(2),2419(8),2419(20),2419(24),2419(36),3062(39),2516(26),2517(27)]),flip(a)].
% 1.81/2.10 3076 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(c_0))))))),inverse(multiply(inverse(inverse(inverse(multiply(D,inverse(c_0))))),inverse(multiply(multiply(A,C),inverse(c_0))))))),inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(multiply(F,inverse(c_0)))))),F)),inverse(c_0)))))) = inverse(multiply(inverse(c_0),multiply(inverse(E),D))). [back_rewrite(220),rewrite([2419(2),2419(10),2419(19),2419(26),2516(34),2517(35),2419(37),2516(45),2517(46),2419(49),2516(57),2517(58),2419(59),2516(46),2517(47)])].
% 1.81/2.10 3091 inverse(multiply(inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)),inverse(multiply(inverse(C),inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(D,inverse(c_0)))))),D)),inverse(multiply(E,inverse(c_0)))))),E)),inverse(c_0))))))),c_0)) = C. [back_rewrite(71),rewrite([2419(4),2516(12),2517(13),2419(15),2516(23),2517(24),2419(26),2516(34),2517(35),2419(37),2516(45),2517(46),2419(49),2516(57),2517(58),2530(59),2419(34),2516(42),2517(43),2419(46),2516(54),2517(55),2516(57),2531(24)])].
% 1.81/2.10 3109 multiply(inverse(multiply(A,inverse(c_0))),multiply(inverse(multiply(B,inverse(c_0))),C)) = multiply(inverse(c_0),multiply(inverse(multiply(B,A)),C)). [back_rewrite(2427),rewrite([2516(5),2517(6)]),flip(a)].
% 1.81/2.10 3126 inverse(c_0) = c_0. [para(2419(a,1),2494(a,1,2,1)),rewrite([2419(6)]),flip(a)].
% 1.81/2.10 3141 multiply(inverse(multiply(A,c_0)),multiply(inverse(multiply(B,c_0)),C)) = multiply(c_0,multiply(inverse(multiply(B,A)),C)). [back_rewrite(3109),rewrite([3126(2),3126(5),3126(10)])].
% 1.81/2.10 3150 inverse(multiply(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)),inverse(multiply(inverse(C),inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(D,c_0))))),D)),inverse(multiply(E,c_0))))),E)),c_0)))))),c_0)) = C. [back_rewrite(3091),rewrite([3126(2),3126(3),3126(12),3126(13),3126(15),3126(23),3126(31)])].
% 1.81/2.10 3165 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,c_0)))))),inverse(multiply(inverse(inverse(inverse(multiply(D,c_0)))),inverse(multiply(multiply(A,C),c_0)))))),inverse(multiply(inverse(E),inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(B,inverse(multiply(F,c_0))))),F)),c_0))))) = inverse(multiply(c_0,multiply(inverse(E),D))). [back_rewrite(3076),rewrite([3126(2),3126(9),3126(15),3126(23),3126(24),3126(32),3126(38)])].
% 1.81/2.10 3168 inverse(multiply(c_0,multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),multiply(B,C))))),D))) = multiply(inverse(multiply(B,inverse(multiply(inverse(inverse(inverse(multiply(D,c_0)))),inverse(multiply(C,c_0)))))),A). [back_rewrite(3073),rewrite([3126(2),3126(3),3126(13),3126(18)])].
% 1.81/2.10 3177 inverse(multiply(inverse(multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),B)))),inverse(multiply(inverse(C),inverse(multiply(inverse(multiply(B,c_0)),c_0)))))),inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(D,c_0))))),D))))) = C. [back_rewrite(3061),rewrite([3126(2),3126(9),3126(12),3126(19),3126(20)])].
% 1.81/2.10 3186 multiply(A,multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),B)))),C)) = multiply(c_0,multiply(inverse(inverse(multiply(B,c_0))),C)). [back_rewrite(3049),rewrite([3126(2),3126(10),3126(11)])].
% 1.81/2.10 3330 multiply(inverse(inverse(multiply(c_0,multiply(A,B)))),inverse(multiply(B,c_0))) = multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(C,c_0))))),C)). [back_rewrite(2661),rewrite([3126(2),3126(7),3126(11),3126(12)])].
% 1.81/2.10 3336 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,c_0)))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),c_0)))))),E)),F)),multiply(inverse(multiply(B,E)),c_0)) = multiply(inverse(multiply(D,F)),c_0). [back_rewrite(2636),rewrite([3126(3),3126(12)])].
% 1.81/2.10 3340 multiply(c_0,multiply(c_0,A)) = multiply(A,c_0). [back_rewrite(2529),rewrite([3126(2),3126(3),3126(3),3126(6)])].
% 1.81/2.10 3344 multiply(c_0,multiply(inverse(inverse(multiply(inverse(inverse(A)),inverse(multiply(B,c_0))))),B)) = A. [back_rewrite(2521),rewrite([3126(2),3126(5)])].
% 1.81/2.10 3347 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(2517),rewrite([3126(7)])].
% 1.81/2.10 3348 inverse(multiply(c_0,inverse(multiply(A,c_0)))) = A. [back_rewrite(2514),rewrite([3126(2),3126(2),3126(3)])].
% 1.81/2.10 3351 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(2494),rewrite([3126(2),3126(2),3126(4)])].
% 1.81/2.10 3367 multiply(multiply(c_0,A),c_0) = multiply(c_0,multiply(A,c_0)). [para(3340(a,1),3340(a,1,2)),flip(a)].
% 1.81/2.10 3407 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,c_0)))))),inverse(multiply(inverse(inverse(inverse(multiply(D,c_0)))),inverse(multiply(multiply(A,C),c_0)))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(multiply(inverse(inverse(multiply(B,inverse(multiply(F,c_0))))),F),c_0)))))) = inverse(multiply(c_0,multiply(inverse(E),D))). [back_rewrite(3165),rewrite([3367(32)])].
% 1.81/2.10 3411 inverse(multiply(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)),inverse(multiply(inverse(C),inverse(multiply(c_0,multiply(multiply(inverse(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(D,c_0))))),D)),inverse(multiply(E,c_0))))),E),c_0))))))),c_0)) = C. [back_rewrite(3150),rewrite([3367(31)])].
% 1.81/2.10 3414 multiply(c_0,A) = multiply(A,c_0). [para(3351(a,1),3340(a,1,2)),rewrite([3347(8),3126(5),3340(6)])].
% 1.81/2.10 3416 inverse(multiply(c_0,inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)),inverse(multiply(inverse(C),inverse(multiply(c_0,multiply(inverse(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(D,c_0))))),D)),inverse(multiply(E,c_0))))),E))))))))) = C. [back_rewrite(3411),rewrite([3414(30,R),3340(31),3414(29,R),3414(36,R)])].
% 1.81/2.10 3420 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,c_0)))))),inverse(multiply(inverse(inverse(inverse(multiply(D,c_0)))),inverse(multiply(c_0,multiply(A,C))))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(inverse(inverse(multiply(B,inverse(multiply(F,c_0))))),F)))))) = inverse(multiply(c_0,multiply(inverse(E),D))). [back_rewrite(3407),rewrite([3414(15,R),3414(31,R),3340(32),3414(30,R)])].
% 1.81/2.10 3473 multiply(c_0,inverse(multiply(inverse(A),B))) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(3347),rewrite([3414(5,R)])].
% 1.81/2.10 3474 multiply(c_0,multiply(A,c_0)) = multiply(A,c_0). [back_rewrite(3340),rewrite([3414(3)])].
% 1.81/2.10 3476 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,c_0)))))),inverse(multiply(inverse(D),inverse(multiply(c_0,multiply(A,C))))))),E)),F)),multiply(c_0,inverse(multiply(B,E)))) = multiply(c_0,inverse(multiply(D,F))). [back_rewrite(3336),rewrite([3414(12,R),3414(25,R),3414(30,R)])].
% 1.81/2.10 3532 inverse(multiply(inverse(multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),B)))),inverse(multiply(inverse(C),B)))),inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(D,c_0))))),D))))) = C. [back_rewrite(3177),rewrite([3414(12,R),3348(13)])].
% 1.81/2.10 3559 multiply(a2,c_0) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(2420),rewrite([3414(3)])].
% 1.81/2.10 3560 multiply(A,c_0) = A. [back_rewrite(3351),rewrite([3473(6),3126(3),3414(3),3474(4)])].
% 1.81/2.10 3561 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3559),rewrite([3560(3)]),xx(a)].
% 1.81/2.10 3588 inverse(multiply(inverse(multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),B)))),inverse(multiply(inverse(C),B)))),inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(D)))),D))))) = C. [back_rewrite(3532),rewrite([3560(14)])].
% 1.81/2.10 3644 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(C))))),inverse(multiply(inverse(D),inverse(multiply(c_0,multiply(A,C))))))),E)),F)),multiply(c_0,inverse(multiply(B,E)))) = multiply(c_0,inverse(multiply(D,F))). [back_rewrite(3476),rewrite([3560(3)])].
% 1.81/2.10 3687 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(C))))),inverse(multiply(inverse(inverse(inverse(D))),inverse(multiply(c_0,multiply(A,C))))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(inverse(inverse(multiply(B,inverse(F)))),F)))))) = inverse(multiply(c_0,multiply(inverse(E),D))). [back_rewrite(3420),rewrite([3560(2),3560(7),3560(20)])].
% 1.81/2.10 3690 inverse(multiply(c_0,inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(B)))),B)),inverse(multiply(inverse(C),inverse(multiply(c_0,multiply(inverse(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(D)))),D)),inverse(E)))),E))))))))) = C. [back_rewrite(3416),rewrite([3560(4),3560(14),3560(20)])].
% 1.81/2.10 3692 multiply(c_0,A) = A. [back_rewrite(3414),rewrite([3560(4)])].
% 1.81/2.10 3696 inverse(inverse(A)) = A. [back_rewrite(3348),rewrite([3560(3),3692(3)])].
% 1.81/2.10 3699 multiply(multiply(A,inverse(B)),B) = A. [back_rewrite(3344),rewrite([3696(3),3560(3),3696(5),3692(5)])].
% 1.81/2.10 3702 multiply(multiply(A,B),inverse(B)) = A. [back_rewrite(3330),rewrite([3692(3),3696(3),3560(3),3560(6),3696(8),3699(7),3692(5)])].
% 1.81/2.10 3719 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(3186),rewrite([3692(4),3696(4),3560(7),3696(7),3692(7)])].
% 1.81/2.10 3720 inverse(multiply(multiply(inverse(A),multiply(B,C)),D)) = multiply(inverse(multiply(B,inverse(multiply(inverse(D),inverse(C))))),A). [back_rewrite(3168),rewrite([3692(6),3696(6),3692(6),3560(7),3696(7),3560(8)])].
% 1.81/2.10 3721 multiply(inverse(multiply(A,B)),C) = multiply(inverse(B),multiply(inverse(A),C)). [back_rewrite(3141),rewrite([3560(2),3560(3),3692(9)]),flip(a)].
% 1.81/2.10 3722 multiply(A,inverse(multiply(inverse(B),A))) = B. [back_rewrite(3690),rewrite([3696(6),3699(5),3692(3),3696(9),3699(8),3692(6),3696(8),3699(7),3692(5),3696(4),3692(7),3696(6)])].
% 1.81/2.10 3723 multiply(multiply(inverse(A),inverse(multiply(B,C))),multiply(B,multiply(C,D))) = inverse(multiply(inverse(D),A)). [back_rewrite(3687),rewrite([3696(7),3692(9),3721(11),3696(4),3696(17),3699(16),3692(14),3721(16),3721(16),3696(10),3722(14),3721(10),3696(6),3696(6),3692(11)])].
% 1.81/2.10 3732 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(3644),rewrite([3692(10),3721(12),3696(5),3721(13),3721(13),3696(10),3696(10),3721(11),3696(6),3696(6),3723(8),3721(3),3696(6),3720(6),3721(8),3696(5),3696(5),3692(9),3702(8),3692(7)]),flip(a)].
% 1.81/2.10 3741 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(3588),rewrite([3692(4),3732(3),3696(3),3732(3),3696(3),3732(5),3696(5),3732(6),3732(3),3696(3),3732(5),3696(5),3732(9),3696(8),3732(9),3696(8),3699(9),3692(7),3732(8),3696(2),3732(6),3732(3),3696(3),3732(5),3696(5),3719(6)])].
% 1.81/2.10 3800 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(3719(a,1),3741(a,1,2)),rewrite([3696(4)]),flip(a)].
% 1.81/2.10 3801 $F # answer(prove_these_axioms). [resolve(3800,a,3561,a)].
% 1.81/2.10
% 1.81/2.10 % SZS output end Refutation
% 1.81/2.10 ============================== end of proof ==========================
% 1.81/2.10
% 1.81/2.10 ============================== STATISTICS ============================
% 1.81/2.10
% 1.81/2.10 Given=54. Generated=8753. Kept=3799. proofs=1.
% 1.81/2.10 Usable=14. Sos=19. Demods=32. Limbo=0, Disabled=3767. Hints=0.
% 1.81/2.10 Megabytes=10.69.
% 1.81/2.10 User_CPU=1.05, System_CPU=0.01, Wall_clock=1.
% 1.81/2.10
% 1.81/2.10 ============================== end of statistics =====================
% 1.81/2.10
% 1.81/2.10 ============================== end of search =========================
% 1.81/2.10
% 1.81/2.10 THEOREM PROVED
% 1.81/2.10 % SZS status Unsatisfiable
% 1.81/2.10
% 1.81/2.10 Exiting with 1 proof.
% 1.81/2.10
% 1.81/2.10 Process 19241 exit (max_proofs) Mon Jun 13 21:05:56 2022
% 1.81/2.10 Prover9 interrupted
%------------------------------------------------------------------------------