TSTP Solution File: GRP324-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 11:18:38 EDT 2022
% Result : Unsatisfiable 36.42s 36.72s
% Output : Refutation 36.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP324-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.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 03:14:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.38/2.66 ============================== Prover9 ===============================
% 2.38/2.66 Prover9 (32) version 2009-11A, November 2009.
% 2.38/2.66 Process 14544 was started by sandbox2 on n023.cluster.edu,
% 2.38/2.66 Tue Jun 14 03:14:06 2022
% 2.38/2.66 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14391_n023.cluster.edu".
% 2.38/2.66 ============================== end of head ===========================
% 2.38/2.66
% 2.38/2.66 ============================== INPUT =================================
% 2.38/2.66
% 2.38/2.66 % Reading from file /tmp/Prover9_14391_n023.cluster.edu
% 2.38/2.66
% 2.38/2.66 set(prolog_style_variables).
% 2.38/2.66 set(auto2).
% 2.38/2.66 % set(auto2) -> set(auto).
% 2.38/2.66 % set(auto) -> set(auto_inference).
% 2.38/2.66 % set(auto) -> set(auto_setup).
% 2.38/2.66 % set(auto_setup) -> set(predicate_elim).
% 2.38/2.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.38/2.66 % set(auto) -> set(auto_limits).
% 2.38/2.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.38/2.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.38/2.66 % set(auto) -> set(auto_denials).
% 2.38/2.66 % set(auto) -> set(auto_process).
% 2.38/2.66 % set(auto2) -> assign(new_constants, 1).
% 2.38/2.66 % set(auto2) -> assign(fold_denial_max, 3).
% 2.38/2.66 % set(auto2) -> assign(max_weight, "200.000").
% 2.38/2.66 % set(auto2) -> assign(max_hours, 1).
% 2.38/2.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.38/2.66 % set(auto2) -> assign(max_seconds, 0).
% 2.38/2.66 % set(auto2) -> assign(max_minutes, 5).
% 2.38/2.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.38/2.66 % set(auto2) -> set(sort_initial_sos).
% 2.38/2.66 % set(auto2) -> assign(sos_limit, -1).
% 2.38/2.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.38/2.66 % set(auto2) -> assign(max_megs, 400).
% 2.38/2.66 % set(auto2) -> assign(stats, some).
% 2.38/2.66 % set(auto2) -> clear(echo_input).
% 2.38/2.66 % set(auto2) -> set(quiet).
% 2.38/2.66 % set(auto2) -> clear(print_initial_clauses).
% 2.38/2.66 % set(auto2) -> clear(print_given).
% 2.38/2.66 assign(lrs_ticks,-1).
% 2.38/2.66 assign(sos_limit,10000).
% 2.38/2.66 assign(order,kbo).
% 2.38/2.66 set(lex_order_vars).
% 2.38/2.66 clear(print_given).
% 2.38/2.66
% 2.38/2.66 % formulas(sos). % not echoed (40 formulas)
% 2.38/2.66
% 2.38/2.66 ============================== end of input ==========================
% 2.38/2.66
% 2.38/2.66 % From the command line: assign(max_seconds, 300).
% 2.38/2.66
% 2.38/2.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.38/2.66
% 2.38/2.66 % Formulas that are not ordinary clauses:
% 2.38/2.66
% 2.38/2.66 ============================== end of process non-clausal formulas ===
% 2.38/2.66
% 2.38/2.66 ============================== PROCESS INITIAL CLAUSES ===============
% 2.38/2.66
% 2.38/2.66 ============================== PREDICATE ELIMINATION =================
% 2.38/2.66
% 2.38/2.66 ============================== end predicate elimination =============
% 2.38/2.66
% 2.38/2.66 Auto_denials: (non-Horn, no changes).
% 2.38/2.66
% 2.38/2.66 Term ordering decisions:
% 2.38/2.66
% 2.38/2.66 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 2.38/2.66 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 2.38/2.66
% 2.38/2.66 ============================== end of process initial clauses ========
% 2.38/2.66
% 2.38/2.66 ============================== CLAUSES FOR SEARCH ====================
% 2.38/2.66
% 2.38/2.66 ============================== end of clauses for search =============
% 2.38/2.66
% 2.38/2.66 ============================== SEARCH ================================
% 2.38/2.66
% 2.38/2.66 % Starting search at 0.02 seconds.
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=56.000, iters=3559
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=52.000, iters=3390
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=51.000, iters=3409
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=49.000, iters=3386
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=48.000, iters=3541
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=47.000, iters=3546
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=46.000, iters=3496
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=43.000, iters=3373
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=42.000, iters=3377
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=41.000, iters=3362
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=40.000, iters=3391
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=39.000, iters=3336
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=38.000, iters=3348
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=37.000, iters=3349
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=36.000, iters=3373
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=35.000, iters=3364
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=34.000, iters=3340
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=33.000, iters=3444
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=32.000, iters=3366
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=30.000, iters=3336
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=29.000, iters=3337
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=27.000, iters=3346
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=23.000, iters=3349
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=18.000, iters=3372
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=17.000, iters=3352
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=16.000, iters=3384
% 2.38/2.66
% 2.38/2.66 Low Water (keep): wt=15.000, iters=3364
% 36.42/36.72
% 36.42/36.72 Low Water (keep): wt=14.000, iters=3334
% 36.42/36.72
% 36.42/36.72 Low Water (keep): wt=13.000, iters=3344
% 36.42/36.72
% 36.42/36.72 Low Water (keep): wt=12.000, iters=3335
% 36.42/36.72
% 36.42/36.72 ============================== PROOF =================================
% 36.42/36.72 % SZS status Unsatisfiable
% 36.42/36.72 % SZS output start Refutation
% 36.42/36.72
% 36.42/36.72 % Proof 1 at 34.76 (+ 0.92) seconds.
% 36.42/36.72 % Length of proof is 164.
% 36.42/36.72 % Level of proof is 31.
% 36.42/36.72 % Maximum clause weight is 56.000.
% 36.42/36.72 % Given clauses 4377.
% 36.42/36.72
% 36.42/36.72 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 36.42/36.72 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 36.42/36.72 3 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 36.42/36.72 4 inverse(sk_c1) = sk_c7 | inverse(sk_c8) = sk_c6 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 36.42/36.72 5 inverse(sk_c1) = sk_c7 | inverse(sk_c5) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 36.42/36.72 7 inverse(sk_c2) = sk_c8 | inverse(sk_c8) = sk_c6 # label(prove_this_34) # label(negated_conjecture). [assumption].
% 36.42/36.72 8 inverse(sk_c2) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 36.42/36.72 10 multiply(sk_c7,sk_c8) = sk_c6 | inverse(sk_c8) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 36.42/36.72 12 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 36.42/36.72 13 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c8) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 36.42/36.72 14 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 36.42/36.72 15 inverse(sk_c1) = sk_c7 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 36.42/36.72 16 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 36.42/36.72 17 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 36.42/36.72 19 multiply(sk_c8,sk_c3) = sk_c7 | inverse(sk_c8) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 36.42/36.72 22 multiply(sk_c2,sk_c8) = sk_c3 | inverse(sk_c8) = sk_c6 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 36.42/36.72 26 inverse(sk_c2) = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_35) # label(negated_conjecture). [assumption].
% 36.42/36.72 27 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 36.42/36.72 31 multiply(sk_c1,sk_c7) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 36.42/36.72 34 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 36.42/36.72 35 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 36.42/36.72 38 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 36.42/36.72 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 36.42/36.72 40 multiply(sk_c7,sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(D,sk_c8) != sk_c7 | inverse(D) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(E,sk_c7) != sk_c6 | inverse(E) != sk_c7 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 36.42/36.72 69 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c1) = identity. [para(4(a,1),2(a,1,1))].
% 36.42/36.72 72 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c2) = identity. [para(7(a,1),2(a,1,1))].
% 36.42/36.72 74 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 36.42/36.72 77 inverse(sk_c8) = sk_c6 | multiply(sk_c7,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(10(a,1),39(a,1,1)),flip(b)].
% 36.42/36.72 78 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c7,sk_c8)) = multiply(A,sk_c6). [para(10(a,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 84 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c8). [para(13(a,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 90 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c7). [para(16(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 92 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c5,sk_c7)) = multiply(A,sk_c6). [para(17(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 95 inverse(sk_c8) = sk_c6 | multiply(sk_c8,multiply(sk_c3,A)) = multiply(sk_c7,A). [para(19(a,1),39(a,1,1)),flip(b)].
% 36.42/36.72 96 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,sk_c7). [para(19(a,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 102 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(22(a,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 110 inverse(sk_c2) = sk_c8 | multiply(A,multiply(sk_c5,sk_c7)) = multiply(A,sk_c6). [para(26(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.42/36.72 125 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(34(b,1),39(a,1,1)),flip(b)].
% 36.42/36.72 128 multiply(sk_c8,sk_c3) = sk_c7 | multiply(A,multiply(sk_c5,sk_c7)) = multiply(A,sk_c6). [para(35(b,1),39(a,2,2)),rewrite([39(9)])].
% 36.42/36.72 133 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c5,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(38(b,1),39(a,1,1)),flip(b)].
% 36.42/36.72 141 multiply(sk_c7,sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c8,multiply(B,multiply(C,sk_c8))) != sk_c7 | inverse(multiply(B,C)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(D,sk_c8) != sk_c7 | inverse(D) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(E,sk_c7) != sk_c6 | inverse(E) != sk_c7. [resolve(40,e,39,a)].
% 36.42/36.72 961 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),74(a,1,2))].
% 36.42/36.72 973 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c8),sk_c6) = sk_c7. [para(15(b,1),74(a,1,2))].
% 36.42/36.72 985 multiply(sk_c8,sk_c7) = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(27(a,1),74(a,1,2))].
% 36.42/36.72 989 multiply(sk_c1,sk_c7) = sk_c8 | multiply(inverse(sk_c4),sk_c7) = sk_c8. [para(31(b,1),74(a,1,2))].
% 36.42/36.72 999 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(74(a,1),74(a,1,2))].
% 36.42/36.72 1000 multiply(A,identity) = A. [back_rewrite(961),rewrite([999(4)])].
% 36.42/36.72 1013 inverse(identity) = identity. [para(1000(a,1),2(a,1))].
% 36.42/36.72 1091 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c1. [para(69(b,1),74(a,1,2)),rewrite([1000(8)])].
% 36.42/36.72 1092 inverse(sk_c8) = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(1091(b,1),2(a,1,1))].
% 36.42/36.72 1109 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c2. [para(72(b,1),74(a,1,2)),rewrite([1000(8)])].
% 36.42/36.72 1126 inverse(sk_c8) = sk_c6 | multiply(sk_c2,sk_c8) = identity. [para(1109(b,1),2(a,1,1))].
% 36.42/36.72 1172 multiply(A,inverse(A)) = identity. [para(999(a,1),2(a,1))].
% 36.42/36.72 1231 multiply(A,multiply(inverse(A),B)) = B. [para(999(a,1),74(a,1))].
% 36.42/36.72 1232 inverse(inverse(A)) = A. [para(999(a,1),1000(a,1)),rewrite([1000(2)]),flip(a)].
% 36.42/36.72 1306 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c8) = identity. [para(3(b,1),1172(a,1,2))].
% 36.42/36.72 1307 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c7) = identity. [para(5(b,1),1172(a,1,2))].
% 36.42/36.72 1309 inverse(sk_c2) = sk_c8 | multiply(sk_c5,sk_c7) = identity. [para(8(b,1),1172(a,1,2))].
% 36.42/36.72 1310 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1172(a,1),39(a,1)),flip(a)].
% 36.42/36.72 1388 inverse(sk_c8) = sk_c6 | multiply(sk_c6,sk_c2) = sk_c7. [para(72(b,1),77(b,1,2)),rewrite([1000(11)]),flip(c),merge(b)].
% 36.42/36.72 1435 inverse(sk_c8) = sk_c6 | identity = sk_c8. [para(1092(b,1),13(a,1)),merge(c)].
% 36.42/36.72 1440 identity = sk_c8 | multiply(sk_c8,sk_c6) = identity. [para(1435(a,1),1172(a,1,2))].
% 36.42/36.72 1811 inverse(sk_c8) = sk_c6 | multiply(A,sk_c8) = A. [para(1092(b,1),84(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 2638 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c6),sk_c7) = sk_c2. [para(1388(b,1),74(a,1,2))].
% 36.42/36.72 2716 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = identity. [para(1811(b,1),2(a,1))].
% 36.42/36.72 2763 inverse(sk_c1) = sk_c7 | multiply(A,sk_c7) = A. [para(1306(b,1),90(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 2909 inverse(sk_c8) = sk_c6 | multiply(sk_c8,A) = A. [para(2716(b,1),74(a,1,1)),rewrite([1(8)])].
% 36.42/36.72 2985 inverse(sk_c1) = sk_c7 | multiply(A,sk_c6) = A. [para(1307(b,1),92(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 3764 inverse(sk_c8) = sk_c6 | multiply(sk_c7,inverse(sk_c3)) = sk_c8. [para(1172(a,1),95(b,1,2)),rewrite([1000(7)]),flip(b)].
% 36.42/36.72 3899 inverse(sk_c1) = sk_c7 | sk_c6 = sk_c8. [para(2763(b,1),15(b,1)),flip(c),merge(b)].
% 36.42/36.72 3966 sk_c6 = sk_c8 | multiply(sk_c1,sk_c7) = identity. [para(3899(a,1),1172(a,1,2))].
% 36.42/36.72 4911 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),A) = A. [para(2909(b,1),74(a,1,2))].
% 36.42/36.72 4978 inverse(sk_c8) = sk_c6 | multiply(A,sk_c3) = A. [para(1126(b,1),102(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 5073 inverse(sk_c1) = sk_c7 | identity = sk_c8. [para(2985(b,1),1440(b,1)),flip(c),merge(c)].
% 36.42/36.72 5103 identity = sk_c8 | inverse(sk_c7) = sk_c1. [para(5073(a,1),1232(a,1,1))].
% 36.42/36.72 5104 identity = sk_c8 | multiply(sk_c1,sk_c7) = identity. [para(5073(a,1),1172(a,1,2))].
% 36.42/36.72 5320 identity = sk_c8 | inverse(sk_c4) = sk_c8. [para(5104(b,1),12(a,1)),merge(b)].
% 36.42/36.72 5321 identity = sk_c8 | inverse(sk_c5) = sk_c7. [para(5104(b,1),14(a,1)),merge(b)].
% 36.42/36.72 5342 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(5320(b,1),1232(a,1,1))].
% 36.42/36.72 5456 identity = sk_c8 | multiply(sk_c7,sk_c5) = identity. [para(5321(b,1),2(a,1,1))].
% 36.42/36.72 5458 identity = sk_c8 | inverse(sk_c7) = sk_c5. [para(5321(b,1),1232(a,1,1))].
% 36.42/36.72 5462 identity = sk_c8 | sk_c4 = sk_c6. [para(5342(b,1),1435(a,1)),merge(c)].
% 36.42/36.72 5473 sk_c4 = sk_c6 | inverse(sk_c8) = identity. [para(5462(a,1),1013(a,1,1))].
% 36.42/36.72 5557 identity = sk_c8 | sk_c5 = sk_c1. [para(5458(b,1),5103(b,1)),merge(b)].
% 36.42/36.72 5688 sk_c5 = sk_c1 | multiply(sk_c8,A) = A. [para(5557(a,1),1(a,1,1))].
% 36.42/36.72 5778 sk_c4 = sk_c6 | inverse(sk_c8) = sk_c8. [para(5462(a,1),5473(b,2)),merge(b)].
% 36.42/36.72 6720 inverse(sk_c2) = sk_c8 | multiply(A,sk_c6) = A. [para(1309(b,1),110(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 9035 inverse(sk_c2) = sk_c8 | identity = sk_c8. [para(6720(b,1),1440(b,1)),flip(c),merge(c)].
% 36.42/36.72 9072 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,multiply(sk_c8,multiply(sk_c5,sk_c7))) = multiply(sk_c7,sk_c6). [para(128(b,1),125(b,2)),merge(b)].
% 36.42/36.72 9086 identity = sk_c8 | inverse(sk_c8) = sk_c2. [para(9035(a,1),1232(a,1,1))].
% 36.42/36.72 9090 identity = sk_c8 | sk_c4 = sk_c2. [para(9086(b,1),5342(b,1)),flip(c),merge(b)].
% 36.42/36.72 9161 sk_c4 = sk_c2 | multiply(sk_c8,A) = A. [para(9090(a,1),1(a,1,1))].
% 36.42/36.72 9730 identity = sk_c8 | multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c6,sk_c5) = sk_c5. [para(5456(b,1),133(b,1,2)),rewrite([1000(11)]),flip(c)].
% 36.42/36.72 10021 multiply(sk_c7,sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(B,sk_c8) != sk_c7 | inverse(multiply(inverse(sk_c8),B)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(D,sk_c7) != sk_c6 | inverse(D) != sk_c7. [para(1231(a,1),141(d,1))].
% 36.42/36.72 10040 multiply(sk_c7,sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(B,sk_c8) != sk_c7 | inverse(multiply(inverse(sk_c8),B)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c6. [factor(10021,c,k)].
% 36.42/36.72 10053 multiply(sk_c7,sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(B,sk_c8) != sk_c7 | inverse(multiply(inverse(sk_c8),B)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | inverse(B) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(A,sk_c7) != sk_c6. [factor(10040,d,g)].
% 36.42/36.72 10060 multiply(sk_c7,sk_c8) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(multiply(inverse(sk_c8),A)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | inverse(A) != sk_c8 | inverse(sk_c8) != sk_c6. [factor(10053,f,i)].
% 36.42/36.72 10926 inverse(sk_c1) = sk_c7 | inverse(sk_c8) = sk_c7. [para(973(b,1),2985(b,1)),flip(c),merge(b)].
% 36.42/36.72 10933 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c1) = identity. [para(10926(a,1),2(a,1,1))].
% 36.42/36.72 10948 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c7,sk_c1)) = A. [para(10933(b,1),39(a,2,2)),rewrite([39(8),1000(10)])].
% 36.42/36.72 11111 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1310(a,1),74(a,1,2)),rewrite([1000(3)]),flip(a)].
% 36.42/36.72 11238 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(11111(a,1),74(a,1,2)),flip(a)].
% 36.42/36.72 11282 multiply(sk_c7,sk_c8) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(sk_c8,multiply(inverse(A),sk_c8)) != sk_c7 | sk_c8 != A | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,inverse(sk_c8)) != sk_c8 | inverse(sk_c8) != sk_c6. [para(11111(a,1),10060(e,1,1)),rewrite([11238(18),1232(17),39(19),1232(23),11238(32),1232(31),11238(32),1232(30)]),flip(e)].
% 36.42/36.72 12959 inverse(sk_c8) = sk_c6 | multiply(sk_c2,A) = A. [para(1109(b,1),4911(b,1,1)),merge(b)].
% 36.42/36.72 12967 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c3. [para(4911(b,1),4978(b,1)),flip(c),merge(b)].
% 36.42/36.72 13004 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8. [para(12967(b,1),1232(a,1,1))].
% 36.42/36.72 13005 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(12967(b,1),1172(a,1,2))].
% 36.42/36.72 13017 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c8) = sk_c8. [para(13004(b,1),3764(b,1,2)),merge(b)].
% 36.42/36.72 13020 inverse(sk_c8) = sk_c6 | inverse(sk_c2) = identity. [para(12959(b,1),1172(a,1))].
% 36.42/36.72 13107 inverse(sk_c8) = sk_c6 | multiply(A,sk_c7) = A. [para(13005(b,1),96(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 13471 inverse(sk_c8) = sk_c6 | sk_c6 = sk_c8. [para(13017(b,1),10(a,1)),flip(b),merge(c)].
% 36.42/36.72 13492 sk_c6 = sk_c8 | sk_c4 = sk_c6. [para(13471(a,1),5778(b,1)),merge(c)].
% 36.42/36.72 13544 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = identity. [para(13107(b,1),2(a,1))].
% 36.42/36.72 13566 inverse(sk_c8) = sk_c6 | inverse(sk_c6) = sk_c2. [para(13107(b,1),2638(b,1)),merge(b)].
% 36.42/36.72 13655 inverse(sk_c8) = sk_c6 | multiply(sk_c7,A) = A. [para(13544(b,1),74(a,1,1)),rewrite([1(8)])].
% 36.42/36.72 13666 inverse(sk_c8) = sk_c6 | inverse(sk_c2) = sk_c6. [para(13566(b,1),1232(a,1,1))].
% 36.42/36.72 13730 inverse(sk_c8) = sk_c6 | identity = sk_c6. [para(13666(b,1),13020(b,1)),flip(c),merge(b)].
% 36.42/36.72 13737 identity = sk_c6 | sk_c4 = sk_c6. [para(13730(a,1),5473(b,1)),flip(c),merge(c)].
% 36.42/36.72 13805 sk_c4 = sk_c6 | inverse(sk_c6) = identity. [para(13737(a,1),1013(a,1,1))].
% 36.42/36.72 14107 sk_c4 = sk_c6 | inverse(sk_c6) = sk_c6. [para(13737(a,1),13805(b,2)),merge(b)].
% 36.42/36.72 14222 sk_c4 = sk_c6 | multiply(sk_c6,sk_c6) = identity. [para(14107(b,1),2(a,1,1))].
% 36.42/36.72 14514 sk_c4 = sk_c6 | multiply(sk_c6,sk_c6) = sk_c8. [para(5462(a,1),14222(b,2)),merge(b)].
% 36.42/36.72 14691 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c7),A) = A. [para(13655(b,1),74(a,1,2))].
% 36.42/36.72 18113 multiply(sk_c7,sk_c8) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(sk_c8,multiply(inverse(A),multiply(inverse(B),sk_c8))) != sk_c7 | multiply(B,A) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(B,multiply(A,inverse(sk_c8))) != sk_c8 | inverse(sk_c8) != sk_c6. [para(11238(a,1),11282(d,1,2,1)),rewrite([39(20),39(35)]),flip(e)].
% 36.42/36.72 18696 multiply(sk_c7,sk_c8) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(sk_c8,inverse(sk_c7)) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,multiply(sk_c7,inverse(sk_c8))) != sk_c8 | inverse(sk_c8) != sk_c6. [factor(18113,b,e),rewrite([2(21),1000(19)])].
% 36.42/36.72 20880 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c8. [para(14691(b,1),1811(b,1)),flip(c),merge(b)].
% 36.42/36.72 20897 inverse(sk_c8) = sk_c6 | multiply(sk_c7,sk_c8) = identity. [para(20880(b,1),1172(a,1,2))].
% 36.42/36.72 20930 inverse(sk_c8) = sk_c6 | multiply(A,sk_c6) = A. [para(20897(b,1),78(b,1,2)),rewrite([1000(10)]),flip(c),merge(b)].
% 36.42/36.72 20965 inverse(sk_c8) = sk_c6. [para(20930(b,1),4911(b,1)),merge(b),merge(c)].
% 36.42/36.72 21991 multiply(sk_c7,sk_c8) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c8 | sk_c6 != sk_c7 | multiply(sk_c8,inverse(sk_c7)) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,multiply(sk_c7,sk_c6)) != sk_c8. [back_rewrite(18696),rewrite([20965(12),20965(28),20965(33)]),xx(g)].
% 36.42/36.72 23691 sk_c6 = sk_c7 | multiply(A,multiply(sk_c7,sk_c1)) = A. [back_rewrite(10948),rewrite([20965(2)])].
% 36.42/36.72 23698 sk_c6 = sk_c7 | multiply(sk_c7,sk_c1) = identity. [back_rewrite(10933),rewrite([20965(2)])].
% 36.42/36.72 24489 inverse(sk_c6) = sk_c8. [para(20965(a,1),1232(a,1,1))].
% 36.42/36.72 24490 multiply(sk_c8,sk_c6) = identity. [para(20965(a,1),1172(a,1,2))].
% 36.42/36.72 24491 multiply(sk_c8,multiply(sk_c6,A)) = A. [para(20965(a,1),1231(a,1,2,1))].
% 36.42/36.72 24908 multiply(sk_c8,sk_c7) = sk_c6. [para(985(b,1),11238(a,1,1)),rewrite([20965(7),24489(8),1232(10)]),flip(b),merge(b)].
% 36.42/36.72 25873 multiply(sk_c7,sk_c8) != sk_c6 | sk_c6 != sk_c8 | sk_c6 != sk_c7 | multiply(sk_c8,inverse(sk_c7)) != sk_c7 | multiply(sk_c8,multiply(sk_c7,sk_c6)) != sk_c8. [back_rewrite(21991),rewrite([24908(8),24908(20)]),xx(e)].
% 36.42/36.72 26445 multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(24908(a,1),39(a,1,1)),flip(a)].
% 36.42/36.72 26446 multiply(sk_c6,sk_c6) = sk_c7. [para(24908(a,1),74(a,1,2)),rewrite([20965(2)])].
% 36.42/36.72 26455 sk_c5 = sk_c1 | sk_c6 = sk_c7. [para(24908(a,1),5688(b,1))].
% 36.42/36.72 26463 sk_c4 = sk_c2 | sk_c6 = sk_c7. [para(24908(a,1),9161(b,1))].
% 36.42/36.72 26474 multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(24908(a,1),11238(a,1,1)),rewrite([24489(2),20965(5)]),flip(a)].
% 36.42/36.72 26476 multiply(sk_c7,sk_c8) != sk_c6 | sk_c6 != sk_c8 | sk_c6 != sk_c7 | multiply(sk_c8,inverse(sk_c7)) != sk_c7 | sk_c7 != sk_c8. [back_rewrite(25873),rewrite([26445(22),26446(20)])].
% 36.42/36.72 26523 sk_c4 = sk_c6 | sk_c7 = sk_c8. [back_rewrite(14514),rewrite([26446(6)])].
% 36.42/36.72 26551 multiply(sk_c8,sk_c8) = inverse(sk_c7). [para(26446(a,1),11238(a,1,1)),rewrite([24489(4),24489(5)]),flip(a)].
% 36.42/36.72 26940 multiply(sk_c7,sk_c8) = sk_c6. [para(26474(a,1),74(a,1,2)),rewrite([1232(3)])].
% 36.42/36.72 27133 sk_c6 != sk_c8 | sk_c6 != sk_c7 | multiply(sk_c8,inverse(sk_c7)) != sk_c7 | sk_c7 != sk_c8. [back_rewrite(26476),rewrite([26940(3)]),xx(a)].
% 36.42/36.72 28347 sk_c6 = sk_c8 | multiply(sk_c1,sk_c7) = sk_c8. [para(13492(b,1),989(b,1,1,1)),rewrite([24489(10),24908(11)]),merge(c)].
% 36.42/36.72 28371 multiply(sk_c6,inverse(sk_c7)) = sk_c8. [para(26940(a,1),11238(a,1,1)),rewrite([24489(2),20965(3)]),flip(a)].
% 36.42/36.72 28499 multiply(sk_c8,multiply(sk_c8,A)) = multiply(inverse(sk_c7),A). [para(26551(a,1),39(a,1,1)),flip(a)].
% 36.42/36.72 29945 sk_c6 = sk_c8 | identity = sk_c8. [para(28347(b,1),3966(b,1)),flip(c),merge(b)].
% 36.42/36.72 29974 sk_c6 = sk_c8 | identity = sk_c6. [para(29945(b,1),1013(a,1,1)),rewrite([20965(5)]),flip(b)].
% 36.42/36.72 30018 sk_c6 = sk_c8. [para(29974(b,1),29945(b,1)),merge(b),merge(c)].
% 36.42/36.72 30532 multiply(sk_c8,inverse(sk_c7)) = sk_c8. [back_rewrite(28371),rewrite([30018(1)])].
% 36.42/36.72 30822 sk_c7 != sk_c8. [back_rewrite(27133),rewrite([30018(1),30018(4),30532(10)]),flip(b),flip(c),xx(a),merge(b),merge(c)].
% 36.42/36.72 30944 sk_c4 = sk_c8. [back_rewrite(26523),rewrite([30018(2)]),unit_del(b,30822)].
% 36.42/36.72 30952 sk_c2 = sk_c8. [back_rewrite(26463),rewrite([30944(1),30018(4)]),flip(a),flip(b),unit_del(b,30822)].
% 36.42/36.72 30955 sk_c5 = sk_c1. [back_rewrite(26455),rewrite([30018(4)]),flip(b),unit_del(b,30822)].
% 36.42/36.72 30958 inverse(sk_c7) = sk_c7. [back_rewrite(26446),rewrite([30018(1),30018(2),26551(3)])].
% 36.42/36.72 30979 multiply(sk_c7,A) = A. [back_rewrite(24491),rewrite([30018(2),28499(4),30958(2)])].
% 36.42/36.72 30980 identity = sk_c7. [back_rewrite(24490),rewrite([30018(2),26551(3),30958(2)]),flip(a)].
% 36.42/36.72 30981 sk_c1 = sk_c7. [back_rewrite(23698),rewrite([30018(1),30979(6),30980(5)]),flip(a),unit_del(a,30822)].
% 36.42/36.72 30982 multiply(A,sk_c7) = A. [back_rewrite(23691),rewrite([30018(1),30981(5),30979(6)]),flip(a),unit_del(a,30822)].
% 36.42/36.72 30985 sk_c3 = sk_c7. [back_rewrite(9730),rewrite([30980(1),30952(4),26551(6),30958(5),30018(7),30955(8),30981(8),30982(9),30955(8),30981(8)]),flip(b),flip(c),merge(c),unit_del(a,30822)].
% 36.42/36.72 30986 $F. [back_rewrite(9072),rewrite([30985(2),30982(3),30944(4),30955(6),30981(6),30982(8),30982(7),26551(6),30958(5),30018(6),30979(7)]),flip(a),merge(b),unit_del(a,30822)].
% 36.42/36.72
% 36.42/36.72 % SZS output end Refutation
% 36.42/36.72 ============================== end of proof ==========================
% 36.42/36.72
% 36.42/36.72 ============================== STATISTICS ============================
% 36.42/36.72
% 36.42/36.72 Given=4377. Generated=1741711. Kept=30985. proofs=1.
% 36.42/36.72 Usable=399. Sos=1550. Demods=38. Limbo=968, Disabled=28108. Hints=0.
% 36.42/36.72 Megabytes=27.36.
% 36.42/36.72 User_CPU=34.76, System_CPU=0.92, Wall_clock=36.
% 36.42/36.72
% 36.42/36.72 ============================== end of statistics =====================
% 36.42/36.72
% 36.42/36.72 ============================== end of search =========================
% 36.42/36.72
% 36.42/36.72 THEOREM PROVED
% 36.42/36.72 % SZS status Unsatisfiable
% 36.42/36.72
% 36.42/36.72 Exiting with 1 proof.
% 36.42/36.72
% 36.42/36.72 Process 14544 exit (max_proofs) Tue Jun 14 03:14:42 2022
% 36.42/36.72 Prover9 interrupted
%------------------------------------------------------------------------------