TSTP Solution File: GRP055-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP055-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 1.98s 2.26s
% Output : Refutation 1.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 08:21:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.98/2.26 ============================== Prover9 ===============================
% 1.98/2.26 Prover9 (32) version 2009-11A, November 2009.
% 1.98/2.26 Process 32372 was started by sandbox on n003.cluster.edu,
% 1.98/2.26 Tue Jun 14 08:21:10 2022
% 1.98/2.26 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32219_n003.cluster.edu".
% 1.98/2.26 ============================== end of head ===========================
% 1.98/2.26
% 1.98/2.26 ============================== INPUT =================================
% 1.98/2.26
% 1.98/2.26 % Reading from file /tmp/Prover9_32219_n003.cluster.edu
% 1.98/2.26
% 1.98/2.26 set(prolog_style_variables).
% 1.98/2.26 set(auto2).
% 1.98/2.26 % set(auto2) -> set(auto).
% 1.98/2.26 % set(auto) -> set(auto_inference).
% 1.98/2.26 % set(auto) -> set(auto_setup).
% 1.98/2.26 % set(auto_setup) -> set(predicate_elim).
% 1.98/2.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.98/2.26 % set(auto) -> set(auto_limits).
% 1.98/2.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.98/2.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.98/2.26 % set(auto) -> set(auto_denials).
% 1.98/2.26 % set(auto) -> set(auto_process).
% 1.98/2.26 % set(auto2) -> assign(new_constants, 1).
% 1.98/2.26 % set(auto2) -> assign(fold_denial_max, 3).
% 1.98/2.26 % set(auto2) -> assign(max_weight, "200.000").
% 1.98/2.26 % set(auto2) -> assign(max_hours, 1).
% 1.98/2.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.98/2.26 % set(auto2) -> assign(max_seconds, 0).
% 1.98/2.26 % set(auto2) -> assign(max_minutes, 5).
% 1.98/2.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.98/2.26 % set(auto2) -> set(sort_initial_sos).
% 1.98/2.26 % set(auto2) -> assign(sos_limit, -1).
% 1.98/2.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.98/2.26 % set(auto2) -> assign(max_megs, 400).
% 1.98/2.26 % set(auto2) -> assign(stats, some).
% 1.98/2.26 % set(auto2) -> clear(echo_input).
% 1.98/2.26 % set(auto2) -> set(quiet).
% 1.98/2.26 % set(auto2) -> clear(print_initial_clauses).
% 1.98/2.26 % set(auto2) -> clear(print_given).
% 1.98/2.26 assign(lrs_ticks,-1).
% 1.98/2.26 assign(sos_limit,10000).
% 1.98/2.26 assign(order,kbo).
% 1.98/2.26 set(lex_order_vars).
% 1.98/2.26 clear(print_given).
% 1.98/2.26
% 1.98/2.26 % formulas(sos). % not echoed (2 formulas)
% 1.98/2.26
% 1.98/2.26 ============================== end of input ==========================
% 1.98/2.26
% 1.98/2.26 % From the command line: assign(max_seconds, 300).
% 1.98/2.26
% 1.98/2.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.98/2.26
% 1.98/2.26 % Formulas that are not ordinary clauses:
% 1.98/2.26
% 1.98/2.26 ============================== end of process non-clausal formulas ===
% 1.98/2.26
% 1.98/2.26 ============================== PROCESS INITIAL CLAUSES ===============
% 1.98/2.26
% 1.98/2.26 ============================== PREDICATE ELIMINATION =================
% 1.98/2.26
% 1.98/2.26 ============================== end predicate elimination =============
% 1.98/2.26
% 1.98/2.26 Auto_denials:
% 1.98/2.26 % copying label prove_these_axioms to answer in negative clause
% 1.98/2.26
% 1.98/2.26 Term ordering decisions:
% 1.98/2.26
% 1.98/2.26 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.98/2.26 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.98/2.26
% 1.98/2.26 ============================== end of process initial clauses ========
% 1.98/2.26
% 1.98/2.26 ============================== CLAUSES FOR SEARCH ====================
% 1.98/2.26
% 1.98/2.26 ============================== end of clauses for search =============
% 1.98/2.26
% 1.98/2.26 ============================== SEARCH ================================
% 1.98/2.26
% 1.98/2.26 % Starting search at 0.01 seconds.
% 1.98/2.26
% 1.98/2.26 ============================== PROOF =================================
% 1.98/2.26 % SZS status Unsatisfiable
% 1.98/2.26 % SZS output start Refutation
% 1.98/2.26
% 1.98/2.26 % Proof 1 at 1.28 (+ 0.01) seconds: prove_these_axioms.
% 1.98/2.26 % Length of proof is 229.
% 1.98/2.26 % Level of proof is 61.
% 1.98/2.26 % Maximum clause weight is 182.000.
% 1.98/2.26 % Given clauses 48.
% 1.98/2.26
% 1.98/2.26 1 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 1.98/2.26 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].
% 1.98/2.26 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)].
% 1.98/2.26 4 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))). [para(1(a,1),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 5 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(C,inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))))))),multiply(A,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))) = B. [para(1(a,1),1(a,1,1,1,1,2,1,2,1)),rewrite([1(14)])].
% 1.98/2.26 6 multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,A))). [para(1(a,1),1(a,1,1,1,1,2)),flip(a)].
% 1.98/2.26 8 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(D),multiply(inverse(multiply(A,C)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,multiply(inverse(F),inverse(multiply(inverse(F),F))))))),multiply(E,F))))) = D. [para(4(a,1),1(a,1,1,2))].
% 1.98/2.26 9 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)))) = B. [para(4(a,1),1(a,1,1))].
% 1.98/2.26 10 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(B),multiply(inverse(F),inverse(multiply(inverse(F),F))))))),multiply(E,F)),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(D,V6))). [para(4(a,2),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 13 multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(B),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E)))),multiply(C,A))). [para(4(a,2),1(a,1,1,1,1,2)),flip(a)].
% 1.98/2.26 14 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = B. [para(4(a,2),1(a,1))].
% 1.98/2.26 49 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),multiply(inverse(C),inverse(multiply(inverse(C),C))))) = B. [para(6(a,1),1(a,1,1,1,1))].
% 1.98/2.26 55 multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(inverse(B),multiply(inverse(A),inverse(multiply(inverse(A),A)))))),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = B. [para(6(a,2),1(a,1))].
% 1.98/2.26 61 multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(B),inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(A,D)) = inverse(multiply(inverse(multiply(E,inverse(multiply(multiply(inverse(multiply(F,C)),multiply(F,B)),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(E,V6))). [para(6(a,2),4(a,1,1,1,2,1,1))].
% 1.98/2.26 65 multiply(inverse(multiply(A,multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))),multiply(A,B)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(B),C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))). [para(6(a,2),4(a,1,1,1,2))].
% 1.98/2.26 69 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = multiply(inverse(D),inverse(multiply(inverse(inverse(multiply(B,multiply(inverse(D),inverse(multiply(inverse(D),D)))))),multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D)))))))). [para(6(a,2),4(a,2))].
% 1.98/2.26 82 inverse(multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(B,multiply(inverse(A),inverse(multiply(inverse(A),A)))))),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = B. [para(6(a,2),9(a,1,1))].
% 1.98/2.26 83 multiply(A,inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(C,inverse(multiply(A,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D)))))),inverse(multiply(inverse(inverse(multiply(A,inverse(multiply(inverse(multiply(C,inverse(multiply(A,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D)))))),inverse(multiply(A,inverse(multiply(inverse(multiply(C,inverse(multiply(A,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D))))))))))) = inverse(multiply(inverse(multiply(E,B)),multiply(E,inverse(multiply(inverse(multiply(C,inverse(multiply(A,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D)))))). [para(9(a,1),6(a,1,1)),rewrite([9(14),9(29),9(44)])].
% 1.98/2.26 84 multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))),multiply(C,A))). [para(9(a,1),6(a,1,2,1,1))].
% 1.98/2.26 85 multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),multiply(inverse(C),inverse(multiply(inverse(C),C)))) = B. [para(6(a,1),14(a,1,1,1))].
% 1.98/2.26 92 inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))). [para(6(a,1),6(a,1))].
% 1.98/2.26 104 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(92(a,1),1(a,1,1,1,1,2,1,1)),rewrite([1(17)])].
% 1.98/2.26 107 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(C,D)),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))))))),multiply(A,multiply(C,D)))) = B. [para(92(a,1),1(a,1,1,1,1,2,1,2,2))].
% 1.98/2.26 108 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(inverse(D),D))))))),multiply(A,D))) = multiply(inverse(D),C). [para(92(a,1),1(a,1,1,1,1,2))].
% 1.98/2.26 113 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(C,D)),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))))))),multiply(A,multiply(C,D))) = inverse(multiply(inverse(multiply(F,inverse(multiply(B,multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))). [para(92(a,1),4(a,1,1,1,2,1,2,2))].
% 1.98/2.26 117 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(inverse(multiply(E,F)),inverse(multiply(inverse(multiply(V6,F)),multiply(V6,F)))))))),multiply(D,multiply(E,F)))). [para(92(a,1),4(a,2,1,1,1,2,1,2,2))].
% 1.98/2.26 122 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(multiply(C,D)),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))))))),multiply(A,multiply(C,D))))) = B. [para(92(a,1),9(a,1,1,1,1,1,2,1,2,2))].
% 1.98/2.26 125 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(multiply(C,D)),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))))))),multiply(A,multiply(C,D))) = B. [para(92(a,1),14(a,1,1,1,2,1,2,2))].
% 1.98/2.26 128 multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(E,multiply(inverse(multiply(F,C)),multiply(F,D)))),multiply(E,A))). [para(92(a,1),6(a,1,2,1,1))].
% 1.98/2.26 140 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E))) = inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E))). [para(92(a,1),92(a,1,1,1))].
% 1.98/2.26 150 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(C,inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))))))),multiply(A,inverse(multiply(inverse(multiply(F,inverse(multiply(C,multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6)))))) = B. [para(4(a,1),5(a,1,1,2,2))].
% 1.98/2.26 152 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(B),multiply(inverse(F),inverse(multiply(inverse(F),F))))))),multiply(E,F)),multiply(V6,inverse(multiply(V6,multiply(inverse(multiply(V7,inverse(multiply(inverse(V6),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(V7,V8))))))))),multiply(D,multiply(inverse(multiply(V7,inverse(multiply(inverse(V6),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(V7,V8))))). [para(4(a,2),5(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 162 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(E,inverse(multiply(E,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))))))),multiply(D,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))))))))),multiply(A,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(E,inverse(multiply(E,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))))))),multiply(D,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6)))))))) = B. [para(5(a,1),9(a,1,1,1,1,1,2,1,2,1)),rewrite([5(35)])].
% 1.98/2.26 166 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),multiply(E,inverse(multiply(E,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))))))),multiply(D,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6)))). [para(5(a,1),14(a,1,1,1,2,1,1,1))].
% 1.98/2.26 175 multiply(inverse(multiply(A,B)),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(C),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))))),multiply(E,inverse(multiply(E,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))))))),multiply(D,multiply(inverse(multiply(F,inverse(multiply(inverse(E),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))). [para(6(a,2),5(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 198 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(C,inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))))))),multiply(A,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E)))) = inverse(multiply(inverse(multiply(F,inverse(multiply(B,multiply(V6,inverse(multiply(V6,multiply(inverse(multiply(V7,inverse(multiply(inverse(V6),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(V7,V8))))))))),multiply(F,multiply(inverse(multiply(V7,inverse(multiply(inverse(V6),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(V7,V8))))). [para(5(a,1),5(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 201 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),D)). [para(1(a,1),104(a,1,1)),flip(a)].
% 1.98/2.26 213 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E)))) = inverse(multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E)))). [para(104(a,1),92(a,1,1,2))].
% 1.98/2.26 214 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(92(a,1),104(a,1,1))].
% 1.98/2.26 216 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(C,inverse(multiply(C,multiply(inverse(multiply(D,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))))))))),multiply(A,multiply(inverse(multiply(F,inverse(multiply(inverse(C),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(F,E))))) = B. [para(104(a,1),5(a,1,1,1,1,2,1,2,2,1,2))].
% 1.98/2.26 220 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(104(a,1),104(a,1,2))].
% 1.98/2.26 226 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(E,inverse(multiply(E,multiply(inverse(inverse(multiply(inverse(multiply(F,E)),multiply(F,V6)))),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))))))),multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(F,E)),multiply(F,V6)))),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))). [para(49(a,1),4(a,2,1,1,1,2,1,2,1)),rewrite([49(25)])].
% 1.98/2.26 231 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(multiply(C,multiply(inverse(inverse(multiply(inverse(multiply(D,C)),multiply(D,E)))),multiply(inverse(E),inverse(multiply(inverse(E),E))))))))))),multiply(A,multiply(inverse(inverse(multiply(inverse(multiply(D,C)),multiply(D,E)))),multiply(inverse(E),inverse(multiply(inverse(E),E)))))))) = B. [para(49(a,1),9(a,1,1,1,1,1,2,1,2,1)),rewrite([49(13)])].
% 1.98/2.26 232 inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))) = inverse(inverse(multiply(inverse(multiply(D,B)),multiply(D,C)))). [para(49(a,1),9(a,1,1,1,1,1,2))].
% 1.98/2.26 238 multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,multiply(inverse(inverse(multiply(inverse(multiply(D,B)),multiply(D,E)))),multiply(inverse(E),inverse(multiply(inverse(E),E)))))),multiply(C,A))). [para(49(a,1),6(a,1,2,1,1))].
% 1.98/2.26 239 multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(B),B)))),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(C,multiply(inverse(inverse(multiply(inverse(multiply(D,C)),multiply(D,B)))),A))). [para(49(a,1),6(a,2,1,1))].
% 1.98/2.26 251 multiply(inverse(multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),C)). [para(49(a,1),104(a,1,1)),flip(a)].
% 1.98/2.26 252 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))))),multiply(inverse(multiply(A,E)),inverse(multiply(inverse(multiply(A,E)),multiply(A,E)))))) = C. [para(104(a,1),49(a,1,1,1,1,1,2))].
% 1.98/2.26 253 multiply(inverse(A),inverse(multiply(inverse(A),A))) = inverse(multiply(inverse(inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(multiply(C,B)),multiply(C,A)))),D)))),multiply(inverse(D),inverse(multiply(inverse(D),D))))). [para(49(a,1),49(a,1,1,1,1,1,1)),flip(a)].
% 1.98/2.26 261 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(multiply(E,F)),multiply(E,V6)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(V7,F)),multiply(V7,V6)))),inverse(multiply(inverse(multiply(E,F)),multiply(E,V6)))))))))),multiply(D,inverse(multiply(inverse(multiply(E,F)),multiply(E,V6)))))). [para(232(a,1),4(a,2,1,1,1,2,1,2,2,1,1))].
% 1.98/2.26 264 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,E)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(F,D)),multiply(F,E)))),inverse(multiply(inverse(multiply(F,D)),multiply(F,E)))))))))),multiply(A,inverse(multiply(inverse(multiply(F,D)),multiply(F,E))))))) = B. [para(232(a,1),9(a,1,1,1,1,1,2,1,2,1))].
% 1.98/2.26 266 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,E)))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(F,D)),multiply(F,E)))),inverse(multiply(inverse(multiply(F,D)),multiply(F,E)))))))))),multiply(A,inverse(multiply(inverse(multiply(F,D)),multiply(F,E))))) = B. [para(232(a,1),14(a,1,1,1,2,1,2,1))].
% 1.98/2.26 281 inverse(inverse(multiply(inverse(multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))),multiply(A,C)))) = inverse(inverse(multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),C)))). [para(49(a,1),232(a,1,1,1,1)),flip(a)].
% 1.98/2.26 347 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(D),multiply(inverse(multiply(A,C)),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))),inverse(multiply(inverse(E),multiply(inverse(B),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(multiply(F,inverse(multiply(D,multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))) = E. [para(14(a,1),8(a,1,1,1,1,2,1,2,1,1)),rewrite([14(39),14(40)])].
% 1.98/2.26 353 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),inverse(multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))))))),inverse(multiply(inverse(D),multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))),inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))),inverse(multiply(inverse(multiply(E,C)),multiply(E,A)))))))))),inverse(multiply(inverse(multiply(F,inverse(multiply(B,multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))) = D. [para(6(a,1),8(a,1,1,1,1,2,1,2,2,1,2))].
% 1.98/2.26 369 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(C,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(B,D))))),multiply(A,E))) = inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,inverse(multiply(inverse(C),multiply(inverse(V7),inverse(multiply(inverse(V7),V7))))))),inverse(multiply(inverse(F),multiply(inverse(multiply(V6,V7)),inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,V7)))))))),E))). [para(8(a,1),92(a,1,1,1)),flip(a)].
% 1.98/2.26 374 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(inverse(D),D))))))),inverse(multiply(inverse(E),multiply(inverse(multiply(A,D)),inverse(multiply(inverse(multiply(A,D)),multiply(A,D)))))))),inverse(multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(D),C),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))) = E. [para(92(a,1),8(a,1,1,1,1,1,1,2))].
% 1.98/2.26 378 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(multiply(D,E)),multiply(D,inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))),inverse(multiply(inverse(multiply(F,inverse(multiply(B,multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))))) = multiply(inverse(multiply(A,C)),E). [para(92(a,1),8(a,1,1,1,1,2))].
% 1.98/2.26 392 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(C,multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(B,D))))),multiply(A,E)))) = inverse(inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,inverse(multiply(inverse(C),multiply(inverse(V7),inverse(multiply(inverse(V7),V7))))))),inverse(multiply(inverse(F),multiply(inverse(multiply(V6,V7)),inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,V7)))))))),E)))). [para(8(a,1),232(a,1,1,1,1)),flip(a)].
% 1.98/2.26 399 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = multiply(inverse(inverse(multiply(D,multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(B),multiply(inverse(F),inverse(multiply(inverse(F),F))))))),inverse(multiply(inverse(D),multiply(inverse(multiply(E,F)),inverse(multiply(inverse(multiply(E,F)),multiply(E,F)))))))),V6)))),multiply(inverse(V6),inverse(multiply(inverse(V6),V6)))). [para(8(a,1),85(a,1,1,1,1,1)),flip(a)].
% 1.98/2.26 420 inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))))))) = inverse(inverse(multiply(inverse(multiply(D,multiply(inverse(inverse(multiply(inverse(A),A))),C))),multiply(D,A)))). [para(108(a,1),9(a,1,1,1,1,1,2)),flip(a)].
% 1.98/2.26 422 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(A,D)) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(F,C)),multiply(F,inverse(multiply(inverse(B),B))))))),multiply(E,B)). [para(108(a,1),14(a,1,1,1,2,1,1,1))].
% 1.98/2.26 426 multiply(inverse(A),inverse(multiply(multiply(inverse(B),C),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(D,multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(F,C)),multiply(F,inverse(multiply(inverse(B),B))))))),multiply(E,B)))),multiply(D,A))). [para(108(a,1),6(a,1,2,1,1))].
% 1.98/2.26 427 inverse(multiply(inverse(multiply(A,multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(multiply(C,D)),multiply(C,inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))))))),multiply(A,B))) = multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),D)). [para(108(a,1),6(a,1,2)),flip(a)].
% 1.98/2.26 430 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),inverse(multiply(inverse(multiply(D,multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),multiply(D,B))))))),multiply(A,multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B)))))),C). [para(6(a,1),108(a,1,1,1,1,2,1,2))].
% 1.98/2.26 431 inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(inverse(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))))))))),inverse(multiply(inverse(multiply(E,D)),multiply(E,A))))) = multiply(inverse(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))),C). [para(6(a,1),108(a,1,1,2))].
% 1.98/2.26 437 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),inverse(multiply(inverse(F),F))))))),multiply(A,F))) = multiply(inverse(F),multiply(E,D)). [para(92(a,1),108(a,1,1,1,1,2,1,1))].
% 1.98/2.26 442 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(multiply(C,D)),multiply(C,inverse(multiply(inverse(multiply(A,E)),multiply(A,E)))))))),multiply(inverse(multiply(F,B)),multiply(F,E)))) = multiply(inverse(multiply(A,E)),D). [para(104(a,1),108(a,1,1,2))].
% 1.98/2.26 445 multiply(inverse(A),multiply(inverse(B),inverse(multiply(inverse(B),B)))) = inverse(multiply(inverse(multiply(C,inverse(multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),inverse(multiply(inverse(A),A))))))),multiply(C,A))). [para(49(a,1),108(a,1,1,1,1,2,1,1)),flip(a)].
% 1.98/2.26 449 multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),D) = multiply(inverse(inverse(multiply(inverse(multiply(E,B)),multiply(E,C)))),D). [para(232(a,1),108(a,2,1)),rewrite([108(28)])].
% 1.98/2.26 578 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),C))))),multiply(inverse(multiply(inverse(C),B)),D)) = multiply(E,multiply(inverse(inverse(multiply(inverse(multiply(F,E)),multiply(F,C)))),D)). [para(49(a,1),214(a,2,1))].
% 1.98/2.26 838 multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(A),multiply(inverse(multiply(E,C)),multiply(E,D))). [para(220(a,1),108(a,1,1,1,1,2,1,1,1)),rewrite([437(21)])].
% 1.98/2.26 865 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))). [para(220(a,1),214(a,1))].
% 1.98/2.26 869 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E)))),multiply(inverse(multiply(F,C)),V6))),multiply(inverse(multiply(V7,multiply(F,multiply(A,E)))),V8)) = multiply(inverse(multiply(V9,multiply(V7,V6))),multiply(V9,V8)). [para(220(a,2),214(a,1,1,1,1,1))].
% 1.98/2.26 871 multiply(inverse(multiply(inverse(multiply(A,multiply(B,multiply(C,D)))),multiply(A,E))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,F)),V6)),multiply(inverse(multiply(V7,F)),multiply(V7,D)))),V8)) = multiply(inverse(multiply(V9,multiply(inverse(multiply(B,V6)),E))),multiply(V9,V8)). [para(220(a,2),214(a,1,2,1,1))].
% 1.98/2.26 920 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(1(a,1),838(a,1,1)),rewrite([1(18)])].
% 1.98/2.26 1018 multiply(A,multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(B,C)),multiply(B,D)))),E)),multiply(inverse(inverse(multiply(inverse(multiply(F,C)),multiply(F,D)))),V6))) = multiply(A,multiply(inverse(multiply(V7,E)),multiply(V7,V6))). [para(449(a,1),920(a,1,2,1,1))].
% 1.98/2.26 1075 inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))))) = inverse(inverse(multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))))). [para(865(a,1),232(a,1,1,1))].
% 1.98/2.26 1128 multiply(A,multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,E)))) = multiply(A,multiply(inverse(multiply(F,multiply(V6,D))),multiply(F,multiply(V6,E)))). [para(865(a,1),920(a,1,2))].
% 1.98/2.26 1523 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D)))),multiply(A,E))),multiply(inverse(multiply(F,multiply(inverse(multiply(V6,C)),multiply(V6,D)))),V7))) = inverse(multiply(inverse(multiply(V8,multiply(F,E))),multiply(V8,V7))). [para(920(a,1),140(a,1,1,1,1,1,1))].
% 1.98/2.26 1530 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),multiply(inverse(multiply(E,multiply(F,C))),V6))) = inverse(multiply(inverse(multiply(inverse(multiply(V7,V8)),multiply(V7,multiply(F,D)))),multiply(inverse(multiply(E,V8)),V6))). [para(865(a,1),140(a,2,1,1,1)),flip(a)].
% 1.98/2.26 1611 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(B,V6)),D))),multiply(F,V7)))) = inverse(multiply(inverse(multiply(V8,E)),multiply(V8,multiply(inverse(multiply(inverse(multiply(V9,V6)),multiply(V9,C))),V7)))). [para(214(a,1),213(a,1,1,1,1,1,1))].
% 1.98/2.26 1617 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E))),F)),multiply(inverse(multiply(V6,multiply(V7,E))),multiply(V6,V8)))) = inverse(multiply(inverse(multiply(V9,F)),multiply(V9,multiply(inverse(multiply(V7,multiply(D,C))),V8)))). [para(214(a,2),213(a,1,1,1,1,1,1))].
% 1.98/2.26 1650 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E)))),F)),multiply(inverse(multiply(V6,multiply(V7,multiply(A,E)))),multiply(V6,V8)))) = inverse(multiply(inverse(multiply(V9,F)),multiply(V9,multiply(inverse(multiply(V7,C)),V8)))). [para(220(a,2),213(a,1,1,1,1,1,1))].
% 1.98/2.26 1651 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,multiply(C,D)))),E)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,F)),V6)),multiply(inverse(multiply(V7,F)),multiply(V7,D)))),multiply(inverse(multiply(B,V6)),V8)))) = inverse(multiply(inverse(multiply(V9,E)),multiply(V9,multiply(A,V8)))). [para(220(a,2),213(a,1,1,2,1,1))].
% 1.98/2.26 1731 inverse(inverse(multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),D))),multiply(A,multiply(inverse(multiply(inverse(multiply(E,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,V7))))))) = inverse(inverse(multiply(inverse(multiply(V8,multiply(V9,D))),multiply(V8,multiply(V9,multiply(B,multiply(E,V7))))))). [para(220(a,2),1075(a,1,1,1,2,2))].
% 1.98/2.26 1736 inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),multiply(inverse(multiply(E,multiply(F,C))),multiply(E,V6))))) = inverse(inverse(multiply(inverse(multiply(V7,multiply(V8,multiply(F,D)))),multiply(V7,multiply(V8,V6))))). [para(865(a,1),1075(a,1,1,1,1,1))].
% 1.98/2.26 2016 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,F))))),multiply(inverse(multiply(V6,B)),multiply(V6,V7))) = multiply(inverse(multiply(V8,multiply(inverse(multiply(V9,multiply(V10,E))),multiply(V9,multiply(V10,F))))),multiply(V8,multiply(A,V7))). [para(1128(a,1),220(a,1,1,1))].
% 1.98/2.26 2021 multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),multiply(inverse(multiply(E,C)),F))),multiply(inverse(multiply(V6,D)),multiply(V6,multiply(B,V7))))) = multiply(A,multiply(inverse(multiply(V8,multiply(V9,F))),multiply(V8,multiply(V9,multiply(E,V7))))). [para(220(a,1),1128(a,1,2,2))].
% 1.98/2.26 2040 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V7)))))) = inverse(multiply(inverse(multiply(V8,multiply(D,C))),multiply(V8,multiply(inverse(multiply(V9,multiply(V10,V6))),multiply(V9,multiply(V10,V7)))))). [para(1128(a,1),140(a,1,1,2))].
% 1.98/2.26 2229 multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(C,multiply(inverse(multiply(E,F)),inverse(multiply(inverse(multiply(V6,F)),multiply(V6,F)))))))),multiply(D,multiply(E,F))))))))))),multiply(A,inverse(multiply(inverse(multiply(D,inverse(multiply(C,multiply(inverse(multiply(E,F)),inverse(multiply(inverse(multiply(V6,F)),multiply(V6,F)))))))),multiply(D,multiply(E,F)))))) = inverse(multiply(inverse(multiply(V7,inverse(multiply(multiply(inverse(multiply(V8,inverse(multiply(inverse(B),multiply(inverse(V9),inverse(multiply(inverse(V9),V9))))))),multiply(V8,V9)),multiply(inverse(V10),inverse(multiply(inverse(V10),V10))))))),multiply(V7,V10))). [para(122(a,1),10(a,1,1,1,2,1,2,1)),rewrite([122(17)])].
% 1.98/2.26 2269 multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(E)),multiply(inverse(multiply(F,V6)),inverse(multiply(inverse(multiply(V7,V6)),multiply(V7,V6)))))))),inverse(multiply(B,multiply(inverse(multiply(D,multiply(F,V6))),inverse(multiply(inverse(multiply(D,multiply(F,V6))),multiply(D,multiply(F,V6))))))))),E)). [para(125(a,1),4(a,2,1,2))].
% 1.98/2.26 2327 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(inverse(E)),multiply(inverse(multiply(F,V6)),inverse(multiply(inverse(multiply(V7,V6)),multiply(V7,V6)))))))),inverse(multiply(multiply(inverse(multiply(V8,inverse(multiply(inverse(B),multiply(inverse(V9),inverse(multiply(inverse(V9),V9))))))),multiply(V8,V9)),multiply(inverse(multiply(D,multiply(F,V6))),inverse(multiply(inverse(multiply(D,multiply(F,V6))),multiply(D,multiply(F,V6))))))))),E)). [para(125(a,1),10(a,2,1,2))].
% 1.98/2.26 2336 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(multiply(C,D)),inverse(multiply(inverse(multiply(E,D)),multiply(E,D)))))))),F)),B) = multiply(inverse(multiply(inverse(multiply(A,V6)),F)),multiply(inverse(multiply(V7,V6)),multiply(V7,multiply(C,D)))). [para(125(a,1),220(a,2,2)),flip(a)].
% 1.98/2.26 2523 multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(C),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(B,D)))),multiply(A,E)))),multiply(inverse(E),inverse(multiply(inverse(E),E)))) = inverse(multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(V6,inverse(multiply(inverse(C),multiply(inverse(V7),inverse(multiply(inverse(V7),V7))))))),multiply(V6,V7)),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(F,V8))). [para(13(a,1),10(a,1,1,1))].
% 1.98/2.26 2696 multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),inverse(multiply(inverse(E),E))))))),multiply(A,E)) = inverse(multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(E),multiply(C,D)),multiply(inverse(V6),inverse(multiply(inverse(V6),V6))))))),multiply(F,V6))). [para(201(a,1),4(a,1,1,1,2,1))].
% 1.98/2.26 2715 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D). [para(14(a,1),201(a,2,2))].
% 1.98/2.26 2753 multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,multiply(C,multiply(D,E)))))),multiply(inverse(multiply(C,multiply(D,E))),inverse(multiply(F,multiply(inverse(multiply(D,inverse(multiply(inverse(F),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E)))))) = B. [para(201(a,1),85(a,1,2,2,1))].
% 1.98/2.26 2785 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(inverse(multiply(V6,inverse(multiply(inverse(F),multiply(inverse(V7),inverse(multiply(inverse(V7),V7))))))),C))),multiply(inverse(multiply(D,multiply(V6,V7))),E)). [para(201(a,1),214(a,2,1,1))].
% 1.98/2.26 2985 multiply(inverse(multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),D))),multiply(inverse(multiply(E,multiply(B,C))),F)) = multiply(V6,multiply(inverse(multiply(E,inverse(multiply(inverse(V6),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),F)). [para(201(a,1),201(a,1,1,1))].
% 1.98/2.26 2995 multiply(inverse(A),inverse(multiply(inverse(A),A))) = inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))))),multiply(B,A))). [para(2715(a,2),1(a,1,1,1,1,2,1)),flip(a)].
% 1.98/2.26 2997 inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),inverse(multiply(inverse(A),A))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))) = B. [para(2715(a,2),1(a,1,1,2))].
% 1.98/2.26 2998 multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D))). [para(1(a,1),2715(a,1,1)),flip(a)].
% 1.98/2.26 2999 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(2715(a,2),3(b,1,1))].
% 1.98/2.26 3023 multiply(inverse(A),A) = multiply(inverse(B),B). [para(14(a,1),2715(a,1,1,1)),rewrite([14(14)])].
% 1.98/2.26 3048 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(2715(a,2),104(a,1,1,1))].
% 1.98/2.26 3049 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(2715(a,2),104(a,1,2))].
% 1.98/2.26 3057 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),multiply(inverse(D),inverse(multiply(inverse(D),D))))) = D. [para(2715(a,2),49(a,1,1,1,1,1))].
% 1.98/2.26 3059 multiply(inverse(A),A) = multiply(B,multiply(inverse(inverse(multiply(inverse(multiply(C,B)),multiply(C,D)))),multiply(inverse(D),inverse(multiply(inverse(D),D))))). [para(49(a,1),2715(a,1,1)),flip(a)].
% 1.98/2.26 3063 inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(D),E)))) = inverse(inverse(multiply(inverse(multiply(F,D)),multiply(F,E)))). [para(2715(a,2),232(a,1,1,1,1,1))].
% 1.98/2.26 3064 inverse(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))))) = inverse(inverse(multiply(inverse(multiply(F,B)),multiply(F,A)))). [para(2715(a,2),232(a,1,1,1,2))].
% 1.98/2.26 3070 multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),multiply(inverse(inverse(D)),inverse(multiply(inverse(inverse(D)),inverse(D))))) = D. [para(2715(a,2),85(a,1,1,1,1))].
% 1.98/2.26 3120 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(inverse(multiply(D,multiply(inverse(E),inverse(multiply(inverse(E),E)))))),E)) = inverse(multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(V6,inverse(multiply(inverse(D),multiply(inverse(V7),inverse(multiply(inverse(V7),V7))))))),multiply(V6,V7)),multiply(inverse(V8),inverse(multiply(inverse(V8),V8))))))),multiply(F,V8))). [para(2715(a,2),10(a,1,1,1))].
% 1.98/2.26 3146 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,F)))) = multiply(inverse(multiply(inverse(multiply(A,V6)),C)),multiply(inverse(multiply(V7,V6)),multiply(V7,B))). [para(2715(a,2),220(a,2,2)),flip(a)].
% 1.98/2.26 3147 multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,multiply(D,E))))),multiply(A,multiply(inverse(multiply(inverse(multiply(D,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,E))))) = multiply(inverse(V7),V7). [para(220(a,1),2715(a,1,1,1,2))].
% 1.98/2.26 3154 multiply(A,multiply(inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D)))),multiply(inverse(E),F))) = multiply(A,multiply(inverse(multiply(V6,E)),multiply(V6,F))). [para(2715(a,2),920(a,1,2,1,1))].
% 1.98/2.26 3155 multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,F))))) = multiply(A,multiply(inverse(multiply(V6,C)),multiply(V6,B))). [para(2715(a,2),920(a,1,2,2))].
% 1.98/2.26 3202 inverse(inverse(multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,F))))))) = inverse(inverse(multiply(inverse(multiply(V6,multiply(V7,C))),multiply(V6,multiply(V7,B))))). [para(2715(a,2),1075(a,1,1,1,2,2))].
% 1.98/2.26 3211 multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),D))),multiply(B,multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V6)))))) = multiply(A,multiply(inverse(multiply(V7,multiply(V8,D))),multiply(V7,multiply(V8,C)))). [para(2715(a,2),1128(a,1,2,2,2))].
% 1.98/2.26 3212 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V6))))) = multiply(A,multiply(inverse(multiply(V7,multiply(V8,D))),multiply(V7,multiply(V8,C)))). [para(2715(a,2),1128(a,1,2,2))].
% 1.98/2.26 3256 multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(inverse(C),C)),multiply(B,A))). [para(2715(a,1),13(a,2,1,1,1)),rewrite([1(34)])].
% 1.98/2.26 3267 multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),inverse(multiply(inverse(D),D))))))),multiply(C,D)))),multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V6))))). [para(2715(a,2),13(a,2,1,2))].
% 1.98/2.26 3274 multiply(inverse(multiply(A,multiply(B,multiply(C,multiply(D,E))))),multiply(A,F)) = multiply(V6,multiply(inverse(multiply(B,inverse(multiply(inverse(V6),multiply(inverse(multiply(C,multiply(D,E))),inverse(multiply(inverse(V7),V7))))))),F)). [para(2715(a,1),201(a,2,2,1,1,2,1,2,2,1))].
% 1.98/2.26 3276 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(multiply(D,E)),F)) = multiply(V6,multiply(inverse(multiply(D,inverse(multiply(inverse(V6),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),F)). [para(2715(a,2),201(a,1,1,1))].
% 1.98/2.26 3277 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),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),A)). [para(2715(a,2),201(a,1,2))].
% 1.98/2.26 3290 multiply(inverse(A),A) = c_0. [new_symbol(3023)].
% 1.98/2.26 3291 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_unit_del(2999),rewrite([3290(4),3290(5),3290(9)]),xx(a)].
% 1.98/2.26 3301 multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),multiply(inverse(C),inverse(c_0)))))),D)) = multiply(inverse(multiply(inverse(D),multiply(B,C))),c_0). [back_rewrite(3277),rewrite([3290(10),3290(10)]),flip(a)].
% 1.98/2.26 3302 multiply(inverse(multiply(inverse(A),multiply(B,C))),c_0) = multiply(inverse(c_0),multiply(inverse(multiply(B,C)),A)). [back_rewrite(3276),rewrite([3290(6),3290(10),3301(17)]),flip(a)].
% 1.98/2.26 3304 multiply(inverse(multiply(A,multiply(B,multiply(C,multiply(D,E))))),multiply(A,F)) = multiply(inverse(c_0),multiply(inverse(multiply(B,multiply(C,multiply(D,E)))),F)). [back_rewrite(3274),rewrite([3290(13),3301(20),3302(15)])].
% 1.98/2.26 3308 inverse(multiply(inverse(c_0),multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(c_0)))))),multiply(A,C))),D))) = multiply(inverse(D),inverse(multiply(B,c_0))). [back_rewrite(3267),rewrite([3290(3),3290(6),3290(9),3290(10),3290(7),3290(10),3290(25),3302(21)]),flip(a)].
% 1.98/2.26 3314 inverse(multiply(inverse(c_0),multiply(A,B))) = multiply(inverse(B),inverse(multiply(A,c_0))). [back_rewrite(3256),rewrite([3290(3),3290(6),3290(9),3290(10),3290(7),3290(7)]),flip(a)].
% 1.98/2.26 3332 multiply(A,multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,E)))) = multiply(A,multiply(inverse(c_0),multiply(inverse(multiply(F,D)),multiply(F,E)))). [back_rewrite(3212),rewrite([3290(11),3302(7)]),flip(a)].
% 1.98/2.26 3333 multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),D))),multiply(B,c_0))) = multiply(A,multiply(inverse(multiply(E,multiply(F,D))),multiply(E,multiply(F,C)))). [back_rewrite(3211),rewrite([3290(10)])].
% 1.98/2.26 3340 inverse(inverse(multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,c_0)))) = inverse(inverse(multiply(inverse(multiply(D,multiply(E,C))),multiply(D,multiply(E,B))))). [back_rewrite(3202),rewrite([3290(10)])].
% 1.98/2.26 3365 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(inverse(D),C)),c_0)). [back_rewrite(3155),rewrite([3290(9)]),flip(a)].
% 1.98/2.26 3366 multiply(A,multiply(inverse(multiply(inverse(B),C)),c_0)) = multiply(A,multiply(inverse(c_0),multiply(inverse(C),B))). [back_rewrite(3154),rewrite([3290(6),3365(11)]),flip(a)].
% 1.98/2.26 3369 multiply(inverse(c_0),multiply(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(C),c_0))),multiply(inverse(multiply(inverse(multiply(A,D)),C)),multiply(inverse(c_0),multiply(inverse(D),B))))) = c_0. [back_rewrite(3147),rewrite([3365(6),3366(7),3365(17),3366(18),3304(20),3314(9),3290(23)])].
% 1.98/2.26 3370 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(c_0),multiply(inverse(B),D))) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),c_0). [back_rewrite(3146),rewrite([3290(10),3365(15),3366(16)]),flip(a)].
% 1.98/2.26 3385 multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,multiply(inverse(B),inverse(c_0))))),B)) = inverse(multiply(inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),inverse(c_0)))))),multiply(D,E)),multiply(inverse(F),inverse(c_0)))))),multiply(C,F))). [back_rewrite(3120),rewrite([3290(6),3290(5),3290(15),3290(25)])].
% 1.98/2.26 3411 multiply(inverse(inverse(c_0)),multiply(inverse(inverse(A)),inverse(c_0))) = A. [back_rewrite(3070),rewrite([3290(6),3290(9)])].
% 1.98/2.26 3413 inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))) = inverse(inverse(multiply(inverse(multiply(inverse(C),B)),c_0))). [back_rewrite(3064),rewrite([3290(9)]),flip(a)].
% 1.98/2.26 3414 inverse(inverse(multiply(inverse(multiply(inverse(A),B)),c_0))) = inverse(multiply(inverse(A),inverse(multiply(inverse(B),c_0)))). [back_rewrite(3063),rewrite([3290(6),3314(6),3413(13)]),flip(a)].
% 1.98/2.26 3415 multiply(A,multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),c_0))),inverse(c_0)))) = c_0. [back_rewrite(3059),rewrite([3290(2),3413(7),3414(8),3290(11),3365(14),3366(13)]),flip(a)].
% 1.98/2.26 3417 inverse(multiply(inverse(inverse(c_0)),multiply(inverse(A),inverse(c_0)))) = A. [back_rewrite(3057),rewrite([3290(6),3290(6)])].
% 1.98/2.26 3418 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(3049),rewrite([3290(9)]),flip(a)].
% 1.98/2.26 3419 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(3048),rewrite([3290(6),3418(9)]),flip(a)].
% 1.98/2.26 3431 multiply(A,multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),multiply(inverse(B),inverse(c_0))))),B))) = c_0. [back_rewrite(2998),rewrite([3290(2),3290(5),3418(12),3419(13)]),flip(a)].
% 1.98/2.26 3432 multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(inverse(B),multiply(inverse(A),inverse(c_0))))),c_0))) = B. [back_rewrite(2997),rewrite([3290(5),3290(16),3419(12),3314(13)])].
% 1.98/2.26 3433 multiply(inverse(A),inverse(multiply(inverse(inverse(c_0)),c_0))) = multiply(inverse(A),inverse(c_0)). [back_rewrite(2995),rewrite([3290(3),3290(10),3418(10),3419(11),3314(12)]),flip(a)].
% 1.98/2.26 3439 multiply(multiply(inverse(A),inverse(multiply(inverse(multiply(B,C)),c_0))),multiply(inverse(multiply(D,multiply(B,C))),E)) = multiply(inverse(c_0),multiply(inverse(multiply(D,A)),E)). [back_rewrite(2985),rewrite([3290(4),3301(11),3419(6),3314(7),3290(16),3301(23),3419(18)])].
% 1.98/2.26 3519 multiply(multiply(inverse(A),inverse(multiply(inverse(B),c_0))),multiply(inverse(multiply(C,B)),D)) = multiply(inverse(c_0),multiply(inverse(multiply(C,A)),D)). [back_rewrite(2785),rewrite([3418(4),3419(5),3314(6),3290(14),3301(21),3419(16),3314(17),3439(22)])].
% 1.98/2.26 3532 multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(inverse(A)),c_0))),inverse(c_0))) = A. [back_rewrite(2753),rewrite([3418(7),3419(8),3314(9),3290(17),3418(24),3419(25),3431(26),3418(17),3419(12)])].
% 1.98/2.26 3549 multiply(inverse(A),inverse(multiply(inverse(inverse(multiply(multiply(inverse(B),multiply(C,D)),multiply(inverse(A),inverse(c_0))))),c_0))) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(inverse(c_0)),inverse(multiply(inverse(multiply(C,D)),c_0)))),B)). [back_rewrite(2696),rewrite([3290(4),3290(11),3301(13),3419(8),3314(9),3418(13),3419(14),3290(20),3418(27),3419(28),3314(29)]),flip(a)].
% 1.98/2.27 3593 multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),multiply(inverse(B),inverse(c_0))))),inverse(multiply(inverse(B),c_0)))),inverse(c_0)))) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,c_0))),inverse(c_0))). [back_rewrite(2523),rewrite([3290(4),3418(11),3419(12),3418(16),3419(17),3314(15),3432(15),3314(5),3290(9),3418(11),3419(10),3290(14),3418(21),3419(22),3290(25),3418(32),3419(33),3314(34),3549(34),3419(27),3314(28),3419(32)]),flip(a)].
% 1.98/2.27 3622 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(multiply(C,D)),inverse(c_0)))))),E)),B) = multiply(inverse(c_0),multiply(inverse(E),multiply(A,multiply(C,D)))). [back_rewrite(2336),rewrite([3290(8),3418(23),3419(24),3370(25),3419(21)])].
% 1.98/2.27 3629 multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,multiply(inverse(B),inverse(c_0))))),B)) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,c_0))),inverse(c_0))). [back_rewrite(2327),rewrite([3290(3),3418(10),3419(11),3290(19),3290(26),3418(33),3419(34),3290(43),3622(45),3314(39),3549(39),3419(28),3314(29),3419(33),3593(34)])].
% 1.98/2.27 3641 multiply(inverse(inverse(c_0)),inverse(multiply(inverse(inverse(multiply(A,c_0))),c_0))) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),c_0))),inverse(c_0))). [back_rewrite(2269),rewrite([3290(4),3418(11),3419(12),3629(12),3290(19),3290(31),3622(33),3629(26),3314(22)]),flip(a)].
% 1.98/2.27 3649 multiply(inverse(multiply(A,inverse(multiply(B,multiply(A,inverse(c_0)))))),c_0) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,c_0))),inverse(c_0))). [back_rewrite(2229),rewrite([3290(6),3418(12),3419(13),3629(13),3314(11),3641(11),3415(12),3290(13),3418(19),3419(20),3629(20),3314(18),3641(18),3418(20),3314(12),3641(12),3532(12),3290(13),3418(20),3419(21),3629(21),3290(23),3418(30),3419(31),3629(31),3314(31),3641(31),3314(23),3641(23),3532(23)])].
% 1.98/2.27 3869 multiply(A,multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(A),c_0)))),C)) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(B),inverse(c_0))),C)). [back_rewrite(578),rewrite([3290(4),3418(6),3419(7),3314(8),3519(13),3418(13),3419(14),3314(15)]),flip(a)].
% 1.98/2.27 3879 multiply(inverse(A),inverse(multiply(B,c_0))) = multiply(inverse(A),multiply(inverse(B),inverse(c_0))). [back_rewrite(445),rewrite([3290(4),3418(10),3419(11),3314(12),3290(15),3869(17),3314(18),3419(16),3314(17),3433(17),3418(18),3419(19),3417(17),3314(11)]),flip(a)].
% 1.98/2.27 3882 multiply(inverse(multiply(A,B)),multiply(inverse(inverse(C)),inverse(c_0))) = multiply(inverse(multiply(A,B)),C). [back_rewrite(442),rewrite([3290(8),3418(8),3419(9),3314(10),3879(10),3411(11),3418(8),3419(9),3370(10),3419(6),3314(7),3879(7)])].
% 1.98/2.27 3886 multiply(inverse(inverse(multiply(inverse(A),c_0))),B) = multiply(inverse(multiply(inverse(inverse(A)),inverse(c_0))),B). [back_rewrite(431),rewrite([3290(6),3290(9),3290(12),3290(13),3290(10),3290(11),3290(14),3290(17),3290(18),3290(15),3290(13),3418(7),3419(8),3314(9),3879(9),3411(10),3418(7),3419(8),3314(9),3879(9),3418(11),3419(10),3314(11),3879(11),3882(12),3290(10),3290(13),3290(16),3290(17),3290(14)]),flip(a)].
% 1.98/2.27 3887 multiply(inverse(c_0),multiply(inverse(inverse(A)),inverse(c_0))) = multiply(inverse(c_0),A). [back_rewrite(430),rewrite([3290(5),3290(8),3290(11),3290(12),3290(9),3418(8),3419(9),3314(10),3290(8),3418(8),3419(7),3314(8),3879(8),3411(9),3290(4),3290(7),3290(10),3290(11),3290(8),3418(5),3419(6),3314(7),3879(7),3290(10),3290(13),3290(16),3290(17),3290(14)])].
% 1.98/2.27 3889 multiply(inverse(A),multiply(inverse(inverse(c_0)),B)) = multiply(inverse(A),B). [back_rewrite(427),rewrite([3290(2),3290(7),3290(10),3290(11),3290(10),3290(13),3290(14),3290(11),3418(9),3419(10),3314(11),3879(11),3411(12),3418(8),3419(9),3314(10),3419(8),3314(9),3879(9),3411(10),3290(5),3290(8),3290(9)]),flip(a)].
% 1.98/2.27 3890 multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(C)),inverse(c_0)))),inverse(c_0))) = multiply(inverse(A),multiply(inverse(multiply(inverse(B),C)),inverse(c_0))). [back_rewrite(426),rewrite([3290(5),3290(8),3290(11),3290(12),3290(9),3879(7),3290(12),3418(14),3419(15),3314(16),3879(16),3411(17),3418(12),3419(13),3418(17),3419(18),3314(16),3879(16),3314(20),3879(20)]),flip(a)].
% 1.98/2.27 3893 multiply(inverse(c_0),multiply(inverse(multiply(inverse(A),B)),inverse(c_0))) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(422),rewrite([3290(6),3418(13),3649(14),3419(7),3314(8),3879(8),3890(14),3290(13),3418(15),3419(16),3314(17),3879(17),3411(18),3418(13),3419(14)])].
% 1.98/2.27 3895 inverse(multiply(inverse(A),multiply(inverse(inverse(B)),inverse(c_0)))) = inverse(multiply(inverse(A),B)). [back_rewrite(420),rewrite([3290(5),3290(8),3290(9),3418(7),3419(8),3314(9),3879(9),3411(10),3290(5),3418(11),3889(9),3419(8),3314(9),3879(9)]),flip(a)].
% 1.98/2.27 3914 multiply(inverse(c_0),multiply(inverse(inverse(A)),c_0)) = multiply(inverse(c_0),multiply(A,c_0)). [back_rewrite(399),rewrite([3290(3),3418(10),3649(11),3887(10),3290(9),3290(21),3301(26),3418(17),3649(18),3886(16),3893(18),3889(14),3419(14),3314(15),3419(13),3314(14),3879(14),3887(15),3290(15),3418(17),3419(16),3893(16)]),flip(a)].
% 1.98/2.27 3919 inverse(multiply(inverse(A),multiply(inverse(c_0),multiply(inverse(B),inverse(c_0))))) = inverse(multiply(inverse(A),multiply(inverse(B),inverse(c_0)))). [back_rewrite(392),rewrite([3290(3),3418(10),3649(11),3887(10),3314(6),3879(6),3418(11),3419(12),3314(10),3879(10),3411(11),3314(5),3879(5),3290(11),3290(23),3301(28),3418(19),3649(20),3886(18),3893(20),3889(16),3419(16),3314(17),3419(15),3914(15),3314(14),3879(14)]),flip(a)].
% 1.98/2.27 3930 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(c_0)))))),D)),multiply(inverse(B),inverse(c_0)))) = multiply(inverse(multiply(A,C)),D). [back_rewrite(378),rewrite([3290(4),3290(15),3418(15),3419(16),3314(17),3879(17),3411(18),3290(14),3418(21),3649(22),3887(21),3314(17),3879(17),3919(20)])].
% 1.98/2.27 3932 inverse(multiply(inverse(c_0),inverse(A))) = A. [back_rewrite(374),rewrite([3290(4),3418(6),3419(7),3314(8),3879(8),3411(9),3290(9),3290(17),3418(24),3649(25),3887(24),3314(20),3879(20),3893(21),3370(18),3649(14),3886(10),3893(12),3889(8)])].
% 1.98/2.27 3935 multiply(inverse(A),inverse(multiply(inverse(c_0),B))) = multiply(inverse(A),multiply(inverse(B),inverse(c_0))). [back_rewrite(369),rewrite([3290(3),3418(10),3649(11),3887(10),3314(6),3879(6),3418(11),3919(10),3419(9),3314(10),3419(8),3889(8),3290(10),3290(22),3301(27),3418(18),3649(19),3886(17),3893(19),3889(15),3419(15),3932(13),3314(11),3879(11)])].
% 1.98/2.27 3938 multiply(inverse(multiply(inverse(A),B)),inverse(multiply(inverse(C),multiply(inverse(c_0),multiply(inverse(B),A))))) = C. [back_rewrite(353),rewrite([3290(5),3290(8),3290(11),3290(12),3290(9),3290(10),3290(13),3290(16),3290(17),3290(14),3290(15),3290(18),3290(21),3290(22),3290(19),3290(17),3886(10),3290(20),3290(23),3290(26),3290(27),3290(24),3879(22),3895(24),3290(23),3290(26),3290(29),3290(30),3290(27),3879(25),3895(27),3418(26),3419(27),3314(28),3879(28),3418(30),3419(29),3314(30),3879(30),3290(31),3419(21),3290(28),3418(35),3649(36),3887(35),3314(31),3879(31),3919(34),3930(31),3895(8)])].
% 1.98/2.27 3939 multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),inverse(c_0))))) = B. [back_rewrite(347),rewrite([3290(5),3290(17),3290(24),3290(32),3418(39),3649(40),3887(39),3314(35),3879(35),3919(38),3930(35),3418(12),3649(13),3886(11),3893(13),3889(9),3932(6)])].
% 1.98/2.27 3983 inverse(inverse(multiply(A,multiply(inverse(multiply(inverse(B),A)),C)))) = inverse(multiply(inverse(C),multiply(inverse(B),inverse(c_0)))). [back_rewrite(281),rewrite([3290(3),3418(8),3419(9),3314(10),3419(8),3889(8),3935(6),3418(11),3419(12),3314(13),3879(13),3895(15)]),flip(a)].
% 1.98/2.27 3987 multiply(inverse(inverse(A)),c_0) = A. [back_rewrite(266),rewrite([3418(6),3419(7),3314(8),3879(8),3895(10),3418(9),3419(10),3314(11),3879(11),3895(13),3418(12),3419(13),3314(14),3879(14),3418(16),3419(15),3314(16),3879(16),3290(17),3419(7),3418(15),3419(16),3314(17),3879(17),3418(20),3895(8),3938(13)])].
% 1.98/2.27 3988 inverse(multiply(inverse(multiply(inverse(A),B)),inverse(multiply(C,multiply(inverse(c_0),multiply(inverse(B),A)))))) = C. [back_rewrite(264),rewrite([3418(4),3419(5),3314(6),3879(6),3895(8),3418(7),3419(8),3314(9),3879(9),3895(11),3418(10),3419(11),3314(12),3879(12),3418(14),3419(13),3314(14),3879(14),3290(15),3419(5),3418(13),3419(14),3314(15),3879(15),3418(18),3895(8),3419(14),3314(15),3987(13)])].
% 1.98/2.27 3991 inverse(multiply(A,c_0)) = multiply(inverse(A),c_0). [back_rewrite(261),rewrite([3290(4),3418(11),3939(9),3418(7),3419(8),3314(9),3879(9),3895(11),3418(10),3419(11),3314(12),3879(12),3895(14),3418(13),3419(14),3314(15),3879(15),3418(17),3419(16),3314(17),3879(17),3290(18),3419(8),3418(16),3419(17),3314(18),3879(18),3418(21),3895(11),3988(15)]),flip(a)].
% 1.98/2.27 3994 multiply(inverse(A),inverse(c_0)) = multiply(inverse(A),c_0). [back_rewrite(253),rewrite([3290(3),3418(8),3419(9),3314(10),3991(9),3987(9),3983(11),3290(14),3418(16),3417(13),3991(7)])].
% 1.98/2.27 3995 multiply(inverse(c_0),A) = A. [back_rewrite(252),rewrite([3418(8),3419(9),3370(10),3419(6),3314(7),3991(6),3987(6),3290(10),3994(9),3418(9),3419(6),3314(7),3991(6),3987(6)])].
% 1.98/2.27 3996 multiply(A,multiply(inverse(inverse(multiply(inverse(A),B))),C)) = multiply(B,C). [back_rewrite(251),rewrite([3290(3),3994(4),3418(7),3419(8),3991(6),3987(6),3995(4),3418(5),3419(6),3995(6)]),flip(a)].
% 1.98/2.27 4005 multiply(inverse(A),multiply(inverse(B),c_0)) = inverse(multiply(B,A)). [back_rewrite(239),rewrite([3290(4),3994(5),3991(5),3987(5),3290(3),3290(6),3290(9),3290(10),3290(7),3991(4),3418(9),3419(10),3995(10),3996(11)])].
% 1.98/2.27 4006 inverse(multiply(inverse(inverse(multiply(A,inverse(multiply(inverse(B),A))))),C)) = inverse(multiply(B,C)). [back_rewrite(238),rewrite([3290(3),3290(6),3290(9),3290(10),3290(7),3991(4),4005(5),3418(6),3419(7),3995(7),3290(9),3994(10),4005(10),3418(11),3419(12),3995(12)]),flip(a)].
% 1.98/2.27 4012 inverse(multiply(A,inverse(multiply(B,multiply(A,inverse(multiply(A,inverse(multiply(C,inverse(multiply(inverse(A),C))))))))))) = B. [back_rewrite(231),rewrite([3418(4),3419(5),3995(5),3290(7),3994(8),4005(8),3418(16),3419(17),3995(17),3290(19),3994(20),4005(20),3418(19),4006(18),3991(15),3987(15)])].
% 1.98/2.27 4017 multiply(inverse(inverse(inverse(multiply(A,B)))),A) = multiply(inverse(B),c_0). [back_rewrite(226),rewrite([3290(4),3994(5),4005(5),3418(7),3419(8),3995(8),3418(9),3419(10),3995(10),3290(12),3994(13),4005(13),3418(21),3419(22),3995(22),3290(24),3994(25),4005(25),3418(24),4006(23),4012(17),3991(8)])].
% 1.98/2.27 4024 multiply(A,inverse(multiply(inverse(B),multiply(A,inverse(multiply(A,multiply(inverse(A),c_0))))))) = B. [back_rewrite(216),rewrite([3290(5),3994(6),4005(6),3418(8),3419(9),4017(8),4005(7),3991(4),3290(15),3994(16),4005(16),3418(18),3419(19),4017(18),4005(17),3991(14),3418(16),3991(4),3987(4),3991(14),3987(14)])].
% 1.98/2.27 4035 multiply(A,inverse(multiply(B,multiply(A,inverse(multiply(A,multiply(inverse(A),c_0))))))) = multiply(inverse(B),c_0). [back_rewrite(198),rewrite([3290(5),3994(6),4005(6),3418(8),3419(9),4017(8),4005(7),3991(4),3290(15),3994(16),4005(16),3418(18),3419(19),4017(18),4005(17),3991(14),3418(16),3991(4),3987(4),4024(10),3290(7),3994(8),4005(8),3418(10),3419(11),4017(10),4005(9),3991(6),3290(17),3994(18),4005(18),3418(20),3419(21),4017(20),4005(19),3991(16),3418(18),3991(7),3987(7),3991(16),3987(16)]),flip(a)].
% 1.98/2.27 4041 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(175),rewrite([3418(4),3419(5),3995(5),3290(6),3290(9),3290(12),3290(13),3290(10),3991(7),3987(7),3290(8),3994(9),4005(9),3418(11),3419(12),4017(11),4005(10),3991(7),3290(18),3994(19),4005(19),3418(21),3419(22),4017(21),4005(20),3991(17),3418(19),3991(6),3987(6),4035(13),3419(7),3995(7),3419(7),3995(7)]),flip(a)].
% 1.98/2.27 4050 multiply(inverse(multiply(multiply(A,c_0),multiply(inverse(multiply(A,inverse(multiply(A,multiply(multiply(inverse(A),c_0),c_0))))),B))),c_0) = multiply(multiply(inverse(B),c_0),c_0). [back_rewrite(166),rewrite([3290(4),3994(5),4005(5),3418(7),4041(6),4017(5),3290(10),3994(11),4005(11),3418(13),4041(12),4017(11),4041(16),3290(21),3994(22),4005(22),3418(24),4041(23),4017(22),3418(24),3991(11),3991(9),3987(9)]),flip(a)].
% 1.98/2.27 4054 inverse(multiply(multiply(A,c_0),inverse(multiply(B,multiply(A,inverse(multiply(A,multiply(multiply(inverse(A),c_0),c_0)))))))) = B. [back_rewrite(162),rewrite([3290(5),3994(6),4005(6),3418(8),4041(7),4017(6),4041(11),3290(16),3994(17),4005(17),3418(19),4041(18),4017(17),3418(19),3991(6),3991(4),3987(4),4050(16),3290(17),3994(18),4005(18),3418(20),4041(19),4017(18),4041(23),3290(28),3994(29),4005(29),3418(31),4041(30),4017(29),3418(31),3991(18),3991(16),3987(16),4050(28),3418(19),3991(6),3991(4),3987(4),3991(17),3987(17)])].
% 1.98/2.27 4064 multiply(multiply(inverse(inverse(multiply(A,multiply(inverse(B),c_0)))),B),c_0) = multiply(multiply(A,c_0),c_0). [back_rewrite(152),rewrite([3290(3),3994(4),3418(9),4041(8),3290(13),3994(14),4005(14),3418(16),4041(15),4017(14),3290(18),3994(19),4005(19),3418(21),4041(20),4017(19),3290(30),3994(31),4005(31),3418(33),4041(32),4017(31),3418(33),3991(15),3991(13),3987(13),4054(28),3991(17),3991(15),3991(13),3987(13)])].
% 1.98/2.27 4066 multiply(A,c_0) = A. [back_rewrite(150),rewrite([3290(5),3994(6),4005(6),3418(8),4041(7),4017(6),4041(11),3290(15),3994(16),3418(21),4041(20),4064(21),3991(17),3991(15),3418(19),3991(6),3991(4),3987(4),4050(16),3991(6),3991(4),3987(4)])].
% 1.98/2.27 4080 inverse(multiply(multiply(inverse(A),B),C)) = multiply(inverse(C),multiply(inverse(B),A)). [back_rewrite(128),rewrite([3418(5),4041(4),4066(5),4041(4),3290(5),3290(8),3290(11),3290(12),3290(9),4066(5),4041(4),3418(8),4041(7),4066(8),3418(10),4041(9),4041(7),4066(9)]),flip(a)].
% 1.98/2.27 4084 multiply(inverse(inverse(multiply(A,inverse(multiply(B,C))))),multiply(B,C)) = A. [back_rewrite(122),rewrite([3290(6),3994(5),4066(4),3418(9),4041(8),4066(9),4041(8),4041(8)])].
% 1.98/2.27 4087 multiply(multiply(inverse(A),inverse(B)),B) = inverse(A). [back_rewrite(117),rewrite([3290(4),3994(5),4066(4),4041(4),3418(7),4041(6),4041(4),4066(6),3290(10),3994(9),4066(8),3418(13),4041(12),4084(11),4066(6)])].
% 1.98/2.27 4090 multiply(inverse(A),inverse(multiply(B,inverse(A)))) = inverse(B). [back_rewrite(113),rewrite([3290(7),3994(6),4066(5),4041(5),3418(9),4041(8),4041(5),4087(6),4066(3),3290(4),3994(5),4066(4),3418(8),4041(7),4066(8),4041(7)]),flip(a)].
% 1.98/2.27 4094 inverse(inverse(A)) = A. [back_rewrite(107),rewrite([3290(7),3994(6),4066(5),4041(5),3418(9),4041(8),4041(5),4087(6),4066(3)])].
% 1.98/2.27 4111 multiply(inverse(A),inverse(multiply(B,multiply(c_0,inverse(multiply(c_0,inverse(c_0))))))) = inverse(multiply(B,A)). [back_rewrite(84),rewrite([3290(3),4094(4),3290(4),4094(5),3290(5),3290(14),3994(15),4066(14),3418(18),4090(16),4094(13),4066(13),3418(16),4041(15),4094(13),4066(14)])].
% 1.98/2.27 4112 multiply(A,multiply(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(A,inverse(A)),inverse(multiply(A,inverse(A))))))),B)) = multiply(A,B). [back_rewrite(83),rewrite([3290(4),3994(5),4066(4),3418(8),4090(6),4094(3),4066(3),4094(5),3290(6),3994(7),4066(6),3418(10),4090(8),4094(5),4066(5),4094(7),3290(8),3994(9),4066(8),3418(12),4090(10),4094(7),4066(7),4041(13),3290(18),3994(19),4066(18),3418(22),4090(20),4094(17),4066(17),3418(18),4094(15),4066(17),4094(16)])].
% 1.98/2.27 4113 multiply(multiply(A,inverse(B)),B) = A. [back_rewrite(82),rewrite([3290(4),3994(5),4066(4),4094(5),3290(5),4094(6),3290(6),4094(7),3290(7),4111(13),4094(5)])].
% 1.98/2.27 4122 multiply(inverse(multiply(A,B)),A) = inverse(B). [back_rewrite(69),rewrite([3290(4),3994(5),4066(4),4041(4),4094(2),3418(5),4041(4),4066(5),3290(7),3994(8),4066(7),4094(8),3290(8),4094(9),3290(9),4094(10),3290(10),4111(16),4113(6)])].
% 1.98/2.27 4124 multiply(inverse(multiply(c_0,A)),B) = multiply(inverse(A),B). [back_rewrite(65),rewrite([3290(2),4094(3),3290(4),4094(5),3290(5),4094(8),3290(8),4094(9),3290(9),4094(12),3290(12),4094(13),3290(13),4041(20),4112(20),3418(6),4041(5),4066(6),3290(9),3994(10),4066(9),4080(9),4094(6),3418(11),4041(10),4122(9),4041(7),4066(8),4041(7)])].
% 1.98/2.27 4128 multiply(inverse(A),multiply(multiply(c_0,inverse(c_0)),B)) = multiply(inverse(A),B). [back_rewrite(61),rewrite([3290(4),4094(5),3290(5),4094(6),3290(6),4041(11),4124(10),4094(7),3290(10),3994(11),4066(10),4080(10),4094(2),3418(12),4041(11),4122(10),4041(8),4066(9),3418(11),4041(10),4066(11),3290(12),3994(13),4066(12),4080(12),4094(9),3418(14),4041(13),4122(12),4041(10),4066(11),4041(10)])].
% 1.98/2.27 4132 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(55),rewrite([3290(5),3994(6),4066(5),4041(5),4094(3),3290(5),4094(6),3290(6),4094(7),3290(7),4041(12),4124(11),4094(7),4128(8)])].
% 1.98/2.27 4150 multiply(multiply(multiply(inverse(A),B),multiply(C,D)),multiply(inverse(D),E)) = multiply(multiply(inverse(A),B),multiply(C,E)). [back_rewrite(2016),rewrite([3418(8),3418(6),4041(5),4066(6),4041(5),4066(6),4041(6),4041(3),3418(8),4041(7),4066(8),3418(13),3418(11),4041(10),4066(11),4041(10),4066(11),3418(14),4041(13),4041(10),4066(13)])].
% 1.98/2.27 4159 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(3308),rewrite([3994(7),4066(6),4041(6),4094(4),3418(7),4132(5),4066(5),4094(4),3995(4),4066(5)])].
% 1.98/2.27 4161 multiply(A,multiply(multiply(multiply(inverse(B),inverse(C)),inverse(D)),multiply(D,multiply(C,E)))) = multiply(A,multiply(inverse(B),E)). [back_rewrite(3333),rewrite([4159(4),4159(3),4094(3),4066(6),4113(5),4159(6),4159(5)]),flip(a)].
% 1.98/2.27 4162 multiply(A,multiply(multiply(inverse(B),inverse(C)),multiply(C,D))) = multiply(A,multiply(inverse(B),D)). [back_rewrite(3332),rewrite([4159(3),4159(2),4161(9),4159(7),3995(11)]),flip(a)].
% 1.98/2.27 4168 multiply(multiply(multiply(inverse(A),B),inverse(C)),multiply(C,multiply(D,E))) = multiply(multiply(inverse(A),B),multiply(D,E)). [back_rewrite(2040),rewrite([4159(2),4159(6),4159(2),4159(7),4094(5),4094(5),4159(7),4159(11),4159(10),4161(17),4159(13),4159(7),4159(3),4094(3),4159(6),4094(4),4094(4),4159(10),4159(6),4159(11),4094(9),4094(9),4162(10),4150(7),4159(7),4159(6),4159(12),4159(11),4161(18),4159(14),4159(8),4159(7),4094(7),4159(14),4094(10),4159(12),4094(10),4094(10)]),flip(a)].
% 1.98/2.27 4177 multiply(A,multiply(multiply(inverse(B),multiply(C,D)),multiply(inverse(D),E))) = multiply(A,multiply(inverse(B),multiply(C,E))). [back_rewrite(2021),rewrite([4159(2),4159(5),4159(5),4094(3),4094(3),4159(5),4159(9),4159(5),4159(5),4094(3),4094(3),4159(7),4159(5),4094(8),4159(10),4162(15),4150(12),4162(9),4159(10),4159(9),4168(16),4162(14)])].
% 1.98/2.27 4210 multiply(multiply(inverse(A),inverse(B)),multiply(B,C)) = multiply(inverse(A),C). [back_rewrite(3340),rewrite([4159(4),4159(3),4094(3),4066(6),4113(5),4159(3),4094(3),4159(3),4094(3),4159(5),4159(4),4168(10),4159(8),4159(4),4159(9),4094(7),4094(7),4159(8),4159(4),4159(9),4094(7),4094(7)]),flip(a)].
% 1.98/2.27 4212 multiply(multiply(inverse(A),B),multiply(multiply(inverse(B),inverse(C)),D)) = multiply(multiply(inverse(A),inverse(C)),D). [back_rewrite(1736),rewrite([4159(3),4159(2),4168(8),4210(5),4159(3),4094(3),4159(5),4159(4),4159(11),4159(8),4159(2),4159(9),4094(5),4159(7),4094(5),4094(5),4210(6),4159(6),4094(6),4159(7),4159(3),4094(3),4159(6),4159(4),4094(7),4159(11),4159(10),4159(9),4159(18),4159(10),4159(9),4159(20),4094(14),4159(18),4094(14),4159(16),4094(14),4094(14),4168(16),4210(13),4159(11),4159(9),4094(12)])].
% 1.98/2.27 4214 multiply(multiply(inverse(A),multiply(B,C)),multiply(inverse(C),multiply(D,E))) = multiply(inverse(A),multiply(B,multiply(D,E))). [back_rewrite(1731),rewrite([4159(2),4159(6),4159(5),4159(5),4094(3),4094(3),4159(7),4159(10),4159(10),4094(8),4094(8),4159(10),4210(13),4177(12),4168(10),4159(8),4159(4),4159(2),4094(5),4159(8),4159(6),4094(9),4159(10),4159(5),4159(5),4094(3),4094(3),4159(8),4159(8),4094(6),4094(6),4159(10),4159(9),4168(17),4210(14),4159(12),4159(10),4159(9),4094(14),4159(14),4159(14),4094(10),4159(12),4094(10),4094(10)])].
% 1.98/2.27 4224 multiply(multiply(inverse(A),multiply(B,multiply(C,D))),multiply(multiply(multiply(multiply(inverse(D),inverse(C)),inverse(B)),inverse(E)),F)) = multiply(multiply(inverse(A),inverse(E)),F). [back_rewrite(1651),rewrite([4159(4),4159(3),4159(2),4159(9),4159(9),4094(3),4159(7),4094(3),4159(5),4094(3),4094(3),4159(7),4159(10),4159(10),4094(8),4094(8),4159(10),4210(13),4159(12),4159(8),4094(8),4159(11),4159(9),4094(12),4212(12),4159(11),4159(16),4159(10),4159(5),4159(5),4094(3),4094(3),4159(8),4159(8),4094(6),4094(6),4214(7),4159(10),4159(8),4159(7),4159(6),4094(13),4159(15),4210(19),4159(17),4159(15),4094(18)])].
% 1.98/2.27 4225 multiply(multiply(inverse(A),multiply(B,multiply(C,D))),multiply(multiply(multiply(inverse(D),inverse(C)),E),F)) = multiply(multiply(inverse(A),multiply(B,E)),F). [back_rewrite(1650),rewrite([4159(2),4159(5),4159(5),4094(3),4094(3),4159(5),4210(8),4159(7),4159(3),4094(3),4159(6),4159(4),4094(7),4212(7),4159(6),4159(6),4159(6),4094(4),4094(4),4159(9),4159(8),4159(7),4159(16),4159(10),4159(2),4159(11),4094(5),4159(9),4094(5),4159(7),4094(5),4094(5),4210(7),4159(10),4159(8),4159(6),4094(9),4094(10),4159(12),4159(15),4210(19),4159(17),4159(15),4159(15),4094(13),4094(13),4094(15)])].
% 1.98/2.27 4239 multiply(multiply(multiply(inverse(A),multiply(B,C)),inverse(D)),multiply(D,E)) = multiply(multiply(inverse(A),multiply(B,C)),E). [back_rewrite(871),rewrite([4159(4),4159(3),4159(2),4159(10),4159(2),4159(11),4094(5),4159(9),4094(5),4159(7),4094(5),4094(5),4210(7),4159(6),4159(9),4159(9),4094(7),4094(7),4159(9),4210(12),4159(11),4159(7),4094(7),4159(10),4159(8),4094(11),4212(11),4225(10),4159(6),4159(10),4159(9),4159(9),4094(7),4094(7)]),flip(a)].
% 1.98/2.27 4240 multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),multiply(C,D)) = multiply(multiply(inverse(A),inverse(B)),D). [back_rewrite(869),rewrite([4159(2),4159(5),4159(5),4094(3),4094(3),4159(5),4210(8),4159(7),4159(3),4094(3),4159(6),4159(4),4094(7),4212(7),4159(6),4159(10),4159(5),4159(5),4094(3),4094(3),4159(8),4159(8),4094(6),4094(6),4214(7),4159(8),4159(7),4159(6),4224(13),4159(7),4159(6)]),flip(a)].
% 1.98/2.27 4251 multiply(multiply(inverse(A),multiply(B,C)),multiply(multiply(inverse(C),multiply(D,E)),F)) = multiply(multiply(inverse(A),multiply(B,multiply(D,E))),F). [back_rewrite(1617),rewrite([4159(2),4210(5),4159(3),4094(3),4159(4),4212(7),4159(5),4159(5),4094(3),4094(3),4159(5),4159(5),4159(3),4094(6),4159(9),4159(8),4240(13),4159(12),4159(5),4159(5),4094(3),4094(3),4159(10),4159(8),4159(8),4094(6),4094(6),4094(8),4159(10),4159(14),4159(13),4210(19),4159(17),4159(15),4159(15),4094(11),4159(13),4094(11),4094(11),4094(14)])].
% 1.98/2.27 4252 multiply(multiply(inverse(A),multiply(B,multiply(C,D))),multiply(inverse(D),E)) = multiply(inverse(A),multiply(B,multiply(C,E))). [back_rewrite(1530),rewrite([4159(3),4159(2),4168(8),4210(5),4159(3),4094(3),4159(5),4159(4),4159(10),4159(7),4159(7),4094(3),4159(5),4094(3),4094(3),4159(7),4094(7),4159(9),4210(13),4159(11),4159(9),4094(12),4159(13),4159(17),4159(12),4159(12),4094(10),4094(10),4159(15),4159(15),4094(13),4094(13),4214(14)])].
% 1.98/2.27 4269 multiply(multiply(inverse(A),multiply(inverse(B),C)),D) = multiply(inverse(A),multiply(multiply(inverse(B),C),D)). [back_rewrite(1611),rewrite([4159(3),4159(2),4240(7),4159(5),4159(5),4094(3),4094(3),4159(5),4159(5),4159(3),4094(6),4159(8),4159(12),4159(11),4159(11),4094(9),4094(9),4239(13),4251(11),4210(6),4159(6),4159(6),4159(4),4094(4),4094(5),4159(7),4159(10),4210(13),4159(11),4094(11),4210(13),4159(11),4159(9),4159(9),4094(9),4094(11)]),flip(a)].
% 1.98/2.27 4270 multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)). [back_rewrite(1523),rewrite([4159(2),4210(5),4159(4),4159(3),4094(3),4159(7),4159(2),4159(8),4094(5),4159(6),4094(6),4210(7),4159(6),4210(9),4159(8),4159(7),4094(7),4269(10),4159(11),4159(9),4159(6),4159(6),4094(3),4159(4),4094(4),4159(8),4094(8),4252(8),3290(3),4066(3),4094(4),4159(6),4159(5),4240(10),4159(8),4159(8),4094(6),4094(6)])].
% 1.98/2.27 4283 multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(D,multiply(inverse(D),multiply(C,E)))))) = multiply(A,multiply(inverse(B),E)). [back_rewrite(1018),rewrite([4159(2),4270(5),4132(4),4159(3),4094(3),4159(3),4094(3),4270(3),4159(4),4159(2),4094(5),4270(4),4159(6),4270(9),4132(8),4159(7),4094(7),4159(7),4094(7),4270(7),4270(8),4270(7),4159(11),4270(14),4132(13)])].
% 1.98/2.27 4307 multiply(inverse(A),multiply(multiply(B,C),multiply(inverse(C),D))) = multiply(inverse(A),multiply(B,D)). [back_rewrite(220),rewrite([4159(2),4270(4),4159(5),4159(3),4094(3),4094(4),4270(3),4159(5),4270(8),4132(7),4270(6),4159(8),4270(12),4132(11)])].
% 1.98/2.27 4309 inverse(c_0) = c_0. [back_rewrite(3369),rewrite([4159(4),4066(8),4094(7),4270(6),4159(8),4270(10),4159(11),4159(9),4094(9),4094(10),4270(9),3995(14),4270(12),4307(12),4270(10),4270(9),4283(11),3290(4),4066(4)])].
% 1.98/2.27 4337 multiply(c_0,A) = A. [back_rewrite(3385),rewrite([4309(2),4309(4),4066(4),4159(4),4094(3),4159(4),4094(3),4113(4),4309(6),4066(6),4159(6),4094(4),4094(4),4159(5),4159(4),4270(7),4270(9),4270(8),4132(7),3290(5),4066(5),4309(6),4066(6),4159(6),4094(4),4094(4),4159(5),4159(4),4270(7),4270(9),4270(8),4132(7),3290(5),4066(5),4094(4)])].
% 1.98/2.27 4399 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3291),rewrite([4337(3)]),xx(a)].
% 1.98/2.27 4406 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(4094(a,1),4270(a,1,1,1)),rewrite([4094(4)])].
% 1.98/2.27 4407 $F # answer(prove_these_axioms). [resolve(4406,a,4399,a)].
% 1.98/2.27
% 1.98/2.27 % SZS output end Refutation
% 1.98/2.27 ============================== end of proof ==========================
% 1.98/2.27
% 1.98/2.27 ============================== STATISTICS ============================
% 1.98/2.27
% 1.98/2.27 Given=48. Generated=11713. Kept=4405. proofs=1.
% 1.98/2.27 Usable=13. Sos=26. Demods=38. Limbo=0, Disabled=4367. Hints=0.
% 1.98/2.27 Megabytes=13.25.
% 1.98/2.27 User_CPU=1.29, System_CPU=0.01, Wall_clock=2.
% 1.98/2.27
% 1.98/2.27 ============================== end of statistics =====================
% 1.98/2.27
% 1.98/2.27 ============================== end of search =========================
% 1.98/2.27
% 1.98/2.27 THEOREM PROVED
% 1.98/2.27 % SZS status Unsatisfiable
% 1.98/2.27
% 1.98/2.27 Exiting with 1 proof.
% 1.98/2.27
% 1.98/2.27 Process 32372 exit (max_proofs) Tue Jun 14 08:21:12 2022
% 1.98/2.27 Prover9 interrupted
%------------------------------------------------------------------------------