TSTP Solution File: GRP357-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP357-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:18:45 EDT 2022
% Result : Unsatisfiable 23.18s 23.48s
% Output : Refutation 23.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GRP357-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jun 13 14:56:11 EDT 2022
% 0.10/0.31 % CPUTime :
% 4.45/4.75 ============================== Prover9 ===============================
% 4.45/4.75 Prover9 (32) version 2009-11A, November 2009.
% 4.45/4.75 Process 10035 was started by sandbox on n006.cluster.edu,
% 4.45/4.75 Mon Jun 13 14:56:12 2022
% 4.45/4.75 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9882_n006.cluster.edu".
% 4.45/4.75 ============================== end of head ===========================
% 4.45/4.75
% 4.45/4.75 ============================== INPUT =================================
% 4.45/4.75
% 4.45/4.75 % Reading from file /tmp/Prover9_9882_n006.cluster.edu
% 4.45/4.75
% 4.45/4.75 set(prolog_style_variables).
% 4.45/4.75 set(auto2).
% 4.45/4.75 % set(auto2) -> set(auto).
% 4.45/4.75 % set(auto) -> set(auto_inference).
% 4.45/4.75 % set(auto) -> set(auto_setup).
% 4.45/4.75 % set(auto_setup) -> set(predicate_elim).
% 4.45/4.75 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.45/4.75 % set(auto) -> set(auto_limits).
% 4.45/4.75 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.45/4.75 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.45/4.75 % set(auto) -> set(auto_denials).
% 4.45/4.75 % set(auto) -> set(auto_process).
% 4.45/4.75 % set(auto2) -> assign(new_constants, 1).
% 4.45/4.75 % set(auto2) -> assign(fold_denial_max, 3).
% 4.45/4.75 % set(auto2) -> assign(max_weight, "200.000").
% 4.45/4.75 % set(auto2) -> assign(max_hours, 1).
% 4.45/4.75 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.45/4.75 % set(auto2) -> assign(max_seconds, 0).
% 4.45/4.75 % set(auto2) -> assign(max_minutes, 5).
% 4.45/4.75 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.45/4.75 % set(auto2) -> set(sort_initial_sos).
% 4.45/4.75 % set(auto2) -> assign(sos_limit, -1).
% 4.45/4.75 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.45/4.75 % set(auto2) -> assign(max_megs, 400).
% 4.45/4.75 % set(auto2) -> assign(stats, some).
% 4.45/4.75 % set(auto2) -> clear(echo_input).
% 4.45/4.75 % set(auto2) -> set(quiet).
% 4.45/4.75 % set(auto2) -> clear(print_initial_clauses).
% 4.45/4.75 % set(auto2) -> clear(print_given).
% 4.45/4.75 assign(lrs_ticks,-1).
% 4.45/4.75 assign(sos_limit,10000).
% 4.45/4.75 assign(order,kbo).
% 4.45/4.75 set(lex_order_vars).
% 4.45/4.75 clear(print_given).
% 4.45/4.75
% 4.45/4.75 % formulas(sos). % not echoed (34 formulas)
% 4.45/4.75
% 4.45/4.75 ============================== end of input ==========================
% 4.45/4.75
% 4.45/4.75 % From the command line: assign(max_seconds, 300).
% 4.45/4.75
% 4.45/4.75 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.45/4.75
% 4.45/4.75 % Formulas that are not ordinary clauses:
% 4.45/4.75
% 4.45/4.75 ============================== end of process non-clausal formulas ===
% 4.45/4.75
% 4.45/4.75 ============================== PROCESS INITIAL CLAUSES ===============
% 4.45/4.75
% 4.45/4.75 ============================== PREDICATE ELIMINATION =================
% 4.45/4.75
% 4.45/4.75 ============================== end predicate elimination =============
% 4.45/4.75
% 4.45/4.75 Auto_denials: (non-Horn, no changes).
% 4.45/4.75
% 4.45/4.75 Term ordering decisions:
% 4.45/4.75
% 4.45/4.75 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 4.45/4.75 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c2=1. sk_c6=1. sk_c1=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 4.45/4.75
% 4.45/4.75 ============================== end of process initial clauses ========
% 4.45/4.75
% 4.45/4.75 ============================== CLAUSES FOR SEARCH ====================
% 4.45/4.75
% 4.45/4.75 ============================== end of clauses for search =============
% 4.45/4.75
% 4.45/4.75 ============================== SEARCH ================================
% 4.45/4.75
% 4.45/4.75 % Starting search at 0.02 seconds.
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=52.000, iters=3477
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=50.000, iters=3426
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=48.000, iters=3382
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=47.000, iters=3382
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=46.000, iters=3379
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=45.000, iters=3367
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=44.000, iters=3343
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=43.000, iters=3336
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=42.000, iters=3344
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=41.000, iters=3398
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=40.000, iters=3367
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=39.000, iters=3370
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=38.000, iters=3586
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=37.000, iters=3380
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=36.000, iters=3390
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=35.000, iters=3339
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=34.000, iters=3362
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=33.000, iters=3343
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=32.000, iters=3339
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=31.000, iters=3360
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=30.000, iters=3341
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=29.000, iters=3582
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=28.000, iters=3510
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=27.000, iters=3453
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=24.000, iters=3408
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=23.000, iters=3389
% 4.45/4.75
% 4.45/4.75 Low Water (keep): wt=20.000, iters=3468
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=19.000, iters=3468
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=17.000, iters=3453
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=16.000, iters=3334
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=15.000, iters=3351
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=14.000, iters=3679
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=13.000, iters=3334
% 23.18/23.48
% 23.18/23.48 Low Water (keep): wt=12.000, iters=3337
% 23.18/23.48
% 23.18/23.48 ============================== PROOF =================================
% 23.18/23.48 % SZS status Unsatisfiable
% 23.18/23.48 % SZS output start Refutation
% 23.18/23.48
% 23.18/23.48 % Proof 1 at 21.85 (+ 0.60) seconds.
% 23.18/23.48 % Length of proof is 226.
% 23.18/23.48 % Level of proof is 36.
% 23.18/23.48 % Maximum clause weight is 51.000.
% 23.18/23.48 % Given clauses 3813.
% 23.18/23.48
% 23.18/23.48 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 23.18/23.48 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 23.18/23.48 3 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 23.18/23.48 4 inverse(sk_c8) = sk_c6 | inverse(sk_c4) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 23.18/23.48 5 inverse(sk_c1) = sk_c2 | inverse(sk_c3) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 23.18/23.48 6 inverse(sk_c1) = sk_c2 | inverse(sk_c4) = sk_c8 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 23.18/23.48 7 multiply(sk_c7,sk_c6) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 23.18/23.48 8 multiply(sk_c7,sk_c6) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 23.18/23.48 9 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 23.18/23.48 10 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 23.18/23.48 11 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 23.18/23.48 12 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 23.18/23.48 13 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 23.18/23.48 14 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 23.18/23.48 15 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 23.18/23.48 16 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 23.18/23.48 17 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 23.18/23.48 18 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 23.18/23.48 21 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 23.18/23.48 25 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 23.18/23.48 26 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 23.18/23.48 27 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 23.18/23.48 28 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 23.18/23.48 31 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 23.18/23.48 32 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 23.18/23.48 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 23.18/23.48 34 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 23.18/23.48 62 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 23.18/23.48 63 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 23.18/23.48 64 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 23.18/23.48 65 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 23.18/23.48 66 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 23.18/23.48 71 inverse(sk_c8) = sk_c6 | multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(9(b,1),33(a,1,1)),flip(b)].
% 23.18/23.48 72 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c7)) = multiply(A,sk_c6). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 74 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c3,sk_c8)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 78 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(12(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 80 inverse(sk_c3) = sk_c8 | multiply(A,multiply(sk_c1,sk_c2)) = multiply(A,sk_c8). [para(13(a,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 82 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c1,sk_c2)) = multiply(A,sk_c8). [para(14(a,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 84 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c8,sk_c7)) = multiply(A,sk_c6). [para(15(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 85 inverse(sk_c1) = sk_c2 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(16(b,1),33(a,1,1)),flip(b)].
% 23.18/23.48 86 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c3,sk_c8)) = multiply(A,sk_c7). [para(16(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 87 inverse(sk_c1) = sk_c2 | multiply(sk_c8,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(17(b,1),33(a,1,1)),flip(b)].
% 23.18/23.48 90 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(18(b,1),33(a,2,2)),rewrite([33(8)])].
% 23.18/23.48 105 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(26(b,1),33(a,1,1)),flip(b)].
% 23.18/23.48 140 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8. [resolve(34,j,2,a)].
% 23.18/23.48 280 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8. [factor(140,a,c)].
% 23.18/23.48 768 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),66(a,1,2))].
% 23.18/23.48 772 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c7),sk_c8) = sk_c6. [para(7(a,1),66(a,1,2))].
% 23.18/23.48 773 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c7),sk_c8) = sk_c6. [para(8(a,1),66(a,1,2))].
% 23.18/23.48 774 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),sk_c6) = sk_c7. [para(9(b,1),66(a,1,2))].
% 23.18/23.48 776 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),sk_c7) = sk_c5. [para(11(b,1),66(a,1,2))].
% 23.18/23.48 786 multiply(sk_c8,sk_c7) = sk_c6 | multiply(inverse(sk_c7),sk_c8) = sk_c6. [para(21(a,1),66(a,1,2))].
% 23.18/23.48 796 multiply(sk_c8,sk_c5) = sk_c7 | multiply(inverse(sk_c2),sk_c8) = sk_c7. [para(31(a,1),66(a,1,2))].
% 23.18/23.48 804 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),identity) = sk_c3. [para(62(b,1),66(a,1,2))].
% 23.18/23.48 805 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(66(a,1),66(a,1,2))].
% 23.18/23.48 808 multiply(A,identity) = A. [back_rewrite(768),rewrite([805(4)])].
% 23.18/23.48 809 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c3. [back_rewrite(804),rewrite([808(8)])].
% 23.18/23.48 824 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | sk_c7 != sk_c8 | inverse(inverse(sk_c8)) != sk_c8. [back_rewrite(280),rewrite([808(33)]),flip(h)].
% 23.18/23.48 832 inverse(identity) = identity. [para(808(a,1),2(a,1))].
% 23.18/23.48 896 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = identity. [para(809(b,1),2(a,1,1))].
% 23.18/23.48 899 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c4. [para(63(b,1),66(a,1,2)),rewrite([808(8)])].
% 23.18/23.48 906 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = identity. [para(899(b,1),2(a,1,1))].
% 23.18/23.48 955 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c8,sk_c3)) = A. [para(64(b,1),33(a,2,2)),rewrite([33(8),808(10)])].
% 23.18/23.48 1060 multiply(A,inverse(A)) = identity. [para(805(a,1),2(a,1))].
% 23.18/23.48 1105 multiply(A,multiply(inverse(A),B)) = B. [para(805(a,1),66(a,1))].
% 23.18/23.48 1106 inverse(inverse(A)) = A. [para(805(a,1),808(a,1)),rewrite([808(2)]),flip(a)].
% 23.18/23.48 1123 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(824),rewrite([1106(36)]),xx(i)].
% 23.18/23.48 1178 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c8) = identity. [para(5(b,1),1060(a,1,2))].
% 23.18/23.48 1179 inverse(sk_c1) = sk_c2 | multiply(sk_c4,sk_c8) = identity. [para(6(b,1),1060(a,1,2))].
% 23.18/23.48 1180 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1060(a,1),33(a,1)),flip(a)].
% 23.18/23.48 1438 inverse(sk_c8) = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = sk_c8. [para(1060(a,1),71(b,1,2)),rewrite([808(7)]),flip(b)].
% 23.18/23.48 1565 inverse(sk_c8) = sk_c6 | multiply(A,sk_c7) = A. [para(896(b,1),74(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 23.18/23.48 1639 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = identity. [para(1565(b,1),2(a,1))].
% 23.18/23.48 1659 inverse(sk_c8) = sk_c6 | multiply(sk_c7,A) = A. [para(1639(b,1),66(a,1,1)),rewrite([1(8)])].
% 23.18/23.48 1681 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,multiply(B,sk_c8)) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | sk_c7 != sk_c8. [para(33(a,1),1123(f,1))].
% 23.18/23.48 1706 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c7),A) = A. [para(1659(b,1),66(a,1,2))].
% 23.18/23.48 1850 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7. [para(809(b,1),774(b,1,1)),merge(b)].
% 23.18/23.48 1856 inverse(sk_c8) = sk_c6 | multiply(A,sk_c5) = A. [para(906(b,1),78(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 23.18/23.48 1874 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(1850(b,1),66(a,1,2))].
% 23.18/23.48 1878 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = identity. [para(1856(b,1),2(a,1))].
% 23.18/23.48 1972 inverse(sk_c8) = sk_c6 | multiply(sk_c5,A) = A. [para(1878(b,1),66(a,1,1)),rewrite([1(8)])].
% 23.18/23.48 2014 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c7),multiply(sk_c1,sk_c2)) = sk_c6. [para(772(b,1),80(b,2)),merge(b)].
% 23.18/23.48 2209 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),A) = A. [para(1972(b,1),66(a,1,2))].
% 23.18/23.48 2220 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c7) = sk_c5. [para(809(b,1),776(b,1,1)),merge(b)].
% 23.18/23.48 2223 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c5. [para(776(b,1),1565(b,1)),flip(c),merge(b)].
% 23.18/23.48 2228 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c8. [para(2223(b,1),1106(a,1,1))].
% 23.18/23.48 2230 inverse(sk_c8) = sk_c6 | multiply(sk_c5,sk_c6) = sk_c7. [para(2223(b,1),774(b,1,1)),merge(b)].
% 23.18/23.48 2273 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c7),multiply(sk_c1,sk_c2)) = sk_c6. [para(773(b,1),82(b,2)),merge(b)].
% 23.18/23.48 2425 inverse(sk_c8) = sk_c6 | identity = sk_c8. [para(2228(b,1),1878(b,1)),flip(c),merge(b)].
% 23.18/23.48 2604 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c7) = multiply(sk_c7,sk_c5). [para(17(b,1),85(b,1,2)),merge(b)].
% 23.18/23.48 2614 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c4) = sk_c3. [para(65(b,1),85(b,1,2)),rewrite([808(11)]),flip(c),merge(b)].
% 23.18/23.48 2707 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c3),sk_c5) = sk_c7. [para(2220(b,1),66(a,1,2))].
% 23.18/23.48 2725 inverse(sk_c1) = sk_c2 | multiply(A,sk_c7) = A. [para(1178(b,1),86(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 23.18/23.48 2827 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(2230(b,1),66(a,1,2))].
% 23.18/23.48 2878 inverse(sk_c1) = sk_c2 | multiply(sk_c7,inverse(sk_c5)) = sk_c8. [para(1060(a,1),87(b,1,2)),rewrite([808(7)]),flip(b)].
% 23.18/23.48 2998 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c7),sk_c3) = sk_c4. [para(2614(b,1),66(a,1,2))].
% 23.18/23.48 3241 inverse(sk_c1) = sk_c2 | multiply(A,sk_c6) = multiply(A,sk_c8). [para(2725(b,1),84(b,1,2)),flip(c),merge(b)].
% 23.18/23.48 3458 inverse(sk_c1) = sk_c2 | multiply(A,sk_c5) = A. [para(1179(b,1),90(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 23.18/23.48 4089 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = identity. [para(3458(b,1),2(a,1))].
% 23.18/23.48 4299 inverse(sk_c1) = sk_c2 | multiply(sk_c5,A) = A. [para(4089(b,1),66(a,1,1)),rewrite([1(8)])].
% 23.18/23.48 4367 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c5),A) = A. [para(4299(b,1),66(a,1,2))].
% 23.18/23.48 5620 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1180(a,1),66(a,1,2)),rewrite([808(3)]),flip(a)].
% 23.18/23.48 5801 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(5620(a,1),66(a,1,2)),flip(a)].
% 23.18/23.48 6540 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,multiply(B,sk_c8)) != sk_c7 | multiply(inverse(B),inverse(A)) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(1681),rewrite([5801(30)])].
% 23.18/23.48 7406 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c3. [para(1060(a,1),105(b,1,2)),rewrite([808(8)]),flip(b)].
% 23.18/23.48 7966 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c7. [para(1706(b,1),1565(b,1)),flip(c),merge(b)].
% 23.18/23.48 8025 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c7) = identity. [para(7966(b,1),2(a,1,1))].
% 23.18/23.48 8844 inverse(sk_c8) = sk_c6 | multiply(sk_c8,A) = A. [para(2228(b,1),2209(b,1,1)),merge(b)].
% 23.18/23.48 8917 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),A) = A. [para(8844(b,1),66(a,1,2))].
% 23.18/23.48 9540 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c7. [para(2707(b,1),1856(b,1)),flip(c),merge(b)].
% 23.18/23.48 9547 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(9540(b,1),1874(b,1,1)),merge(b)].
% 23.18/23.48 9578 inverse(sk_c8) = sk_c6 | identity = sk_c6. [para(9547(b,1),8025(b,1)),flip(c),merge(b)].
% 23.18/23.48 9773 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c6. [para(2827(b,1),1565(b,1)),flip(c),merge(b)].
% 23.18/23.48 9783 inverse(sk_c8) = sk_c6 | multiply(sk_c6,A) = A. [para(9773(b,1),2209(b,1,1)),merge(b)].
% 23.18/23.48 9882 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c8. [para(9783(b,1),1438(b,1)),merge(b)].
% 23.18/23.48 9896 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c7) = identity. [para(9882(b,1),2(a,1,1))].
% 23.18/23.48 9994 inverse(sk_c8) = sk_c6 | multiply(A,sk_c6) = A. [para(9896(b,1),72(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 23.18/23.48 10716 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c7. [para(4367(b,1),2725(b,1)),flip(c),merge(b)].
% 23.18/23.48 10729 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c5) = identity. [para(10716(b,1),2(a,1,1))].
% 23.18/23.48 10735 inverse(sk_c1) = sk_c2 | multiply(sk_c7,A) = A. [para(10716(b,1),4367(b,1,1)),merge(b)].
% 23.18/23.48 10839 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c8. [para(10735(b,1),2878(b,1)),merge(b)].
% 23.18/23.48 10843 inverse(sk_c1) = sk_c2 | identity = sk_c8. [para(10839(b,1),4089(b,1)),flip(c),merge(b)].
% 23.18/23.48 10845 inverse(sk_c1) = sk_c2 | multiply(sk_c8,A) = A. [para(10839(b,1),4367(b,1,1)),merge(b)].
% 23.18/23.48 10850 identity = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(10843(a,1),1060(a,1,2))].
% 23.18/23.48 10878 identity = sk_c8 | inverse(sk_c3) = sk_c8. [para(10850(b,1),13(a,1)),merge(b)].
% 23.18/23.48 10879 identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(10850(b,1),14(a,1)),merge(b)].
% 23.18/23.48 10880 identity = sk_c8 | multiply(sk_c8,sk_c7) = sk_c6. [para(10850(b,1),25(a,1)),merge(b)].
% 23.18/23.48 10881 identity = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7. [para(10850(b,1),27(a,1)),merge(b)].
% 23.18/23.48 10898 identity = sk_c8 | inverse(sk_c8) = sk_c3. [para(10878(b,1),1106(a,1,1))].
% 23.18/23.48 10903 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(10879(b,1),1106(a,1,1))].
% 23.18/23.48 10914 identity = sk_c8 | sk_c3 = sk_c6. [para(10898(b,1),2425(a,1)),merge(c)].
% 23.18/23.48 10917 sk_c3 = sk_c6 | inverse(sk_c8) = identity. [para(10914(a,1),832(a,1,1))].
% 23.18/23.48 10994 identity = sk_c8 | sk_c4 = sk_c6. [para(10903(b,1),2425(a,1)),merge(c)].
% 23.18/23.48 10998 sk_c4 = sk_c6 | inverse(sk_c8) = identity. [para(10994(a,1),832(a,1,1))].
% 23.18/23.48 11101 sk_c3 = sk_c6 | identity = sk_c6. [para(10917(b,1),9578(a,1)),merge(c)].
% 23.18/23.48 11105 sk_c3 = sk_c6 | multiply(sk_c6,A) = A. [para(11101(b,1),1(a,1,1))].
% 23.18/23.48 11153 sk_c4 = sk_c6 | identity = sk_c6. [para(10998(b,1),9578(a,1)),merge(c)].
% 23.18/23.48 11155 sk_c4 = sk_c6 | multiply(sk_c6,A) = A. [para(11153(b,1),1(a,1,1))].
% 23.18/23.48 11227 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | sk_c7 != A | multiply(sk_c8,inverse(A)) != sk_c8 | sk_c7 != sk_c8. [para(2(a,1),6540(f,1,2)),rewrite([808(25),1106(28)]),flip(f)].
% 23.18/23.48 11247 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | sk_c7 != sk_c8. [para(1106(a,1),11227(g,1,2)),flip(f)].
% 23.18/23.48 11248 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(A),sk_c8) != sk_c7 | sk_c8 != A | sk_c7 != sk_c8. [para(1105(a,1),11247(g,1)),rewrite([5801(27),1106(27)]),flip(g)].
% 23.18/23.48 11292 identity = sk_c8 | multiply(inverse(sk_c8),sk_c6) = sk_c7. [para(10880(b,1),66(a,1,2))].
% 23.18/23.48 11316 identity = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c5. [para(10881(b,1),66(a,1,2))].
% 23.18/23.48 12421 identity = sk_c8 | multiply(sk_c3,sk_c6) = sk_c7. [para(10898(b,1),11292(b,1,1)),merge(b)].
% 23.18/23.48 12428 identity = sk_c8 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(12421(b,1),66(a,1,2))].
% 23.18/23.48 12434 identity = sk_c8 | multiply(sk_c3,sk_c7) = sk_c5. [para(10898(b,1),11316(b,1,1)),merge(b)].
% 23.18/23.48 12438 identity = sk_c8 | multiply(inverse(sk_c3),sk_c5) = sk_c7. [para(12434(b,1),66(a,1,2))].
% 23.18/23.48 13397 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | sk_c7 != sk_c8. [para(5801(a,1),11248(f,1,1)),rewrite([33(28)]),flip(g)].
% 23.18/23.48 13550 identity = sk_c8 | multiply(inverse(sk_c7),sk_c3) = inverse(sk_c6). [para(12428(b,1),5801(a,1,1)),rewrite([1106(10)]),flip(b)].
% 23.18/23.48 13554 identity = sk_c8 | multiply(inverse(sk_c5),sk_c3) = inverse(sk_c7). [para(12438(b,1),5801(a,1,1)),rewrite([1106(10)]),flip(b)].
% 23.18/23.48 13601 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7 | sk_c7 != sk_c8. [factor(13397,a,g)].
% 23.18/23.48 13980 inverse(sk_c8) = sk_c6. [para(8917(b,1),9994(b,1)),flip(c),merge(b),merge(c)].
% 23.18/23.48 14062 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7 | sk_c7 != sk_c8. [back_rewrite(13601),rewrite([13980(7)]),xx(b)].
% 23.18/23.48 14842 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c7,sk_c6) = sk_c3. [back_rewrite(7406),rewrite([13980(8)])].
% 23.18/23.48 15512 inverse(sk_c6) = sk_c8. [para(13980(a,1),1106(a,1,1))].
% 23.18/23.48 15513 multiply(sk_c8,sk_c6) = identity. [para(13980(a,1),1060(a,1,2))].
% 23.18/23.48 15576 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c7 | sk_c7 != sk_c8. [back_rewrite(14062),rewrite([15512(21)])].
% 23.18/23.48 15598 identity = sk_c8 | multiply(inverse(sk_c7),sk_c3) = sk_c8. [back_rewrite(13550),rewrite([15512(9)])].
% 23.18/23.48 15715 multiply(sk_c8,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c8. [para(786(b,1),5801(a,1,1)),rewrite([15512(7),13980(8),1106(10)]),flip(b)].
% 23.18/23.48 16778 inverse(sk_c1) = sk_c2 | multiply(A,sk_c3) = A. [para(10845(b,1),955(b,1,2)),merge(b)].
% 23.18/23.48 19293 inverse(sk_c1) = sk_c2 | inverse(sk_c7) = sk_c4. [para(16778(b,1),2998(b,1)),merge(b)].
% 23.18/23.48 19318 inverse(sk_c7) = sk_c4 | inverse(sk_c2) = sk_c1. [para(19293(a,1),1106(a,1,1))].
% 23.18/23.48 19347 inverse(sk_c7) = sk_c4 | multiply(sk_c8,sk_c5) = sk_c7 | multiply(sk_c1,sk_c8) = sk_c7. [para(19318(b,1),796(b,1,1))].
% 23.18/23.48 19755 inverse(sk_c1) = sk_c2 | multiply(sk_c3,sk_c7) = identity. [para(10729(b,1),2604(b,2)),merge(b)].
% 23.18/23.48 20644 inverse(sk_c1) = sk_c2 | inverse(sk_c3) = sk_c7. [para(19755(b,1),66(a,1,2)),rewrite([808(8)])].
% 23.18/23.48 20650 inverse(sk_c1) = sk_c2 | inverse(sk_c7) = sk_c3. [para(20644(b,1),1106(a,1,1))].
% 23.18/23.48 20653 inverse(sk_c7) = sk_c3 | inverse(sk_c2) = sk_c1. [para(20650(a,1),1106(a,1,1))].
% 23.18/23.48 20654 inverse(sk_c7) = sk_c3 | multiply(sk_c1,sk_c2) = identity. [para(20650(a,1),1060(a,1,2))].
% 23.18/23.48 20936 inverse(sk_c1) = sk_c2 | multiply(sk_c5,sk_c8) = sk_c6. [para(3241(b,1),4299(b,1)),merge(b)].
% 23.18/23.48 21119 inverse(sk_c7) = sk_c3 | multiply(A,multiply(sk_c1,sk_c2)) = A. [para(20654(b,1),33(a,2,2)),rewrite([33(8),808(10)])].
% 23.18/23.48 21285 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c8) = identity. [para(20936(b,1),87(b,1,2)),rewrite([15513(11)]),flip(c),merge(b)].
% 23.18/23.48 21442 inverse(sk_c1) = sk_c2 | multiply(sk_c7,sk_c6) = identity. [para(21285(b,1),3241(b,2)),merge(b)].
% 23.18/23.48 21500 inverse(sk_c1) = sk_c2 | inverse(sk_c7) = sk_c6. [para(21442(b,1),66(a,1,2)),rewrite([808(8)])].
% 23.18/23.48 21511 inverse(sk_c7) = sk_c6 | multiply(sk_c1,sk_c2) = identity. [para(21500(a,1),1060(a,1,2))].
% 23.18/23.48 21533 inverse(sk_c7) = sk_c6 | inverse(sk_c3) = sk_c8. [para(21511(b,1),2014(b,1,2)),rewrite([808(12)]),merge(c)].
% 23.18/23.48 21534 inverse(sk_c7) = sk_c6 | inverse(sk_c4) = sk_c8. [para(21511(b,1),2273(b,1,2)),rewrite([808(12)]),merge(c)].
% 23.18/23.48 21545 inverse(sk_c7) = sk_c6 | sk_c3 = sk_c6. [para(21533(b,1),1106(a,1,1)),rewrite([13980(6)]),flip(b)].
% 23.18/23.48 21548 sk_c3 = sk_c6 | multiply(sk_c6,sk_c7) = identity. [para(21545(a,1),2(a,1,1))].
% 23.18/23.48 21558 inverse(sk_c7) = sk_c6 | sk_c4 = sk_c6. [para(21534(b,1),1106(a,1,1)),rewrite([13980(6)]),flip(b)].
% 23.18/23.48 21559 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c8) = identity. [para(21534(b,1),1060(a,1,2))].
% 23.18/23.48 21567 sk_c4 = sk_c6 | multiply(sk_c6,sk_c7) = identity. [para(21558(a,1),2(a,1,1))].
% 23.18/23.48 21578 sk_c3 = sk_c6 | identity = sk_c7. [para(21548(b,1),11105(b,1)),merge(b)].
% 23.18/23.48 21586 sk_c3 = sk_c6 | inverse(sk_c7) = identity. [para(21578(b,1),832(a,1,1))].
% 23.18/23.48 21697 sk_c3 = sk_c6 | inverse(sk_c7) = sk_c7. [para(21578(b,1),21586(b,2)),merge(b)].
% 23.18/23.48 21776 sk_c3 = sk_c6 | multiply(sk_c7,sk_c7) = identity. [para(21697(b,1),2(a,1,1))].
% 23.18/23.48 21783 sk_c4 = sk_c6 | identity = sk_c7. [para(21567(b,1),11155(b,1)),merge(b)].
% 23.18/23.48 21789 sk_c4 = sk_c6 | inverse(sk_c7) = identity. [para(21783(b,1),832(a,1,1))].
% 23.18/23.48 21866 sk_c4 = sk_c6 | inverse(sk_c7) = sk_c7. [para(21783(b,1),21789(b,2)),merge(b)].
% 23.18/23.48 21925 sk_c4 = sk_c6 | multiply(sk_c7,sk_c7) = identity. [para(21866(b,1),2(a,1,1))].
% 23.18/23.48 22146 sk_c3 = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(11101(b,1),21776(b,2)),merge(b)].
% 23.18/23.48 22563 sk_c4 = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(11153(b,1),21925(b,2)),merge(b)].
% 23.18/23.48 22583 sk_c3 = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(22146(b,1),66(a,1,2))].
% 23.18/23.48 22609 sk_c4 = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(22563(b,1),66(a,1,2))].
% 23.18/23.48 22642 inverse(sk_c7) = sk_c6 | multiply(sk_c1,sk_c2) = sk_c8 | identity = sk_c5. [para(21559(b,1),28(b,1))].
% 23.18/23.48 22643 inverse(sk_c7) = sk_c6 | multiply(sk_c2,sk_c7) = sk_c8 | identity = sk_c5. [para(21559(b,1),32(b,1))].
% 23.18/23.48 24079 identity = sk_c8 | multiply(sk_c5,inverse(sk_c7)) = sk_c3. [para(13554(b,1),66(a,1,2)),rewrite([1106(6)])].
% 23.18/23.48 24383 multiply(sk_c7,sk_c6) = sk_c3 | identity = sk_c8. [para(14842(a,1),10850(b,1)),flip(c),merge(c)].
% 23.18/23.48 24390 identity = sk_c8 | multiply(inverse(sk_c7),sk_c3) = sk_c6. [para(24383(a,1),66(a,1,2))].
% 23.18/23.48 24402 identity = sk_c8 | sk_c6 = sk_c8. [para(24390(b,1),15598(b,1)),merge(b)].
% 23.18/23.48 24405 sk_c6 = sk_c8 | identity = sk_c6. [para(24402(a,1),832(a,1,1)),rewrite([13980(5)]),flip(b)].
% 23.18/23.48 24446 sk_c6 = sk_c8. [para(24405(b,1),24402(a,1)),merge(b),merge(c)].
% 23.18/23.48 25325 inverse(sk_c7) = sk_c8 | multiply(sk_c2,sk_c7) = sk_c8 | identity = sk_c5. [back_rewrite(22643),rewrite([24446(3)])].
% 23.18/23.48 25326 inverse(sk_c7) = sk_c8 | multiply(sk_c1,sk_c2) = sk_c8 | identity = sk_c5. [back_rewrite(22642),rewrite([24446(3)])].
% 23.18/23.48 25354 sk_c4 = sk_c8 | multiply(inverse(sk_c7),sk_c8) = sk_c7. [back_rewrite(22609),rewrite([24446(2),24446(6)])].
% 23.18/23.48 25369 sk_c3 = sk_c8 | multiply(inverse(sk_c7),sk_c8) = sk_c7. [back_rewrite(22583),rewrite([24446(2),24446(6)])].
% 23.18/23.48 26977 multiply(sk_c8,sk_c7) = sk_c8. [back_rewrite(15715),rewrite([24446(4),24446(6)]),merge(b)].
% 23.18/23.48 27038 multiply(sk_c7,sk_c8) != sk_c8 | inverse(sk_c7) != sk_c8 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c7 | sk_c7 != sk_c8. [back_rewrite(15576),rewrite([24446(2),24446(8),24446(10),26977(12),26977(15),24446(14)]),xx(c),xx(d)].
% 23.18/23.48 27065 multiply(sk_c8,sk_c8) = identity. [back_rewrite(15513),rewrite([24446(2)])].
% 23.18/23.48 27813 inverse(sk_c8) = sk_c8. [back_rewrite(13980),rewrite([24446(3)])].
% 23.18/23.48 28420 identity = sk_c7. [para(26977(a,1),66(a,1,2)),rewrite([27813(2),27065(3)])].
% 23.18/23.48 28580 multiply(sk_c8,sk_c8) = sk_c7. [back_rewrite(27065),rewrite([28420(4)])].
% 23.18/23.48 28621 inverse(sk_c7) = sk_c8 | multiply(sk_c1,sk_c2) = sk_c8 | sk_c5 = sk_c7. [back_rewrite(25326),rewrite([28420(10)]),flip(c)].
% 23.18/23.48 28622 inverse(sk_c7) = sk_c8 | multiply(sk_c2,sk_c7) = sk_c8 | sk_c5 = sk_c7. [back_rewrite(25325),rewrite([28420(10)]),flip(c)].
% 23.18/23.48 28656 sk_c7 = sk_c8 | multiply(sk_c5,inverse(sk_c7)) = sk_c3. [back_rewrite(24079),rewrite([28420(1)])].
% 23.18/23.48 28969 inverse(sk_c7) = sk_c7. [back_rewrite(832),rewrite([28420(1),28420(3)])].
% 23.18/23.48 28970 multiply(A,sk_c7) = A. [back_rewrite(808),rewrite([28420(1)])].
% 23.18/23.48 28972 multiply(sk_c7,A) = A. [back_rewrite(1),rewrite([28420(1)])].
% 23.18/23.48 28973 sk_c7 != sk_c8. [back_rewrite(27038),rewrite([28972(3),28969(5),28969(9),28972(10),28580(9)]),xx(a),xx(c),merge(b)].
% 23.18/23.48 28976 sk_c3 = sk_c8. [back_rewrite(25369),rewrite([28969(5),28972(6)]),flip(b),unit_del(b,28973)].
% 23.18/23.48 28977 sk_c4 = sk_c8. [back_rewrite(25354),rewrite([28969(5),28972(6)]),flip(b),unit_del(b,28973)].
% 23.18/23.48 28995 sk_c5 = sk_c8. [back_rewrite(28656),rewrite([28969(6),28970(6),28976(5)]),unit_del(a,28973)].
% 23.18/23.48 28996 sk_c2 = sk_c8. [back_rewrite(28622),rewrite([28969(2),28970(6),28995(7)]),flip(c),merge(c),unit_del(a,28973)].
% 23.18/23.48 28997 multiply(sk_c1,sk_c8) = sk_c8. [back_rewrite(28621),rewrite([28969(2),28996(5),28995(9)]),flip(c),merge(c),unit_del(a,28973)].
% 23.18/23.48 29000 multiply(A,sk_c8) = A. [back_rewrite(21119),rewrite([28969(2),28976(2),28996(5),28997(6)]),unit_del(a,28973)].
% 23.18/23.48 29003 sk_c1 = sk_c8. [back_rewrite(20653),rewrite([28969(2),28976(2),28996(4),27813(5)]),flip(b),unit_del(a,28973)].
% 23.18/23.48 29004 $F. [back_rewrite(19347),rewrite([28969(2),28977(2),28995(5),29000(6),29003(7),29000(9)]),flip(b),flip(c),merge(b),merge(c),unit_del(a,28973)].
% 23.18/23.48
% 23.18/23.48 % SZS output end Refutation
% 23.18/23.48 ============================== end of proof ==========================
% 23.18/23.48
% 23.18/23.48 ============================== STATISTICS ============================
% 23.18/23.48
% 23.18/23.48 Given=3813. Generated=954621. Kept=29003. proofs=1.
% 23.18/23.48 Usable=356. Sos=2752. Demods=30. Limbo=35, Disabled=25894. Hints=0.
% 23.18/23.48 Megabytes=24.24.
% 23.18/23.48 User_CPU=21.85, System_CPU=0.60, Wall_clock=23.
% 23.18/23.48
% 23.18/23.48 ============================== end of statistics =====================
% 23.18/23.48
% 23.18/23.48 ============================== end of search =========================
% 23.18/23.48
% 23.18/23.48 THEOREM PROVED
% 23.18/23.48 % SZS status Unsatisfiable
% 23.18/23.48
% 23.18/23.48 Exiting with 1 proof.
% 23.18/23.48
% 23.18/23.48 Process 10035 exit (max_proofs) Mon Jun 13 14:56:35 2022
% 23.18/23.48 Prover9 interrupted
%------------------------------------------------------------------------------