TSTP Solution File: GRP024-5 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP024-5 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 11:16:46 EDT 2022
% Result : Unsatisfiable 15.91s 16.16s
% Output : Refutation 15.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP024-5 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 21:59:08 EDT 2022
% 0.15/0.36 % CPUTime :
% 15.91/16.16 ============================== Prover9 ===============================
% 15.91/16.16 Prover9 (32) version 2009-11A, November 2009.
% 15.91/16.16 Process 17462 was started by sandbox on n017.cluster.edu,
% 15.91/16.16 Mon Jun 13 21:59:09 2022
% 15.91/16.16 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17309_n017.cluster.edu".
% 15.91/16.16 ============================== end of head ===========================
% 15.91/16.16
% 15.91/16.16 ============================== INPUT =================================
% 15.91/16.16
% 15.91/16.16 % Reading from file /tmp/Prover9_17309_n017.cluster.edu
% 15.91/16.16
% 15.91/16.16 set(prolog_style_variables).
% 15.91/16.16 set(auto2).
% 15.91/16.16 % set(auto2) -> set(auto).
% 15.91/16.16 % set(auto) -> set(auto_inference).
% 15.91/16.16 % set(auto) -> set(auto_setup).
% 15.91/16.16 % set(auto_setup) -> set(predicate_elim).
% 15.91/16.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 15.91/16.16 % set(auto) -> set(auto_limits).
% 15.91/16.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 15.91/16.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 15.91/16.16 % set(auto) -> set(auto_denials).
% 15.91/16.16 % set(auto) -> set(auto_process).
% 15.91/16.16 % set(auto2) -> assign(new_constants, 1).
% 15.91/16.16 % set(auto2) -> assign(fold_denial_max, 3).
% 15.91/16.16 % set(auto2) -> assign(max_weight, "200.000").
% 15.91/16.16 % set(auto2) -> assign(max_hours, 1).
% 15.91/16.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 15.91/16.16 % set(auto2) -> assign(max_seconds, 0).
% 15.91/16.16 % set(auto2) -> assign(max_minutes, 5).
% 15.91/16.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 15.91/16.16 % set(auto2) -> set(sort_initial_sos).
% 15.91/16.16 % set(auto2) -> assign(sos_limit, -1).
% 15.91/16.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 15.91/16.16 % set(auto2) -> assign(max_megs, 400).
% 15.91/16.16 % set(auto2) -> assign(stats, some).
% 15.91/16.16 % set(auto2) -> clear(echo_input).
% 15.91/16.16 % set(auto2) -> set(quiet).
% 15.91/16.16 % set(auto2) -> clear(print_initial_clauses).
% 15.91/16.16 % set(auto2) -> clear(print_given).
% 15.91/16.16 assign(lrs_ticks,-1).
% 15.91/16.16 assign(sos_limit,10000).
% 15.91/16.16 assign(order,kbo).
% 15.91/16.16 set(lex_order_vars).
% 15.91/16.16 clear(print_given).
% 15.91/16.16
% 15.91/16.16 % formulas(sos). % not echoed (6 formulas)
% 15.91/16.16
% 15.91/16.16 ============================== end of input ==========================
% 15.91/16.16
% 15.91/16.16 % From the command line: assign(max_seconds, 300).
% 15.91/16.16
% 15.91/16.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 15.91/16.16
% 15.91/16.16 % Formulas that are not ordinary clauses:
% 15.91/16.16
% 15.91/16.16 ============================== end of process non-clausal formulas ===
% 15.91/16.16
% 15.91/16.16 ============================== PROCESS INITIAL CLAUSES ===============
% 15.91/16.16
% 15.91/16.16 ============================== PREDICATE ELIMINATION =================
% 15.91/16.16
% 15.91/16.16 ============================== end predicate elimination =============
% 15.91/16.16
% 15.91/16.16 Auto_denials:
% 15.91/16.16 % copying label prove_center to answer in negative clause
% 15.91/16.16
% 15.91/16.16 Term ordering decisions:
% 15.91/16.16
% 15.91/16.16 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 15.91/16.16 Function symbol KB weights: identity=1. a=1. b=1. c=1. multiply=1. commutator=1. inverse=0.
% 15.91/16.16
% 15.91/16.16 ============================== end of process initial clauses ========
% 15.91/16.16
% 15.91/16.16 ============================== CLAUSES FOR SEARCH ====================
% 15.91/16.16
% 15.91/16.16 ============================== end of clauses for search =============
% 15.91/16.16
% 15.91/16.16 ============================== SEARCH ================================
% 15.91/16.16
% 15.91/16.16 % Starting search at 0.01 seconds.
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=138.000, iters=3489
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=133.000, iters=3473
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=126.000, iters=3448
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=109.000, iters=3393
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=94.000, iters=3343
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=92.000, iters=3333
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=87.000, iters=3398
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=84.000, iters=3579
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=73.000, iters=6016
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=47.000, iters=4018
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=44.000, iters=3640
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=43.000, iters=3505
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=42.000, iters=3334
% 15.91/16.16
% 15.91/16.16 Low Water (keep): wt=41.000, iters=3353
% 15.91/16.16
% 15.91/16.16 ============================== PROOF =================================
% 15.91/16.16 % SZS status Unsatisfiable
% 15.91/16.16 % SZS output start Refutation
% 15.91/16.16
% 15.91/16.16 % Proof 1 at 15.08 (+ 0.06) seconds: prove_center.
% 15.91/16.16 % Length of proof is 116.
% 15.91/16.16 % Level of proof is 29.
% 15.91/16.16 % Maximum clause weight is 69.000.
% 15.91/16.16 % Given clauses 162.
% 15.91/16.16
% 15.91/16.16 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 15.91/16.16 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 15.91/16.16 3 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 15.91/16.16 4 commutator(commutator(A,B),C) = commutator(A,commutator(B,C)) # label(associativity_of_commutator) # label(hypothesis). [assumption].
% 15.91/16.16 5 commutator(A,B) = multiply(inverse(A),multiply(inverse(B),multiply(A,B))) # label(name) # label(axiom). [assumption].
% 15.91/16.16 6 multiply(a,commutator(b,c)) != multiply(commutator(b,c),a) # label(prove_center) # label(negated_conjecture) # answer(prove_center). [assumption].
% 15.91/16.16 7 multiply(inverse(b),multiply(inverse(c),multiply(b,multiply(c,a)))) != multiply(a,multiply(inverse(b),multiply(inverse(c),multiply(b,c)))) # answer(prove_center). [copy(6),rewrite([5(4),5(14),3(22),3(21),3(20)]),flip(a)].
% 15.91/16.16 8 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(A,B)))),multiply(inverse(C),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,C)))))) = multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(C),multiply(B,C)))),multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(B,C)))))). [back_rewrite(4),rewrite([5(1),5(6),3(13),3(12),3(11),5(16),5(21)])].
% 15.91/16.16 9 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),3(a,1,1)),rewrite([1(2)]),flip(a)].
% 15.91/16.16 16 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(A,B)))),multiply(inverse(C),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,multiply(C,D))))))) = multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(C),multiply(B,C)))),multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(B,multiply(C,D))))))). [para(8(a,1),3(a,1,1)),rewrite([3(16),3(15),3(14),3(13),3(12),3(11),3(31),3(30),3(29),3(28),3(27)]),flip(a)].
% 15.91/16.16 32 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),9(a,1,2))].
% 15.91/16.16 43 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(9(a,1),9(a,1,2))].
% 15.91/16.16 51 multiply(A,identity) = A. [back_rewrite(32),rewrite([43(4)])].
% 15.91/16.16 64 inverse(identity) = identity. [para(51(a,1),2(a,1))].
% 15.91/16.16 65 multiply(A,inverse(A)) = identity. [para(43(a,1),2(a,1))].
% 15.91/16.16 70 multiply(A,multiply(inverse(A),B)) = B. [para(43(a,1),9(a,1))].
% 15.91/16.16 71 inverse(inverse(A)) = A. [para(43(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 15.91/16.16 75 multiply(inverse(multiply(inverse(A),multiply(B,multiply(C,multiply(A,inverse(multiply(B,C))))))),multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,A))))) = multiply(inverse(A),multiply(inverse(multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(multiply(B,C)),B))))),multiply(A,multiply(B,multiply(C,inverse(B)))))). [para(2(a,1),16(a,1,2,2,2,2,2)),rewrite([71(4),3(6),71(13),51(13),3(12),71(19),3(23),71(27),2(30),51(28),3(27)])].
% 15.91/16.16 137 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(65(a,1),3(a,1)),flip(a)].
% 15.91/16.16 139 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(A,B)))),multiply(B,multiply(inverse(A),multiply(inverse(B),A)))) = identity. [para(65(a,1),8(a,1,2,2,2,2,2)),rewrite([71(8),51(10),71(16),65(16),51(16),2(15),64(15),71(17),65(17),51(17),2(16),51(16),1(15),2(14)])].
% 15.91/16.16 148 multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),multiply(inverse(A),multiply(B,C))))),multiply(A,multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),multiply(inverse(A),multiply(B,multiply(C,D)))))))) = multiply(inverse(multiply(inverse(A),multiply(inverse(multiply(inverse(A),B)),B))),multiply(inverse(C),multiply(inverse(A),multiply(inverse(multiply(inverse(A),B)),multiply(B,multiply(C,D)))))). [para(70(a,1),16(a,1,1,1,2,2)),rewrite([3(16),70(17),3(26),3(37)]),flip(a)].
% 15.91/16.16 149 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(A,B)))),multiply(inverse(C),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,D)))))) = multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(C),multiply(B,C)))),multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(B,D)))))). [para(70(a,1),16(a,1,2,2,2,2,2,2)),rewrite([70(27)])].
% 15.91/16.16 152 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(A,B)))),multiply(inverse(multiply(inverse(B),C)),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(C,D)))))) = multiply(inverse(A),multiply(inverse(multiply(inverse(B),multiply(inverse(multiply(inverse(B),C)),C))),multiply(A,multiply(inverse(B),multiply(inverse(multiply(inverse(B),C)),multiply(C,D)))))). [para(70(a,1),16(a,2,2,1,1,2,2)),rewrite([3(14),70(15),3(32),70(33)])].
% 15.91/16.16 154 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(137(a,1),9(a,1,2)),rewrite([51(3)]),flip(a)].
% 15.91/16.16 158 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(154(a,1),9(a,1,2)),flip(a)].
% 15.91/16.16 159 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(B),multiply(C,multiply(B,D)))))))))) = multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(B),multiply(C,multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(B,D)))))))))). [back_rewrite(152),rewrite([158(6),158(4),158(2),71(5),3(4),71(6),3(5),3(4),158(8),71(8),3(14),3(15),3(14),3(13),158(20),71(20),3(20),158(22),158(20),158(18),71(21),3(20),71(22),3(21),3(20),158(25),71(25),3(26),3(29),3(28),3(27)]),flip(a)].
% 15.91/16.16 161 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(B),multiply(C,D))))))))) = multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(C,D))))))))). [back_rewrite(149),rewrite([158(6),158(4),158(2),71(5),3(4),71(6),3(5),3(4),3(14),3(13),3(12),158(21),158(19),158(17),71(20),3(19),71(21),3(20),3(19),3(27),3(26),3(25)]),flip(a)].
% 15.91/16.16 162 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(B,multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(B,D)))))))))))))) = multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(C,multiply(B,D)))))))))). [back_rewrite(148),rewrite([158(4),71(4),3(9),158(10),158(8),158(7),158(5),158(3),71(6),3(5),71(7),3(6),3(5),3(8),3(7),3(6),71(10),3(9),3(8),3(7),3(6),158(12),71(12),3(18),3(20),3(19),3(18),3(17),3(16),158(25),71(25),3(25),158(27),158(25),158(23),71(26),3(25),71(27),3(26),3(25),158(31),71(31),3(33),3(36),3(35),3(34)])].
% 15.91/16.16 168 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),B))))))) = identity. [back_rewrite(139),rewrite([158(6),158(4),158(2),71(5),3(4),71(6),3(5),3(4),3(11),3(10),3(9)])].
% 15.91/16.16 227 multiply(A,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(B,C)))))))))) = multiply(inverse(C),multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(A,multiply(B,inverse(A))))))))). [back_rewrite(75),rewrite([158(3),158(9),158(7),158(6),158(5),158(4),71(2),71(2),3(3),3(5),3(4),3(7),3(6),3(5),71(9),3(8),3(7),3(6),3(5),3(15),3(14),3(13),3(12),3(11),158(19),3(21),2(20),51(20),158(22),158(21),158(20),71(18),71(18),3(19),3(21),3(20),3(26),3(25),3(24)])].
% 15.91/16.16 258 multiply(inverse(A),multiply(B,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),A)))))) = B. [para(168(a,1),9(a,1,2)),rewrite([71(2),51(2)]),flip(a)].
% 15.91/16.16 263 multiply(A,multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),B))))) = multiply(B,A). [para(258(a,1),9(a,1,2)),rewrite([71(2)]),flip(a)].
% 15.91/16.16 269 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),A)))) = multiply(inverse(B),multiply(A,B)). [para(263(a,1),9(a,1,2)),flip(a)].
% 15.91/16.16 273 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,A)))) = multiply(B,multiply(A,inverse(B))). [para(263(a,1),70(a,1,2)),rewrite([71(7)]),flip(a)].
% 15.91/16.16 275 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,C))))) = multiply(inverse(B),multiply(A,multiply(B,C))). [para(269(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 276 multiply(A,multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(A,B))))))) = multiply(inverse(C),multiply(A,multiply(B,C))). [para(269(a,1),3(a,1)),rewrite([3(3),158(6),3(11)]),flip(a)].
% 15.91/16.16 279 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),inverse(B))))) = multiply(inverse(A),multiply(inverse(B),A)). [para(9(a,1),269(a,2,2)),rewrite([71(4),158(4),3(7),3(9),9(10),158(9),3(11)])].
% 15.91/16.16 281 multiply(A,multiply(inverse(B),multiply(inverse(A),B))) = multiply(B,multiply(A,multiply(inverse(B),inverse(A)))). [para(269(a,1),70(a,1,2)),rewrite([71(7)])].
% 15.91/16.16 282 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,B)))) = multiply(inverse(A),multiply(B,A)). [para(70(a,1),269(a,2,2)),rewrite([158(6),71(6),3(6),3(8),70(9),158(9),71(9),3(9)])].
% 15.91/16.16 324 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(A,C))))) = multiply(A,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C))))). [para(159(a,1),159(a,2,2,2,2,2,2)),rewrite([71(3),71(3),71(5),71(5),71(7),9(13),9(11),70(14),70(12),9(10),71(9),71(11),71(11),71(16),9(18),9(16),9(14),9(13),70(12)]),flip(a)].
% 15.91/16.16 329 multiply(inverse(A),multiply(B,multiply(A,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,C))))))))))) = multiply(B,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,C))))). [para(159(a,2),159(a,1,2,2,2,2,2)),rewrite([71(2),71(2),71(2),71(6),71(7),71(7),71(9),9(10),9(8),9(9),9(7),9(5),71(10),71(10),71(10),71(11),71(11),71(11),71(12),71(14),71(15),9(20),9(23)]),flip(a)].
% 15.91/16.16 332 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(C,D))))))))))))) = multiply(B,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,D))))))). [para(159(a,2),159(a,2,2,2,2,2,2,2,2)),rewrite([71(2),9(18),9(16),9(14),9(14),9(12),71(13),71(15),70(29),9(28)]),flip(a)].
% 15.91/16.16 334 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(A,C))))) = multiply(B,multiply(A,multiply(inverse(B),C))). [para(273(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 336 multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,A)))))) = multiply(C,multiply(B,multiply(A,multiply(inverse(B),inverse(C))))). [para(3(a,1),273(a,1,2,2,2)),rewrite([158(2),3(8),158(12),3(15)])].
% 15.91/16.16 340 multiply(inverse(A),multiply(inverse(B),multiply(A,B))) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))). [para(273(a,1),269(a,1,2,2,2)),rewrite([71(3),71(8),158(11),158(9),158(8),71(7),3(9),71(11),3(10),3(9),3(15),3(14),3(13),3(17),3(16),3(15),9(14),275(12),70(10),9(8),71(9),3(12),3(11),3(10),2(9),51(9)]),flip(a)].
% 15.91/16.16 343 multiply(A,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C))))) = multiply(B,multiply(A,multiply(inverse(B),C))). [back_rewrite(324),rewrite([334(7)]),flip(a)].
% 15.91/16.16 357 multiply(A,multiply(B,multiply(A,multiply(inverse(B),inverse(A))))) = multiply(B,multiply(A,inverse(B))). [back_rewrite(273),rewrite([340(5)])].
% 15.91/16.16 386 multiply(inverse(b),multiply(inverse(c),multiply(b,multiply(c,a)))) != multiply(a,multiply(b,multiply(c,multiply(inverse(b),inverse(c))))) # answer(prove_center). [back_rewrite(7),rewrite([340(21)])].
% 15.91/16.16 388 multiply(inverse(A),multiply(B,multiply(A,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,C))))))))))) = multiply(A,multiply(B,multiply(inverse(A),C))). [back_rewrite(329),rewrite([343(23)])].
% 15.91/16.16 395 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(B,C))))) = multiply(inverse(A),multiply(B,multiply(A,C))). [para(282(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 400 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,B)))) = multiply(A,multiply(B,inverse(A))). [para(71(a,1),282(a,1,2,2,1)),rewrite([71(8)])].
% 15.91/16.16 401 multiply(inverse(A),multiply(B,multiply(A,A))) = multiply(B,multiply(B,multiply(A,inverse(B)))). [para(282(a,1),70(a,1,2)),rewrite([71(2),71(7)]),flip(a)].
% 15.91/16.16 404 multiply(inverse(A),multiply(B,multiply(A,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,multiply(A,inverse(B)))))))))))) = multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(A,multiply(A,B))))). [para(282(a,1),269(a,1,2,2,2)),rewrite([71(3),71(7),158(9),158(7),158(6),3(9),71(11),3(10),3(9),71(12),3(14),3(13),3(12),3(16),3(15),3(14),71(20),3(22),3(21),3(20)])].
% 15.91/16.16 415 multiply(A,multiply(B,multiply(B,multiply(A,inverse(B))))) = multiply(B,multiply(A,A)). [para(401(a,1),9(a,1,2)),rewrite([71(2)])].
% 15.91/16.16 420 multiply(A,multiply(inverse(B),multiply(A,multiply(B,inverse(A))))) = multiply(A,multiply(A,multiply(B,multiply(inverse(A),inverse(B))))). [para(401(a,2),269(a,2,2)),rewrite([158(8),158(7),71(6),3(8),3(9),3(8),2(7),51(7),9(7),3(5),3(4),158(10),158(9),71(8),3(10),3(15),3(14),400(13)]),flip(a)].
% 15.91/16.16 421 multiply(A,multiply(inverse(B),multiply(A,multiply(B,inverse(A))))) = multiply(inverse(B),multiply(A,B)). [para(401(a,2),282(a,2,2)),rewrite([158(8),158(7),71(6),3(8),3(10),3(9),9(8),9(8),3(6),3(5),269(6),158(7),158(6),71(5),3(7),3(12),3(11),400(10)]),flip(a)].
% 15.91/16.16 422 multiply(A,multiply(A,multiply(B,multiply(inverse(A),inverse(B))))) = multiply(inverse(B),multiply(A,B)). [back_rewrite(420),rewrite([421(6)]),flip(a)].
% 15.91/16.16 429 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(inverse(D),multiply(B,multiply(D,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(D),multiply(inverse(B),multiply(D,multiply(C,E))))))))))))) = multiply(inverse(C),multiply(inverse(D),multiply(inverse(A),multiply(D,multiply(C,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(inverse(D),multiply(A,multiply(D,multiply(C,E))))))))))))). [para(3(a,1),161(a,1,2,2,2,2,2,2,2,2)),rewrite([158(4),158(8),3(14),3(16),3(18),158(22),158(29),3(32),3(34),3(38),3(40)])].
% 15.91/16.16 483 multiply(inverse(A),multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(A,C))))) = multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(inverse(A),C))))). [para(161(a,2),161(a,2,2,2,2,2)),rewrite([71(3),71(4),71(4),71(5),71(5),71(8),71(9),70(14),70(14),9(13),9(11),71(10),71(14),71(15),71(15),71(17),9(17),9(19),9(17),9(15)])].
% 15.91/16.16 485 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(inverse(A),C))))) = multiply(inverse(B),multiply(inverse(A),multiply(B,C))). [para(161(a,2),161(a,2,2,2,2,2)),rewrite([71(3),71(4),71(4),71(5),71(5),71(8),71(9),483(12),9(13),275(12),70(7),70(8),70(6),71(7),71(11),71(12),71(12),71(14),9(14),9(16),9(14),9(12)]),flip(a)].
% 15.91/16.16 494 multiply(inverse(A),multiply(B,multiply(A,multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(A),multiply(inverse(B),multiply(A,C))))))))) = multiply(A,multiply(B,multiply(inverse(A),C))). [back_rewrite(388),rewrite([483(10),485(10)])].
% 15.91/16.16 503 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,multiply(B,A))))) = multiply(A,B). [back_rewrite(404),rewrite([494(16),421(6),70(4)]),flip(a)].
% 15.91/16.16 509 multiply(A,multiply(B,multiply(B,multiply(A,multiply(inverse(B),C))))) = multiply(B,multiply(A,multiply(A,C))). [para(415(a,1),3(a,1,1)),rewrite([3(3),3(2),3(8),3(7),3(6)]),flip(a)].
% 15.91/16.16 512 multiply(A,multiply(inverse(B),multiply(inverse(B),multiply(A,B)))) = multiply(inverse(B),multiply(A,A)). [para(71(a,1),415(a,1,2,2,2,2))].
% 15.91/16.16 518 multiply(inverse(A),multiply(B,multiply(A,multiply(A,B)))) = multiply(B,multiply(B,A)). [para(503(a,1),9(a,1,2)),rewrite([71(2)]),flip(a)].
% 15.91/16.16 519 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(B),A)))) = multiply(B,multiply(A,inverse(B))). [para(9(a,1),503(a,1,2,2,2,2)),rewrite([158(2),71(5),3(7),3(9),9(8),3(9)])].
% 15.91/16.16 533 multiply(A,multiply(B,multiply(B,A))) = multiply(B,multiply(A,multiply(A,B))). [para(518(a,1),9(a,1,2)),rewrite([71(2)])].
% 15.91/16.16 551 multiply(A,multiply(B,multiply(inverse(A),B))) = multiply(B,multiply(A,multiply(B,inverse(A)))). [para(9(a,1),533(a,1,2,2)),rewrite([3(4),3(9),3(10),9(11)])].
% 15.91/16.16 567 multiply(inverse(A),multiply(inverse(B),multiply(C,multiply(A,multiply(inverse(C),multiply(B,multiply(C,multiply(inverse(B),multiply(C,multiply(inverse(A),multiply(inverse(C),multiply(B,multiply(A,D))))))))))))) = multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(inverse(B),multiply(C,multiply(B,multiply(A,D))))))))). [para(162(a,1),9(a,1,2)),rewrite([71(2),334(16)]),flip(a)].
% 15.91/16.16 574 multiply(inverse(A),multiply(inverse(B),multiply(C,multiply(D,multiply(inverse(C),multiply(inverse(D),multiply(B,multiply(D,multiply(C,multiply(inverse(D),inverse(C))))))))))) = multiply(inverse(A),multiply(inverse(B),multiply(C,multiply(D,multiply(inverse(C),multiply(inverse(D),multiply(B,multiply(C,multiply(inverse(D),multiply(inverse(C),D)))))))))). [para(162(a,1),158(a,1,1)),rewrite([158(16),158(14),158(12),158(11),158(10),158(8),158(6),158(4),158(3),158(2),3(5),3(7),3(6),71(9),3(8),3(7),3(6),71(10),3(9),3(8),3(7),3(6),340(7),71(11),3(10),3(9),3(8),3(7),3(6),3(12),3(11),3(10),3(9),3(8),3(7),3(14),3(13),3(12),3(11),3(10),3(9),3(8),71(16),3(15),3(14),3(13),3(12),3(11),3(10),3(9),3(8),71(17),3(16),3(15),3(14),3(13),3(12),3(11),3(10),3(9),3(8),340(9),567(35),158(30),158(29),158(28),158(26),158(24),158(22),158(20),158(19),158(18),3(21),3(23),3(22),71(25),3(24),3(23),3(22),71(26),3(25),3(24),3(23),3(22),340(23),71(27),3(26),3(25),3(24),3(23),3(22),71(28),3(27),3(26),3(25),3(24),3(23),3(22),3(29),3(28),3(27),3(26),3(25),3(24),3(23),3(31),3(30),3(29),3(28),3(27),3(26),3(25),3(24),71(33),3(32),3(31),3(30),3(29),3(28),3(27),3(26),3(25),3(24)])].
% 15.91/16.16 594 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(B,multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,C)))))))))))))) = multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(B,multiply(C,C)))))))))). [para(415(a,1),162(a,1,2,2,2,2,2,2,2,2,2,2,2,2)),rewrite([415(31)])].
% 15.91/16.16 650 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),inverse(A))))) = multiply(B,multiply(inverse(A),inverse(B))). [para(551(a,2),70(a,1,2))].
% 15.91/16.16 654 multiply(inverse(A),multiply(B,multiply(inverse(A),multiply(inverse(B),A)))) = multiply(B,multiply(inverse(A),inverse(B))). [para(551(a,2),269(a,1,2,2,2)),rewrite([158(9),158(8),71(6),71(6),3(7),3(14),3(13),9(12),70(10),70(8),65(6),51(6),3(10),3(9)]),flip(a)].
% 15.91/16.16 786 multiply(A,multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),C))))) = multiply(B,multiply(A,multiply(inverse(B),C))). [para(357(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 799 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,multiply(B,C))))) = multiply(A,multiply(B,multiply(inverse(A),C))). [para(400(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 801 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(B,multiply(A,multiply(C,C)))))) = multiply(B,multiply(A,multiply(C,multiply(inverse(A),inverse(B))))). [para(3(a,1),400(a,1,2,2)),rewrite([158(2),3(9),158(12),3(15)])].
% 15.91/16.16 814 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(B,multiply(inverse(A),multiply(C,multiply(A,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,C)))))))))))))) = multiply(C,multiply(A,multiply(inverse(C),multiply(B,multiply(C,multiply(inverse(B),inverse(A))))))). [back_rewrite(594),rewrite([801(32),799(33)])].
% 15.91/16.16 959 multiply(inverse(A),multiply(B,multiply(A,inverse(B)))) = multiply(A,multiply(inverse(B),multiply(inverse(A),B))). [para(422(a,1),70(a,1,2)),rewrite([71(8)]),flip(a)].
% 15.91/16.16 968 multiply(A,multiply(inverse(B),multiply(inverse(B),multiply(A,multiply(B,C))))) = multiply(inverse(B),multiply(A,multiply(A,C))). [para(512(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 1004 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(B),multiply(A,C))))) = multiply(B,multiply(A,multiply(inverse(B),C))). [para(519(a,1),3(a,1,1)),rewrite([3(4),3(3),3(10),3(9),3(8)]),flip(a)].
% 15.91/16.16 1013 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,C)))))))))))) = multiply(C,multiply(A,multiply(inverse(C),multiply(B,multiply(C,multiply(inverse(B),inverse(A))))))). [back_rewrite(814),rewrite([1004(16)])].
% 15.91/16.16 1195 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C)))) = multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),C)))). [para(281(a,1),3(a,1,1)),rewrite([3(6),3(5),3(4),3(11),3(10)]),flip(a)].
% 15.91/16.16 1199 multiply(inverse(b),multiply(inverse(c),multiply(b,multiply(c,a)))) != multiply(a,multiply(c,multiply(inverse(b),multiply(inverse(c),b)))) # answer(prove_center). [para(281(a,2),386(a,2,2))].
% 15.91/16.16 1204 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(B,C)))) = multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),C)))). [para(340(a,1),3(a,1,1)),rewrite([3(6),3(5),3(4),3(11),3(10)]),flip(a)].
% 15.91/16.16 1211 multiply(b,multiply(c,multiply(inverse(b),multiply(inverse(c),a)))) != multiply(a,multiply(c,multiply(inverse(b),multiply(inverse(c),b)))) # answer(prove_center). [back_rewrite(1199),rewrite([1204(11)])].
% 15.91/16.16 1604 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(B),multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(A),multiply(B,multiply(A,multiply(C,multiply(inverse(A),multiply(inverse(C),D))))))))))))) = multiply(B,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,D))))))). [back_rewrite(332),rewrite([1204(10),1204(15)])].
% 15.91/16.16 1868 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(A,B))))))) = multiply(C,multiply(inverse(B),multiply(A,multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(C),multiply(A,C))))))))). [para(227(a,1),70(a,1,2)),rewrite([71(5),71(6),71(17),71(17),786(23)]),flip(a)].
% 15.91/16.16 1925 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(B),C)))) = multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C)))). [para(959(a,1),3(a,1,1)),rewrite([3(6),3(5),3(4),3(11),3(10)]),flip(a)].
% 15.91/16.16 2005 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(A),multiply(B,multiply(A,multiply(C,multiply(inverse(A),multiply(inverse(C),D))))))))))))) = multiply(B,multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,D))))))). [back_rewrite(1604),rewrite([1925(19)])].
% 15.91/16.16 2129 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,C)))))))))))) = multiply(C,multiply(A,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(B,inverse(A))))))). [back_rewrite(1013),rewrite([1925(25)])].
% 15.91/16.16 2253 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),C))))) = multiply(inverse(A),multiply(inverse(B),multiply(A,C))). [para(279(a,1),3(a,1,1)),rewrite([3(5),3(4),3(12),3(11),3(10)]),flip(a)].
% 15.91/16.16 2331 multiply(A,multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(B,D)))))))) = multiply(inverse(C),multiply(A,multiply(B,multiply(C,D)))). [para(275(a,1),3(a,1)),rewrite([3(4),158(7),3(11),3(13)]),flip(a)].
% 15.91/16.16 2410 multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(A,C)))))) = multiply(C,multiply(A,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(B,inverse(A))))))). [back_rewrite(2129),rewrite([2331(14),70(9),1204(8)])].
% 15.91/16.16 2610 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(inverse(A),C))))) = multiply(B,multiply(inverse(A),multiply(inverse(B),C))). [para(650(a,1),3(a,1,1)),rewrite([3(5),3(4),3(12),3(11),3(10)]),flip(a)].
% 15.91/16.16 2658 multiply(inverse(A),multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,C))))) = multiply(B,multiply(inverse(A),multiply(inverse(B),C))). [para(654(a,1),3(a,1,1)),rewrite([3(5),3(4),3(12),3(11),3(10)]),flip(a)].
% 15.91/16.16 2722 multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(C,multiply(B,inverse(C))))))))) = multiply(C,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(inverse(C),multiply(inverse(A),multiply(B,A)))))))). [back_rewrite(227),rewrite([2658(11)]),flip(a)].
% 15.91/16.16 2768 multiply(A,multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(A,B))))))))))) = multiply(C,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(A,multiply(inverse(C),multiply(B,C))))))). [para(422(a,1),276(a,2,2,2)),rewrite([158(13),158(12),158(11),71(9),71(9),3(10),3(12),3(11),3(14),3(13),3(12),3(17),3(16),3(15),2610(17),158(22),158(21),158(20),71(18),71(18),3(19),3(21),3(20),3(26),3(25),3(24)])].
% 15.91/16.16 2782 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(inverse(C),multiply(B,multiply(A,multiply(inverse(B),inverse(A)))))))))))))) = multiply(inverse(C),multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C))))). [para(281(a,1),276(a,1,2,2,2,2,2,2)),rewrite([158(9),158(7),71(7),71(8),3(7),3(17),3(16),1925(17),3(19),3(18),3(26),3(25)])].
% 15.91/16.16 4203 multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,multiply(A,D))))))) = multiply(C,multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(C),D))))). [para(336(a,1),3(a,1,1)),rewrite([3(7),3(6),3(5),3(4),3(16),3(15),3(14),3(13),3(12)]),flip(a)].
% 15.91/16.16 4233 multiply(inverse(A),multiply(inverse(B),multiply(A,multiply(inverse(C),multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(A,multiply(B,inverse(A)))))))))))) = multiply(C,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(A,inverse(C)))))). [para(357(a,1),336(a,1,2,2,2,2,2)),rewrite([158(13),158(12),158(11),71(9),71(9),3(10),3(12),3(11),3(17),3(16),3(15),3(20),3(19),3(18),2253(20),3(26),3(25),3(24),2253(26)])].
% 15.91/16.16 5337 multiply(inverse(A),multiply(B,multiply(A,multiply(inverse(C),multiply(inverse(B),multiply(C,D)))))) = multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(C),D)))))). [para(343(a,1),395(a,1,2,2,2)),flip(a)].
% 15.91/16.16 8378 multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(A,D))))))))))) = multiply(inverse(C),multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(C,multiply(inverse(B),multiply(inverse(A),multiply(B,D))))))))). [para(429(a,1),509(a,2)),rewrite([71(6),1204(12),1925(13),485(13),968(20),1204(15),275(15),1204(13),2610(30),1204(25),1204(30)]),flip(a)].
% 15.91/16.16 8819 multiply(c,multiply(inverse(b),multiply(inverse(c),multiply(b,a)))) != multiply(a,multiply(c,multiply(inverse(b),multiply(inverse(c),b)))) # answer(prove_center). [para(1195(a,2),1211(a,1))].
% 15.91/16.16 8842 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(A),D)))))))) = multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,D)))))). [para(275(a,1),1195(a,2,2,2,2)),rewrite([71(4)])].
% 15.91/16.16 8994 multiply(A,multiply(inverse(B),multiply(C,multiply(inverse(A),multiply(inverse(C),multiply(A,multiply(B,D))))))) = multiply(A,multiply(B,multiply(A,multiply(C,multiply(inverse(A),multiply(inverse(C),multiply(inverse(B),D))))))). [back_rewrite(2005),rewrite([8842(19),4203(15),9(8)]),flip(a)].
% 15.91/16.16 8997 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(A,B))))))) = multiply(C,multiply(B,multiply(C,multiply(A,multiply(inverse(C),multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(A,C))))))))). [back_rewrite(1868),rewrite([8994(23)])].
% 15.91/16.16 9129 multiply(A,multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(A),D))))))) = multiply(inverse(B),multiply(inverse(C),multiply(inverse(A),multiply(C,multiply(B,D))))). [para(3(a,1),485(a,1,2,2,2)),rewrite([158(2),3(10),158(13),3(17),3(19)])].
% 15.91/16.16 9131 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(A,B)))))))) = multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(C,A)))). [para(485(a,1),518(a,2,2)),rewrite([158(8),158(6),158(4),158(3),71(3),3(4),71(6),3(5),3(4),71(7),3(6),3(5),3(4),3(21),3(20),3(19),3(18),3(22),3(21),3(20),3(19),485(23),3(21),3(20),3(19),3(18),70(17),70(15),9(13),5337(12)])].
% 15.91/16.16 13254 multiply(inverse(A),multiply(inverse(B),multiply(inverse(C),multiply(B,multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(C,A)))))))) = inverse(B). [para(574(a,2),422(a,2)),rewrite([71(16),158(27),158(26),158(25),158(23),158(21),158(20),158(19),158(17),71(17),71(18),3(17),3(19),3(18),959(19),3(21),3(20),3(19),71(23),3(22),3(21),3(20),3(19),71(24),3(23),3(22),3(21),3(20),3(19),3(25),3(24),3(23),3(22),3(21),3(20),3(27),3(26),3(25),3(24),3(23),3(22),3(21),3(29),3(28),3(27),3(26),3(25),3(24),3(23),3(22),2782(24),70(13),2658(11),9(9),70(7),70(5),2(3),51(3),158(14),158(13),158(12),158(10),158(8),158(7),158(6),158(4),71(4),71(5),3(4),3(6),3(5),959(6),3(8),3(7),3(6),71(10),3(9),3(8),3(7),3(6),71(11),3(10),3(9),3(8),3(7),3(6),3(12),3(11),3(10),3(9),3(8),3(7),3(14),3(13),3(12),3(11),3(10),3(9),3(8),3(29),3(28),3(27),3(26),3(25),3(24),3(23),3(22),8378(25),422(14),70(20),1925(18),485(18),9129(17)]),flip(a)].
% 15.91/16.16 13264 multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),multiply(C,multiply(inverse(A),multiply(B,A))))))) = multiply(C,B). [back_rewrite(2768),rewrite([13254(13),65(2),51(2)]),flip(a)].
% 15.91/16.16 13270 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(A,B))))))) = multiply(C,A). [back_rewrite(8997),rewrite([13264(21),70(13)])].
% 15.91/16.16 13308 multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(A,multiply(C,multiply(B,inverse(C))))))))) = B. [back_rewrite(2722),rewrite([13270(23),70(15)])].
% 15.91/16.16 13336 multiply(A,multiply(B,multiply(inverse(C),multiply(inverse(B),multiply(C,inverse(A)))))) = multiply(C,multiply(B,multiply(inverse(C),inverse(B)))). [back_rewrite(4233),rewrite([13308(14),340(5)]),flip(a)].
% 15.91/16.16 13370 multiply(inverse(A),multiply(B,multiply(C,multiply(inverse(B),multiply(inverse(C),multiply(A,C)))))) = multiply(B,multiply(C,inverse(B))). [back_rewrite(2410),rewrite([13336(17),357(15)])].
% 15.91/16.16 13400 multiply(A,multiply(inverse(B),multiply(inverse(A),multiply(B,C)))) = multiply(C,multiply(A,multiply(inverse(B),multiply(inverse(A),B)))). [back_rewrite(9131),rewrite([13370(10),959(5)]),flip(a)].
% 15.91/16.16 13401 $F # answer(prove_center). [resolve(13400,a,8819,a)].
% 15.91/16.16
% 15.91/16.16 % SZS output end Refutation
% 15.91/16.16 ============================== end of proof ==========================
% 15.91/16.16
% 15.91/16.16 ============================== STATISTICS ============================
% 15.91/16.16
% 15.91/16.16 Given=162. Generated=75079. Kept=13399. proofs=1.
% 15.91/16.16 Usable=132. Sos=9092. Demods=3990. Limbo=30, Disabled=4150. Hints=0.
% 15.91/16.16 Megabytes=25.50.
% 15.91/16.16 User_CPU=15.08, System_CPU=0.06, Wall_clock=15.
% 15.91/16.16
% 15.91/16.16 ============================== end of statistics =====================
% 15.91/16.16
% 15.91/16.16 ============================== end of search =========================
% 15.91/16.16
% 15.91/16.16 THEOREM PROVED
% 15.91/16.16 % SZS status Unsatisfiable
% 15.91/16.16
% 15.91/16.16 Exiting with 1 proof.
% 15.91/16.16
% 15.91/16.16 Process 17462 exit (max_proofs) Mon Jun 13 21:59:24 2022
% 15.91/16.16 Prover9 interrupted
%------------------------------------------------------------------------------