TSTP Solution File: GRP211-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP211-1 : TPTP v8.1.0. Released v2.5.0.
% 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 11:18:10 EDT 2022
% Result : Unsatisfiable 31.66s 31.95s
% Output : Refutation 31.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP211-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 05:47:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 31.66/31.95 ============================== Prover9 ===============================
% 31.66/31.95 Prover9 (32) version 2009-11A, November 2009.
% 31.66/31.95 Process 12577 was started by sandbox2 on n017.cluster.edu,
% 31.66/31.95 Tue Jun 14 05:47:24 2022
% 31.66/31.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12424_n017.cluster.edu".
% 31.66/31.95 ============================== end of head ===========================
% 31.66/31.95
% 31.66/31.95 ============================== INPUT =================================
% 31.66/31.95
% 31.66/31.95 % Reading from file /tmp/Prover9_12424_n017.cluster.edu
% 31.66/31.95
% 31.66/31.95 set(prolog_style_variables).
% 31.66/31.95 set(auto2).
% 31.66/31.95 % set(auto2) -> set(auto).
% 31.66/31.95 % set(auto) -> set(auto_inference).
% 31.66/31.95 % set(auto) -> set(auto_setup).
% 31.66/31.95 % set(auto_setup) -> set(predicate_elim).
% 31.66/31.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 31.66/31.95 % set(auto) -> set(auto_limits).
% 31.66/31.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 31.66/31.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 31.66/31.95 % set(auto) -> set(auto_denials).
% 31.66/31.95 % set(auto) -> set(auto_process).
% 31.66/31.95 % set(auto2) -> assign(new_constants, 1).
% 31.66/31.95 % set(auto2) -> assign(fold_denial_max, 3).
% 31.66/31.95 % set(auto2) -> assign(max_weight, "200.000").
% 31.66/31.95 % set(auto2) -> assign(max_hours, 1).
% 31.66/31.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 31.66/31.95 % set(auto2) -> assign(max_seconds, 0).
% 31.66/31.95 % set(auto2) -> assign(max_minutes, 5).
% 31.66/31.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 31.66/31.95 % set(auto2) -> set(sort_initial_sos).
% 31.66/31.95 % set(auto2) -> assign(sos_limit, -1).
% 31.66/31.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 31.66/31.95 % set(auto2) -> assign(max_megs, 400).
% 31.66/31.95 % set(auto2) -> assign(stats, some).
% 31.66/31.95 % set(auto2) -> clear(echo_input).
% 31.66/31.95 % set(auto2) -> set(quiet).
% 31.66/31.95 % set(auto2) -> clear(print_initial_clauses).
% 31.66/31.95 % set(auto2) -> clear(print_given).
% 31.66/31.95 assign(lrs_ticks,-1).
% 31.66/31.95 assign(sos_limit,10000).
% 31.66/31.95 assign(order,kbo).
% 31.66/31.95 set(lex_order_vars).
% 31.66/31.95 clear(print_given).
% 31.66/31.95
% 31.66/31.95 % formulas(sos). % not echoed (29 formulas)
% 31.66/31.95
% 31.66/31.95 ============================== end of input ==========================
% 31.66/31.95
% 31.66/31.95 % From the command line: assign(max_seconds, 300).
% 31.66/31.95
% 31.66/31.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 31.66/31.95
% 31.66/31.95 % Formulas that are not ordinary clauses:
% 31.66/31.95
% 31.66/31.95 ============================== end of process non-clausal formulas ===
% 31.66/31.95
% 31.66/31.95 ============================== PROCESS INITIAL CLAUSES ===============
% 31.66/31.95
% 31.66/31.95 ============================== PREDICATE ELIMINATION =================
% 31.66/31.95
% 31.66/31.95 ============================== end predicate elimination =============
% 31.66/31.95
% 31.66/31.95 Auto_denials: (non-Horn, no changes).
% 31.66/31.95
% 31.66/31.95 Term ordering decisions:
% 31.66/31.95
% 31.66/31.95 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 31.66/31.95 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c2=1. sk_c1=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 31.66/31.95
% 31.66/31.95 ============================== end of process initial clauses ========
% 31.66/31.95
% 31.66/31.95 ============================== CLAUSES FOR SEARCH ====================
% 31.66/31.95
% 31.66/31.95 ============================== end of clauses for search =============
% 31.66/31.95
% 31.66/31.95 ============================== SEARCH ================================
% 31.66/31.95
% 31.66/31.95 % Starting search at 0.02 seconds.
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=40.000, iters=3360
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=37.000, iters=3390
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=36.000, iters=3358
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=35.000, iters=3352
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=34.000, iters=3485
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=33.000, iters=3375
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=32.000, iters=3440
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=31.000, iters=3486
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=29.000, iters=3423
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=28.000, iters=3422
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=27.000, iters=3335
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=26.000, iters=3341
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=25.000, iters=3366
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=24.000, iters=3336
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=23.000, iters=3490
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=22.000, iters=3370
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=21.000, iters=3349
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=20.000, iters=3354
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=19.000, iters=3357
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=18.000, iters=3334
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=17.000, iters=3346
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=16.000, iters=3333
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=15.000, iters=3355
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=14.000, iters=3339
% 31.66/31.95
% 31.66/31.95 Low Water (keep): wt=13.000, iters=3341
% 31.66/31.95
% 31.66/31.95 ============================== PROOF =================================
% 31.66/31.95 % SZS status Unsatisfiable
% 31.66/31.95 % SZS output start Refutation
% 31.66/31.95
% 31.66/31.95 % Proof 1 at 29.94 (+ 1.04) seconds.
% 31.66/31.95 % Length of proof is 287.
% 31.66/31.95 % Level of proof is 34.
% 31.66/31.95 % Maximum clause weight is 46.000.
% 31.66/31.95 % Given clauses 4086.
% 31.66/31.95
% 31.66/31.95 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 31.66/31.95 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 31.66/31.95 3 inverse(sk_c1) = sk_c2 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 31.66/31.95 4 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 31.66/31.95 5 inverse(sk_c3) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 31.66/31.95 6 inverse(sk_c3) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 31.66/31.95 7 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 31.66/31.95 8 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 31.66/31.95 9 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 31.66/31.95 10 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 31.66/31.95 11 inverse(sk_c1) = sk_c2 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 31.66/31.95 12 multiply(sk_c2,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 31.66/31.95 14 inverse(sk_c3) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 31.66/31.95 15 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 31.66/31.95 16 inverse(sk_c3) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 31.66/31.95 17 multiply(sk_c3,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 31.66/31.95 18 multiply(sk_c3,sk_c7) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 31.66/31.95 19 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 31.66/31.95 20 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 31.66/31.95 21 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 31.66/31.95 25 multiply(sk_c3,sk_c7) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 31.66/31.95 27 multiply(sk_c3,sk_c7) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 31.66/31.95 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 31.66/31.95 29 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8 | multiply(sk_c8,E) != sk_c7 | multiply(F,sk_c8) != E | inverse(F) != sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 31.66/31.95 35 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8. [factor(29,c,e)].
% 31.66/31.95 36 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8. [factor(29,d,f),merge(f)].
% 31.66/31.95 45 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [factor(35,c,f),merge(e)].
% 31.66/31.95 59 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 31.66/31.95 61 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c4) = identity. [para(5(b,1),2(a,1,1))].
% 31.66/31.95 62 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c5) = identity. [para(6(b,1),2(a,1,1))].
% 31.66/31.95 63 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 31.66/31.95 69 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c8). [para(9(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 71 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 72 inverse(sk_c1) = sk_c2 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(11(b,1),28(a,1,1)),flip(b)].
% 31.66/31.95 73 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(11(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 75 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c8). [para(12(a,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 79 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c8). [para(14(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 81 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(15(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 83 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(16(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 151 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8. [resolve(36,g,2,a)].
% 31.66/31.95 158 identity != sk_c8 | inverse(inverse(A)) != A | multiply(A,sk_c7) != sk_c8 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [para(2(a,1),36(a,1))].
% 31.66/31.95 329 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | multiply(sk_c8,identity) != sk_c7. [factor(151,d,g)].
% 31.66/31.95 351 identity != sk_c8 | inverse(inverse(A)) != A | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [factor(158,c,e)].
% 31.66/31.95 725 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c8,sk_c4)) = multiply(A,identity). [para(59(b,1),28(a,2,2)),rewrite([28(8)])].
% 31.66/31.95 754 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),63(a,1,2))].
% 31.66/31.95 760 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c4),sk_c8) = sk_c7. [para(9(b,1),63(a,1,2))].
% 31.66/31.95 765 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c4),sk_c8) = sk_c7. [para(14(b,1),63(a,1,2))].
% 31.66/31.95 766 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(15(b,1),63(a,1,2))].
% 31.66/31.95 768 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(17(a,1),63(a,1,2))].
% 31.66/31.95 769 inverse(sk_c5) = sk_c8 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(18(a,1),63(a,1,2))].
% 31.66/31.95 785 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(63(a,1),63(a,1,2))].
% 31.66/31.95 789 multiply(A,identity) = A. [back_rewrite(754),rewrite([785(4)])].
% 31.66/31.95 791 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c8,sk_c4)) = A. [back_rewrite(725),rewrite([789(10)])].
% 31.66/31.95 803 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(329),rewrite([789(23)]),flip(f)].
% 31.66/31.95 810 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(inverse(sk_c8)) != sk_c8. [back_rewrite(151),rewrite([789(19)]),flip(f)].
% 31.66/31.95 816 inverse(identity) = identity. [para(789(a,1),2(a,1))].
% 31.66/31.95 901 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c8,sk_c4)) = A. [para(61(b,1),28(a,2,2)),rewrite([28(8),789(10)])].
% 31.66/31.95 922 inverse(sk_c3) = sk_c8 | inverse(sk_c8) = sk_c4. [para(61(b,1),63(a,1,2)),rewrite([789(8)])].
% 31.66/31.95 946 inverse(sk_c3) = sk_c8 | inverse(sk_c8) = sk_c5. [para(62(b,1),63(a,1,2)),rewrite([789(8)])].
% 31.66/31.95 997 multiply(A,inverse(A)) = identity. [para(785(a,1),2(a,1))].
% 31.66/31.95 1032 multiply(A,multiply(inverse(A),B)) = B. [para(785(a,1),63(a,1))].
% 31.66/31.95 1033 inverse(inverse(A)) = A. [para(785(a,1),789(a,1)),rewrite([789(2)]),flip(a)].
% 31.66/31.95 1038 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(810),rewrite([1033(22)]),xx(g)].
% 31.66/31.95 1043 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(803),rewrite([1033(12)]),xx(d)].
% 31.66/31.95 1072 identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [back_rewrite(351),rewrite([1033(5)]),xx(b)].
% 31.66/31.95 1080 inverse(sk_c8) = sk_c4 | inverse(sk_c8) = sk_c3. [para(922(a,1),1033(a,1,1))].
% 31.66/31.95 1081 inverse(sk_c8) = sk_c5 | inverse(sk_c8) = sk_c3. [para(946(a,1),1033(a,1,1))].
% 31.66/31.95 1083 inverse(sk_c1) = sk_c2 | multiply(sk_c5,sk_c8) = identity. [para(4(b,1),997(a,1,2))].
% 31.66/31.95 1085 inverse(sk_c3) = sk_c8 | multiply(sk_c5,sk_c8) = identity. [para(6(b,1),997(a,1,2))].
% 31.66/31.95 1086 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(997(a,1),28(a,1)),flip(a)].
% 31.66/31.95 1107 inverse(sk_c8) = sk_c4 | multiply(sk_c3,sk_c8) = identity. [para(922(a,1),997(a,1,2))].
% 31.66/31.95 1162 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(C,sk_c8) | inverse(C) != sk_c8. [resolve(1032,a,45,e),flip(e)].
% 31.66/31.95 1168 inverse(sk_c1) = sk_c2 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(3(b,1),1032(a,1,2,1))].
% 31.66/31.95 1170 inverse(sk_c3) = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(5(b,1),1032(a,1,2,1))].
% 31.66/31.95 1243 inverse(sk_c8) = sk_c3 | sk_c5 = sk_c4. [para(1081(a,1),1080(a,1)),merge(c)].
% 31.66/31.95 1249 sk_c5 = sk_c4 | multiply(sk_c3,sk_c8) = identity. [para(1243(a,1),2(a,1,1))].
% 31.66/31.95 1330 sk_c5 = sk_c4 | multiply(A,multiply(sk_c3,sk_c8)) = A. [para(1249(b,1),28(a,2,2)),rewrite([28(7),789(9)])].
% 31.66/31.95 1557 inverse(sk_c1) = sk_c2 | identity = sk_c6. [para(1083(b,1),11(b,1)),merge(b)].
% 31.66/31.95 1563 identity = sk_c6 | multiply(sk_c1,sk_c2) = identity. [para(1557(a,1),997(a,1,2))].
% 31.66/31.95 1657 identity = sk_c6 | identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(1563(b,1),7(a,1))].
% 31.66/31.95 1664 inverse(sk_c3) = sk_c8 | identity = sk_c6. [para(1085(b,1),16(b,1)),merge(b)].
% 31.66/31.95 1668 identity = sk_c6 | inverse(sk_c8) = sk_c3. [para(1664(a,1),1033(a,1,1))].
% 31.66/31.95 1837 inverse(sk_c1) = sk_c2 | multiply(sk_c6,sk_c4) = sk_c5. [para(59(b,1),72(b,1,2)),rewrite([789(11)]),flip(c),merge(b)].
% 31.66/31.95 1947 inverse(sk_c1) = sk_c2 | multiply(A,sk_c6) = A. [para(1083(b,1),73(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 2126 multiply(A,multiply(B,C)) != sk_c8 | inverse(multiply(A,B)) != C | multiply(C,sk_c7) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [para(28(a,1),1043(a,1))].
% 31.66/31.95 2182 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = identity. [para(1947(b,1),2(a,1))].
% 31.66/31.95 2335 inverse(sk_c1) = sk_c2 | multiply(sk_c6,A) = A. [para(2182(b,1),63(a,1,1)),rewrite([1(8)])].
% 31.66/31.95 2414 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c6),A) = A. [para(2335(b,1),63(a,1,2))].
% 31.66/31.95 2430 inverse(sk_c1) = sk_c2 | sk_c5 = sk_c4. [para(2335(b,1),1837(b,1)),flip(c),merge(b)].
% 31.66/31.95 2509 sk_c5 = sk_c4 | multiply(sk_c1,sk_c2) = identity. [para(2430(a,1),997(a,1,2))].
% 31.66/31.95 2518 sk_c5 = sk_c4 | identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(2509(b,1),7(a,1))].
% 31.66/31.95 2519 sk_c5 = sk_c4 | identity = sk_c8 | inverse(sk_c5) = sk_c8. [para(2509(b,1),8(a,1))].
% 31.66/31.95 2837 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c8) = sk_c7. [para(3(b,1),760(b,1,1)),merge(b)].
% 31.66/31.95 2910 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(2837(b,1),63(a,1,2))].
% 31.66/31.95 3248 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(5(b,1),765(b,1,1)),merge(b)].
% 31.66/31.95 3322 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(3248(b,1),63(a,1,2))].
% 31.66/31.95 3764 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1086(a,1),63(a,1,2)),rewrite([789(3)]),flip(a)].
% 31.66/31.95 3946 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(3764(a,1),63(a,1,2)),flip(a)].
% 31.66/31.95 4216 multiply(A,multiply(B,C)) != sk_c8 | multiply(inverse(B),inverse(A)) != C | multiply(C,sk_c7) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(2126),rewrite([3946(6)])].
% 31.66/31.95 4434 inverse(sk_c3) = sk_c8 | multiply(A,sk_c6) = A. [para(1085(b,1),83(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 4496 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = identity. [para(4434(b,1),2(a,1))].
% 31.66/31.95 4512 inverse(sk_c3) = sk_c8 | multiply(sk_c6,A) = A. [para(4496(b,1),63(a,1,1)),rewrite([1(8)])].
% 31.66/31.95 4571 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c6),A) = A. [para(4512(b,1),63(a,1,2))].
% 31.66/31.95 4821 sk_c5 = sk_c4 | multiply(inverse(sk_c8),inverse(sk_c3)) = identity. [para(1330(b,1),2(a,1)),rewrite([3946(7)])].
% 31.66/31.95 5138 identity = sk_c6 | identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(1657(c,1),1033(a,1,1))].
% 31.66/31.95 7010 sk_c5 = sk_c4 | identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(2518(c,1),1033(a,1,1))].
% 31.66/31.95 7018 sk_c5 = sk_c4 | identity = sk_c8 | inverse(sk_c8) = sk_c5. [para(2519(c,1),1033(a,1,1))].
% 31.66/31.95 7084 inverse(sk_c1) = sk_c2 | sk_c6 = sk_c8. [para(2910(b,1),71(b,2)),rewrite([63(14)]),merge(b)].
% 31.66/31.95 7145 sk_c6 = sk_c8 | multiply(sk_c2,sk_c1) = identity. [para(7084(a,1),2(a,1,1))].
% 31.66/31.95 7148 sk_c6 = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(7084(a,1),997(a,1,2))].
% 31.66/31.95 7181 sk_c6 = sk_c8 | multiply(A,multiply(sk_c2,sk_c1)) = A. [para(7145(b,1),28(a,2,2)),rewrite([28(7),789(9)])].
% 31.66/31.95 7186 sk_c6 = sk_c8 | identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(7148(b,1),7(a,1))].
% 31.66/31.95 7295 inverse(sk_c3) = sk_c8 | sk_c6 = sk_c8. [para(3322(b,1),766(b,1)),flip(c),merge(b)].
% 31.66/31.95 7302 sk_c6 = sk_c8 | inverse(sk_c8) = sk_c3. [para(7295(a,1),1033(a,1,1))].
% 31.66/31.95 7655 sk_c8 != A | inverse(A) != identity | sk_c7 != sk_c8 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [para(1(a,1),1038(c,1)),rewrite([789(2)]),flip(a),merge(f)].
% 31.66/31.95 7688 inverse(A) != sk_c8 | identity != A | sk_c7 != sk_c8 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [para(1033(a,1),7655(b,1)),flip(a),flip(b)].
% 31.66/31.95 7704 inverse(A) != sk_c8 | identity != A | sk_c7 != sk_c8 | multiply(A,sk_c7) != sk_c8. [factor(7688,a,d)].
% 31.66/31.95 7709 inverse(sk_c4) != sk_c8 | identity != sk_c4 | sk_c7 != sk_c8 | multiply(sk_c1,sk_c2) = sk_c8. [resolve(7704,d,19,b)].
% 31.66/31.95 8053 inverse(sk_c8) = sk_c4 | multiply(inverse(sk_c8),inverse(sk_c3)) = identity. [para(1107(b,1),3946(a,1,1)),rewrite([816(6)]),flip(b)].
% 31.66/31.95 8595 identity = sk_c6 | identity = sk_c8 | sk_c4 = sk_c3. [para(5138(c,1),1668(b,1)),merge(c)].
% 31.66/31.95 9626 sk_c5 = sk_c4 | identity = sk_c8. [para(7018(c,1),7010(c,1)),merge(c),merge(d),merge(e)].
% 31.66/31.95 9631 sk_c5 = sk_c4 | inverse(sk_c8) = identity. [para(9626(b,1),816(a,1,1))].
% 31.66/31.95 9673 sk_c5 = sk_c4 | inverse(sk_c8) = sk_c8. [para(9626(b,1),9631(b,2)),merge(b)].
% 31.66/31.95 9730 sk_c5 = sk_c4 | multiply(sk_c8,sk_c8) = identity. [para(9673(b,1),2(a,1,1))].
% 31.66/31.95 9740 sk_c5 = sk_c4 | multiply(sk_c8,inverse(sk_c3)) = identity. [para(9673(b,1),4821(b,1,1)),merge(b)].
% 31.66/31.95 9933 sk_c5 = sk_c4 | multiply(inverse(sk_c8),inverse(sk_c8)) = identity. [para(9730(b,1),3946(a,1,1)),rewrite([816(5)]),flip(b)].
% 31.66/31.95 9982 sk_c5 = sk_c4 | inverse(sk_c3) = inverse(sk_c8). [para(9740(b,1),63(a,1,2)),rewrite([789(7)]),flip(b)].
% 31.66/31.95 10009 sk_c5 = sk_c4 | inverse(sk_c4) = sk_c8 | identity = sk_c7. [para(9982(b,1),768(b,1,1)),rewrite([2(11)])].
% 31.66/31.95 10010 sk_c5 = sk_c4 | inverse(sk_c5) = sk_c8 | identity = sk_c7. [para(9982(b,1),769(b,1,1)),rewrite([2(11)])].
% 31.66/31.95 10517 sk_c6 = sk_c8 | identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(7186(c,1),1033(a,1,1))].
% 31.66/31.95 11108 identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(B,sk_c8) | inverse(B) != sk_c8. [resolve(1072,d,1032,a),flip(d)].
% 31.66/31.95 11111 identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | sk_c8 != B. [para(1(a,1),1072(e,1)),rewrite([816(18)]),merge(f)].
% 31.66/31.95 11157 identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [resolve(11111,d,1032,a),flip(d)].
% 31.66/31.95 11161 identity != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [factor(11157,b,d),rewrite([1033(12)]),xx(c)].
% 31.66/31.95 11162 identity != sk_c8 | inverse(sk_c3) = sk_c8. [resolve(11161,b,3322,b)].
% 31.66/31.95 11163 identity != sk_c8 | inverse(sk_c1) = sk_c2. [resolve(11161,b,2910,b)].
% 31.66/31.95 11216 identity != sk_c8 | multiply(A,multiply(B,sk_c7)) != sk_c8 | multiply(inverse(B),inverse(A)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(C,sk_c8) | inverse(C) != sk_c8. [para(28(a,1),11108(b,1)),rewrite([3946(10)])].
% 31.66/31.95 11652 sk_c5 = sk_c4 | identity = sk_c7 | inverse(sk_c8) = sk_c4. [para(10009(b,1),1033(a,1,1))].
% 31.66/31.95 11659 sk_c5 = sk_c4 | identity = sk_c7 | inverse(sk_c8) = sk_c5. [para(10010(b,1),1033(a,1,1))].
% 31.66/31.95 11875 sk_c6 = sk_c8 | identity = sk_c8 | sk_c4 = sk_c3. [para(10517(c,1),7302(b,1)),merge(c)].
% 31.66/31.95 11881 sk_c6 = sk_c8 | sk_c4 = sk_c3 | inverse(sk_c8) = identity. [para(11875(b,1),816(a,1,1))].
% 31.66/31.95 12601 sk_c5 = sk_c4 | identity = sk_c7. [para(11659(c,1),11652(c,1)),merge(c),merge(d),merge(e)].
% 31.66/31.95 12620 sk_c5 = sk_c4 | inverse(sk_c8) = sk_c7. [para(12601(b,1),9631(b,2)),merge(b)].
% 31.66/31.95 12675 sk_c5 = sk_c4 | multiply(inverse(sk_c8),sk_c7) = identity. [para(12620(b,1),9933(b,1,2)),merge(b)].
% 31.66/31.95 13103 sk_c5 = sk_c4 | identity != sk_c8. [para(12675(b,1),11161(b,1)),merge(c)].
% 31.66/31.95 13106 sk_c5 = sk_c4. [resolve(13103,b,9626,b),merge(b)].
% 31.66/31.95 13409 multiply(sk_c3,sk_c7) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(27),rewrite([13106(6)])].
% 31.66/31.95 13411 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(21),rewrite([13106(6)])].
% 31.66/31.95 13457 sk_c6 = sk_c8 | sk_c4 = sk_c3 | identity = sk_c3. [para(11881(c,1),7302(b,1)),merge(c)].
% 31.66/31.95 13499 sk_c6 = sk_c8 | sk_c4 = sk_c3 | sk_c3 = sk_c8. [para(13457(c,1),11875(b,1)),merge(c),merge(e)].
% 31.66/31.95 13527 sk_c4 = sk_c3 | sk_c3 = sk_c8 | identity = sk_c8. [para(13499(a,1),8595(a,2)),merge(d),merge(e)].
% 31.66/31.95 13533 sk_c4 = sk_c3 | sk_c3 = sk_c8 | inverse(sk_c3) = sk_c8. [resolve(13527,c,11162,a)].
% 31.66/31.95 13542 sk_c4 = sk_c3 | sk_c3 = sk_c8 | inverse(sk_c8) = identity. [para(13527(c,1),816(a,1,1))].
% 31.66/31.95 14508 sk_c4 = sk_c3 | sk_c3 = sk_c8 | inverse(sk_c8) = sk_c3. [para(13533(c,1),1033(a,1,1))].
% 31.66/31.95 15007 sk_c8 != A | multiply(B,inverse(A)) != B | multiply(B,sk_c7) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [para(2(a,1),4216(a,1,2)),rewrite([789(2),1033(4)]),flip(a)].
% 31.66/31.95 15119 multiply(A,B) != sk_c8 | multiply(C,multiply(inverse(B),inverse(A))) != C | multiply(C,sk_c7) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [para(3946(a,1),15007(b,1,2)),flip(a)].
% 31.66/31.95 15123 multiply(A,sk_c7) != sk_c8 | multiply(A,multiply(inverse(sk_c7),inverse(A))) != A | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8. [factor(15119,a,c)].
% 31.66/31.95 15192 sk_c7 != sk_c8 | inverse(sk_c7) != identity | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(1(a,1),15123(b,1)),rewrite([1(3),816(7),789(7)]),merge(d)].
% 31.66/31.95 15226 sk_c4 = sk_c3 | sk_c3 = sk_c8 | identity = sk_c3. [para(14508(c,1),13542(c,1)),flip(e),merge(c),merge(d)].
% 31.66/31.95 15238 sk_c4 = sk_c3 | sk_c3 = sk_c8. [para(15226(c,1),13527(c,1)),merge(c),merge(d),merge(e)].
% 31.66/31.95 15240 sk_c3 = sk_c8 | inverse(sk_c3) = sk_c8. [para(15238(a,1),5(b,1,1)),merge(c)].
% 31.66/31.95 15244 sk_c3 = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8. [para(15238(a,1),25(b,1,1)),merge(c)].
% 31.66/31.95 15424 sk_c3 = sk_c8 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(15244(b,1),63(a,1,2))].
% 31.66/31.95 15497 sk_c3 = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(15240(b,1),15424(b,1,1)),merge(b)].
% 31.66/31.95 15516 sk_c3 = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(15497(b,1),63(a,1,2))].
% 31.66/31.95 15568 sk_c3 = sk_c8 | identity != sk_c8. [resolve(15516,b,11161,b)].
% 31.66/31.95 17546 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c4) = inverse(sk_c6). [para(791(b,1),2414(b,1)),flip(c),merge(b)].
% 31.66/31.95 17560 inverse(sk_c1) = sk_c2 | multiply(A,inverse(sk_c6)) = A. [para(17546(b,1),791(b,1,2)),merge(b)].
% 31.66/31.95 17592 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c4) = inverse(sk_c6). [para(901(b,1),4571(b,1)),flip(c),merge(b)].
% 31.66/31.95 17598 inverse(sk_c3) = sk_c8 | multiply(A,inverse(sk_c6)) = A. [para(17592(b,1),901(b,1,2)),merge(b)].
% 31.66/31.95 17639 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c7) = sk_c6. [para(10(b,1),1168(b,1,2)),merge(b)].
% 31.66/31.95 17651 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c4),sk_c6) = sk_c7. [para(17639(b,1),63(a,1,2))].
% 31.66/31.95 17678 inverse(sk_c1) = sk_c2 | inverse(sk_c4) = sk_c7. [para(17651(b,1),1947(b,1)),flip(c),merge(b)].
% 31.66/31.95 17684 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c7) = identity. [para(17678(b,1),997(a,1,2))].
% 31.66/31.95 17735 inverse(sk_c1) = sk_c2 | identity = sk_c8. [para(17684(b,1),9(b,1)),merge(b)].
% 31.66/31.95 17737 inverse(sk_c1) = sk_c2 | multiply(A,sk_c8) = A. [para(17684(b,1),69(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 17743 identity = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(17735(a,1),997(a,1,2))].
% 31.66/31.95 17770 identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(17743(b,1),7(a,1)),merge(b)].
% 31.66/31.95 17771 identity = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7. [para(17743(b,1),20(a,1)),merge(b)].
% 31.66/31.95 17772 identity = sk_c8 | multiply(A,multiply(sk_c1,sk_c2)) = A. [para(17743(b,1),28(a,2,2)),rewrite([28(7),789(9)])].
% 31.66/31.95 17779 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(17770(b,1),1033(a,1,1))].
% 31.66/31.95 17781 identity = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(17770(b,1),1032(a,1,2,1))].
% 31.66/31.95 17817 identity = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(17771(b,1),63(a,1,2))].
% 31.66/31.95 18018 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = sk_c8. [para(17737(b,1),2414(b,1)),merge(b)].
% 31.66/31.95 18039 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c6) = identity. [para(18018(b,1),2(a,1,1))].
% 31.66/31.95 18045 inverse(sk_c1) = sk_c2 | multiply(sk_c8,A) = A. [para(18018(b,1),2414(b,1,1)),merge(b)].
% 31.66/31.95 18313 inverse(sk_c1) = sk_c2 | multiply(A,sk_c7) = A. [para(18039(b,1),71(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 18338 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),A) = A. [para(18045(b,1),63(a,1,2))].
% 31.66/31.95 18412 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = sk_c7. [para(18313(b,1),2414(b,1)),merge(b)].
% 31.66/31.95 18500 inverse(sk_c1) = sk_c2 | multiply(sk_c7,A) = A. [para(18412(b,1),2414(b,1,1)),merge(b)].
% 31.66/31.95 18634 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c7),A) = A. [para(18500(b,1),63(a,1,2))].
% 31.66/31.95 18804 identity = sk_c8 | multiply(sk_c4,sk_c8) = multiply(sk_c1,sk_c2). [para(17772(b,1),17781(b,1,2)),merge(b)].
% 31.66/31.95 19481 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = inverse(sk_c8). [para(18338(b,1),17560(b,1)),merge(b)].
% 31.66/31.95 19744 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = inverse(sk_c7). [para(18634(b,1),17560(b,1)),merge(b)].
% 31.66/31.95 19769 inverse(sk_c1) = sk_c2 | multiply(sk_c6,inverse(sk_c7)) = identity. [para(19744(b,1),997(a,1,2))].
% 31.66/31.95 19907 identity = sk_c8 | multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c1,sk_c2) = sk_c6. [para(18804(b,1),13411(b,1))].
% 31.66/31.95 20189 inverse(sk_c1) = sk_c2 | multiply(sk_c7,inverse(sk_c6)) = identity. [para(19769(b,1),3946(a,1,1)),rewrite([816(6),1033(8)]),flip(b)].
% 31.66/31.95 20365 inverse(sk_c1) = sk_c2 | multiply(sk_c7,inverse(sk_c8)) = identity. [para(19481(b,1),20189(b,1,2)),merge(b)].
% 31.66/31.95 20483 identity != sk_c8 | sk_c8 != A | multiply(sk_c7,inverse(A)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(B,sk_c8) | inverse(B) != sk_c8. [para(2(a,1),11216(b,1,2)),rewrite([789(5),1033(8)]),flip(b)].
% 31.66/31.95 20487 identity != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(B,sk_c8) | inverse(B) != sk_c8. [para(1033(a,1),20483(c,1,2)),flip(b)].
% 31.66/31.95 20489 identity != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != multiply(A,sk_c8). [factor(20487,b,e)].
% 31.66/31.95 20509 identity != sk_c8 | multiply(sk_c7,inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != identity. [para(2(a,1),20489(d,2)),rewrite([1033(6)]),xx(b)].
% 31.66/31.95 20549 inverse(sk_c3) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c6. [para(15(b,1),1170(b,1,2)),merge(b)].
% 31.66/31.95 20568 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c4),sk_c6) = sk_c7. [para(20549(b,1),63(a,1,2))].
% 31.66/31.95 20593 inverse(sk_c3) = sk_c8 | inverse(sk_c4) = sk_c7. [para(20568(b,1),4434(b,1)),flip(c),merge(b)].
% 31.66/31.95 20598 inverse(sk_c3) = sk_c8 | multiply(sk_c4,sk_c7) = identity. [para(20593(b,1),997(a,1,2))].
% 31.66/31.95 20656 inverse(sk_c3) = sk_c8 | identity = sk_c8. [para(20598(b,1),14(b,1)),merge(b)].
% 31.66/31.95 20658 inverse(sk_c3) = sk_c8 | multiply(A,sk_c8) = A. [para(20598(b,1),79(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 20661 identity = sk_c8 | multiply(sk_c8,multiply(sk_c3,A)) = A. [para(20656(a,1),63(a,1,1))].
% 31.66/31.95 20662 identity = sk_c8 | inverse(sk_c8) = sk_c3. [para(20656(a,1),1033(a,1,1))].
% 31.66/31.95 20669 identity = sk_c8 | sk_c4 = sk_c3. [para(20662(b,1),17779(b,1)),flip(c),merge(b)].
% 31.66/31.95 20670 identity = sk_c8 | multiply(sk_c3,sk_c7) = sk_c6. [para(20662(b,1),17817(b,1,1)),merge(b)].
% 31.66/31.95 20674 sk_c4 = sk_c3 | inverse(sk_c1) = sk_c2. [resolve(20669,a,11163,a)].
% 31.66/31.95 20675 sk_c4 = sk_c3 | inverse(sk_c3) = sk_c8. [resolve(20669,a,11162,a)].
% 31.66/31.95 20679 sk_c4 = sk_c3 | inverse(sk_c8) = identity. [para(20669(a,1),816(a,1,1))].
% 31.66/31.95 20742 sk_c4 = sk_c3 | multiply(sk_c2,sk_c1) = identity. [para(20674(b,1),2(a,1,1))].
% 31.66/31.95 20751 sk_c4 = sk_c3 | inverse(sk_c8) = sk_c3. [para(20675(b,1),1033(a,1,1))].
% 31.66/31.95 20778 sk_c4 = sk_c3 | identity = sk_c3. [para(20751(b,1),20679(b,1)),flip(c),merge(b)].
% 31.66/31.95 20781 sk_c4 = sk_c3 | inverse(sk_c3) = identity. [para(20778(b,1),816(a,1,1))].
% 31.66/31.95 20849 sk_c4 = sk_c3 | inverse(sk_c3) = sk_c3. [para(20778(b,1),20781(b,2)),merge(b)].
% 31.66/31.95 20850 sk_c4 = sk_c3 | multiply(sk_c3,sk_c3) = identity. [para(20849(b,1),2(a,1,1))].
% 31.66/31.95 20887 sk_c4 = sk_c3 | multiply(sk_c2,sk_c1) = sk_c8. [para(20669(a,1),20742(b,2)),merge(b)].
% 31.66/31.95 20949 sk_c4 = sk_c3 | multiply(sk_c3,sk_c3) = sk_c8. [para(20669(a,1),20850(b,2)),merge(b)].
% 31.66/31.95 20952 sk_c4 = sk_c3 | multiply(inverse(sk_c2),sk_c8) = sk_c1. [para(20887(b,1),63(a,1,2))].
% 31.66/31.95 21003 sk_c4 = sk_c3 | multiply(inverse(sk_c3),sk_c8) = sk_c3. [para(20949(b,1),63(a,1,2))].
% 31.66/31.95 21130 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = sk_c8. [para(20658(b,1),4571(b,1)),merge(b)].
% 31.66/31.95 21144 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c6) = identity. [para(21130(b,1),2(a,1,1))].
% 31.66/31.95 21150 inverse(sk_c3) = sk_c8 | multiply(sk_c8,A) = A. [para(21130(b,1),4571(b,1,1)),merge(b)].
% 31.66/31.95 21318 sk_c4 = sk_c3 | inverse(sk_c4) = sk_c8 | sk_c1 = sk_c7. [para(20952(b,1),75(b,2)),rewrite([63(13)]),flip(c)].
% 31.66/31.95 21341 sk_c4 = sk_c3 | inverse(sk_c4) = sk_c8 | sk_c3 = sk_c7. [para(21003(b,1),768(b,1))].
% 31.66/31.95 21455 inverse(sk_c3) = sk_c8 | multiply(A,sk_c7) = A. [para(21144(b,1),81(b,1,2)),rewrite([789(10)]),flip(c),merge(b)].
% 31.66/31.95 21483 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),A) = A. [para(21150(b,1),63(a,1,2))].
% 31.66/31.95 21557 inverse(sk_c3) = sk_c8 | inverse(sk_c7) = identity. [para(21455(b,1),2(a,1))].
% 31.66/31.95 21566 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = sk_c7. [para(21455(b,1),4571(b,1)),merge(b)].
% 31.66/31.95 21618 inverse(sk_c3) = sk_c8 | multiply(sk_c7,A) = A. [para(21566(b,1),4571(b,1,1)),merge(b)].
% 31.66/31.95 21722 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c7),A) = A. [para(21618(b,1),63(a,1,2))].
% 31.66/31.95 21749 identity = sk_c8 | multiply(sk_c4,A) = multiply(sk_c3,A). [para(20661(b,1),17781(b,1,2)),merge(b)].
% 31.66/31.95 22316 sk_c4 = sk_c3 | sk_c1 = sk_c7 | inverse(sk_c8) = sk_c4. [para(21318(b,1),1033(a,1,1))].
% 31.66/31.95 22439 sk_c4 = sk_c3 | sk_c3 = sk_c7 | inverse(sk_c8) = sk_c4. [para(21341(b,1),1033(a,1,1))].
% 31.66/31.95 22579 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = inverse(sk_c8). [para(21483(b,1),17598(b,1)),merge(b)].
% 31.66/31.95 22658 multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | multiply(C,multiply(D,sk_c8)) != multiply(inverse(sk_c8),sk_c7) | multiply(inverse(D),inverse(C)) != sk_c8. [para(28(a,1),1162(e,2)),rewrite([3946(22)]),flip(e)].
% 31.66/31.95 22662 multiply(inverse(A),inverse(B)) != sk_c8 | inverse(B) != A | multiply(inverse(B),sk_c7) != sk_c8 | sk_c8 != B | multiply(B,multiply(A,sk_c8)) != multiply(inverse(sk_c8),sk_c7). [factor(22658,a,f),rewrite([1033(7),1033(14)]),flip(b),flip(d)].
% 31.66/31.95 22726 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = inverse(sk_c7). [para(21722(b,1),17598(b,1)),merge(b)].
% 31.66/31.95 22754 inverse(sk_c3) = sk_c8 | inverse(sk_c7) = inverse(sk_c8). [para(22726(b,1),22579(b,1)),merge(b)].
% 31.66/31.95 22783 inverse(sk_c7) = inverse(sk_c8) | inverse(sk_c8) = sk_c3. [para(22754(a,1),1033(a,1,1))].
% 31.66/31.95 22794 inverse(sk_c8) = sk_c3 | multiply(inverse(sk_c8),sk_c7) = identity. [para(22783(a,1),2(a,1,1))].
% 31.66/31.95 23125 identity = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8. [para(21749(b,1),25(b,1)),merge(c)].
% 31.66/31.95 23169 identity = sk_c8 | sk_c6 = sk_c8. [para(23125(b,1),20670(b,1)),flip(c),merge(b)].
% 31.66/31.95 23173 sk_c6 = sk_c8 | multiply(sk_c8,A) = A. [para(23169(a,1),1(a,1,1))].
% 31.66/31.95 23276 sk_c6 = sk_c8 | multiply(inverse(sk_c8),A) = A. [para(23173(b,1),63(a,1,2))].
% 31.66/31.95 23415 sk_c6 = sk_c8 | multiply(sk_c2,sk_c1) = inverse(sk_c8). [para(23276(b,1),7181(b,1)),merge(b)].
% 31.66/31.95 23496 sk_c6 = sk_c8 | multiply(A,inverse(sk_c8)) = A. [para(23415(b,1),7181(b,1,2)),merge(b)].
% 31.66/31.95 23918 sk_c4 = sk_c3 | sk_c1 = sk_c7. [para(22316(c,1),20751(b,1)),merge(c),merge(d)].
% 31.66/31.95 23920 sk_c1 = sk_c7 | inverse(sk_c3) = sk_c8. [para(23918(a,1),5(b,1,1)),merge(c)].
% 31.66/31.95 23924 sk_c1 = sk_c7 | multiply(sk_c3,sk_c7) = sk_c8. [para(23918(a,1),25(b,1,1)),merge(c)].
% 31.66/31.95 24070 sk_c1 = sk_c7 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(23924(b,1),63(a,1,2))].
% 31.66/31.95 24105 sk_c1 = sk_c7 | multiply(sk_c8,sk_c8) = sk_c7. [para(23920(b,1),24070(b,1,1)),merge(b)].
% 31.66/31.95 24108 sk_c1 = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(24105(b,1),63(a,1,2))].
% 31.66/31.95 24132 sk_c1 = sk_c7 | identity != sk_c8. [resolve(24108,b,11161,b)].
% 31.66/31.95 24167 sk_c4 = sk_c3 | sk_c3 = sk_c7. [para(22439(c,1),20751(b,1)),merge(c),merge(d)].
% 31.66/31.95 24169 sk_c3 = sk_c7 | inverse(sk_c3) = sk_c8. [para(24167(a,1),5(b,1,1)),merge(c)].
% 31.66/31.95 24171 sk_c3 = sk_c7 | multiply(sk_c3,sk_c7) = sk_c8. [para(24167(a,1),25(b,1,1)),merge(c)].
% 31.66/31.95 24254 sk_c3 = sk_c7 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(24171(b,1),63(a,1,2))].
% 31.66/31.95 24284 sk_c3 = sk_c7 | multiply(sk_c8,sk_c8) = sk_c7. [para(24169(b,1),24254(b,1,1)),merge(b)].
% 31.66/31.95 24300 sk_c3 = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(24284(b,1),63(a,1,2))].
% 31.66/31.95 24305 sk_c3 = sk_c7 | identity != sk_c8. [resolve(24300,b,11161,b)].
% 31.66/31.95 24618 inverse(sk_c8) = sk_c3 | identity != sk_c8. [para(22794(b,1),11161(b,1)),merge(c)].
% 31.66/31.95 24911 multiply(sk_c8,inverse(A)) != sk_c8 | inverse(sk_c8) != inverse(A) | multiply(inverse(A),sk_c7) != sk_c8 | sk_c8 != A | multiply(inverse(sk_c8),sk_c7) != A. [para(2(a,1),22662(e,1,2)),rewrite([1033(3),789(18)]),flip(b),flip(e)].
% 31.66/31.95 24922 multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c6 = sk_c8. [resolve(24911,a,23496,b),xx(a),xx(c),merge(b)].
% 31.66/31.95 24935 sk_c6 = sk_c8 | multiply(sk_c3,sk_c7) != sk_c8. [para(7302(b,1),24922(a,1,1)),merge(c)].
% 31.66/31.95 24939 sk_c6 = sk_c8 | inverse(sk_c4) = sk_c8. [resolve(24935,b,17,a)].
% 31.66/31.95 24942 sk_c6 = sk_c8 | inverse(sk_c8) = sk_c4. [para(24939(b,1),1033(a,1,1))].
% 31.66/31.95 24957 sk_c6 = sk_c8 | multiply(sk_c4,A) = A. [para(24942(b,1),23276(b,1,1)),merge(b)].
% 31.66/31.95 25062 sk_c6 = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8. [para(24957(b,1),13409(b,1)),flip(c),merge(c)].
% 31.66/31.95 25144 sk_c6 = sk_c8. [resolve(25062,b,24935,b),merge(b)].
% 31.66/31.95 25277 identity = sk_c8 | multiply(sk_c1,sk_c2) = sk_c8. [back_rewrite(19907),rewrite([25144(12)]),merge(c)].
% 31.66/31.95 25997 identity = sk_c8. [para(25277(b,1),17743(b,1)),flip(c),merge(b),merge(c)].
% 31.66/31.95 26227 inverse(sk_c8) = sk_c3. [back_rewrite(24618),rewrite([25997(5)]),xx(b)].
% 31.66/31.95 26312 sk_c3 = sk_c7. [back_rewrite(24305),rewrite([25997(4)]),xx(b)].
% 31.66/31.95 26339 sk_c1 = sk_c7. [back_rewrite(24132),rewrite([25997(4)]),xx(b)].
% 31.66/31.95 26828 inverse(sk_c7) = sk_c8. [back_rewrite(21557),rewrite([26312(1),25997(7)]),merge(b)].
% 31.66/31.95 27032 multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(20509),rewrite([25997(1),26227(6),26312(5),26227(10),26312(9),25997(12)]),xx(a),merge(b)].
% 31.66/31.95 27048 sk_c2 = sk_c8. [back_rewrite(20365),rewrite([26339(1),26828(2),26227(6),26312(5),25997(7)]),flip(a),unit_del(b,27032)].
% 31.66/31.95 27790 sk_c7 = sk_c8. [back_rewrite(15568),rewrite([26312(1),25997(4)]),xx(b)].
% 31.66/31.95 27791 multiply(sk_c8,sk_c8) != sk_c8. [back_rewrite(15192),rewrite([27790(1),27790(4),26227(5),26312(4),27790(4),25997(5),26227(8),26312(7),27790(7),27790(8)]),xx(a),xx(b)].
% 31.66/31.95 27997 sk_c4 = sk_c8. [back_rewrite(8053),rewrite([26227(2),26312(1),27790(1),26227(5),26312(4),27790(4),26312(5),27790(5),26227(6),26312(5),27790(5),25997(7)]),flip(a),unit_del(b,27791)].
% 31.66/31.95 27999 $F. [back_rewrite(7709),rewrite([27997(1),26227(2),26312(1),27790(1),25997(4),27997(5),27790(7),26339(10),27790(10),27048(11)]),xx(a),xx(b),xx(c),unit_del(a,27791)].
% 31.66/31.95
% 31.66/31.95 % SZS output end Refutation
% 31.66/31.95 ============================== end of proof ==========================
% 31.66/31.95
% 31.66/31.95 ============================== STATISTICS ============================
% 31.66/31.95
% 31.66/31.95 Given=4086. Generated=1929559. Kept=27998. proofs=1.
% 31.66/31.95 Usable=1451. Sos=4194. Demods=20. Limbo=2002, Disabled=20380. Hints=0.
% 31.66/31.95 Megabytes=22.16.
% 31.66/31.95 User_CPU=29.95, System_CPU=1.04, Wall_clock=31.
% 31.66/31.95
% 31.66/31.95 ============================== end of statistics =====================
% 31.66/31.95
% 31.66/31.95 ============================== end of search =========================
% 31.66/31.95
% 31.66/31.95 THEOREM PROVED
% 31.66/31.95 % SZS status Unsatisfiable
% 31.66/31.95
% 31.66/31.95 Exiting with 1 proof.
% 31.66/31.95
% 31.66/31.95 Process 12577 exit (max_proofs) Tue Jun 14 05:47:55 2022
% 31.66/31.95 Prover9 interrupted
%------------------------------------------------------------------------------