TSTP Solution File: GRP347-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 11:18:43 EDT 2022
% Result : Unsatisfiable 52.49s 52.79s
% Output : Refutation 52.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP347-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 07:57:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 52.49/52.79 ============================== Prover9 ===============================
% 52.49/52.79 Prover9 (32) version 2009-11A, November 2009.
% 52.49/52.79 Process 32019 was started by sandbox on n010.cluster.edu,
% 52.49/52.79 Mon Jun 13 07:57:25 2022
% 52.49/52.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31866_n010.cluster.edu".
% 52.49/52.79 ============================== end of head ===========================
% 52.49/52.79
% 52.49/52.79 ============================== INPUT =================================
% 52.49/52.79
% 52.49/52.79 % Reading from file /tmp/Prover9_31866_n010.cluster.edu
% 52.49/52.79
% 52.49/52.79 set(prolog_style_variables).
% 52.49/52.79 set(auto2).
% 52.49/52.79 % set(auto2) -> set(auto).
% 52.49/52.79 % set(auto) -> set(auto_inference).
% 52.49/52.79 % set(auto) -> set(auto_setup).
% 52.49/52.79 % set(auto_setup) -> set(predicate_elim).
% 52.49/52.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 52.49/52.79 % set(auto) -> set(auto_limits).
% 52.49/52.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 52.49/52.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 52.49/52.79 % set(auto) -> set(auto_denials).
% 52.49/52.79 % set(auto) -> set(auto_process).
% 52.49/52.79 % set(auto2) -> assign(new_constants, 1).
% 52.49/52.79 % set(auto2) -> assign(fold_denial_max, 3).
% 52.49/52.79 % set(auto2) -> assign(max_weight, "200.000").
% 52.49/52.79 % set(auto2) -> assign(max_hours, 1).
% 52.49/52.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 52.49/52.79 % set(auto2) -> assign(max_seconds, 0).
% 52.49/52.79 % set(auto2) -> assign(max_minutes, 5).
% 52.49/52.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 52.49/52.79 % set(auto2) -> set(sort_initial_sos).
% 52.49/52.79 % set(auto2) -> assign(sos_limit, -1).
% 52.49/52.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 52.49/52.79 % set(auto2) -> assign(max_megs, 400).
% 52.49/52.79 % set(auto2) -> assign(stats, some).
% 52.49/52.79 % set(auto2) -> clear(echo_input).
% 52.49/52.79 % set(auto2) -> set(quiet).
% 52.49/52.79 % set(auto2) -> clear(print_initial_clauses).
% 52.49/52.79 % set(auto2) -> clear(print_given).
% 52.49/52.79 assign(lrs_ticks,-1).
% 52.49/52.79 assign(sos_limit,10000).
% 52.49/52.79 assign(order,kbo).
% 52.49/52.79 set(lex_order_vars).
% 52.49/52.79 clear(print_given).
% 52.49/52.79
% 52.49/52.79 % formulas(sos). % not echoed (34 formulas)
% 52.49/52.79
% 52.49/52.79 ============================== end of input ==========================
% 52.49/52.79
% 52.49/52.79 % From the command line: assign(max_seconds, 300).
% 52.49/52.79
% 52.49/52.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 52.49/52.79
% 52.49/52.79 % Formulas that are not ordinary clauses:
% 52.49/52.79
% 52.49/52.79 ============================== end of process non-clausal formulas ===
% 52.49/52.79
% 52.49/52.79 ============================== PROCESS INITIAL CLAUSES ===============
% 52.49/52.79
% 52.49/52.79 ============================== PREDICATE ELIMINATION =================
% 52.49/52.79
% 52.49/52.79 ============================== end predicate elimination =============
% 52.49/52.79
% 52.49/52.79 Auto_denials: (non-Horn, no changes).
% 52.49/52.79
% 52.49/52.79 Term ordering decisions:
% 52.49/52.79
% 52.49/52.79 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 52.49/52.79 Function symbol KB weights: sk_c6=1. sk_c7=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 52.49/52.79
% 52.49/52.79 ============================== end of process initial clauses ========
% 52.49/52.79
% 52.49/52.79 ============================== CLAUSES FOR SEARCH ====================
% 52.49/52.79
% 52.49/52.79 ============================== end of clauses for search =============
% 52.49/52.79
% 52.49/52.79 ============================== SEARCH ================================
% 52.49/52.79
% 52.49/52.79 % Starting search at 0.02 seconds.
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=46.000, iters=3525
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=43.000, iters=3386
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=42.000, iters=3348
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=41.000, iters=3389
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=40.000, iters=3344
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=39.000, iters=3404
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=38.000, iters=3368
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=37.000, iters=3463
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=36.000, iters=3335
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=35.000, iters=3351
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=34.000, iters=3786
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=33.000, iters=3495
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=32.000, iters=3451
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=31.000, iters=3379
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=17.000, iters=3538
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=16.000, iters=3334
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=15.000, iters=3339
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=14.000, iters=3333
% 52.49/52.79
% 52.49/52.79 Low Water (displace): id=4072, wt=52.000
% 52.49/52.79
% 52.49/52.79 Low Water (displace): id=16556, wt=13.000
% 52.49/52.79
% 52.49/52.79 Low Water (displace): id=16568, wt=12.000
% 52.49/52.79
% 52.49/52.79 Low Water (displace): id=16785, wt=11.000
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=13.000, iters=3342
% 52.49/52.79
% 52.49/52.79 Low Water (keep): wt=12.000, iters=3334
% 52.49/52.79
% 52.49/52.79 ============================== PROOF =================================
% 52.49/52.79 % SZS status Unsatisfiable
% 52.49/52.79 % SZS output start Refutation
% 52.49/52.79
% 52.49/52.79 % Proof 1 at 50.58 (+ 1.24) seconds.
% 52.49/52.79 % Length of proof is 172.
% 52.49/52.79 % Level of proof is 35.
% 52.49/52.79 % Maximum clause weight is 50.000.
% 52.49/52.79 % Given clauses 5644.
% 52.49/52.79
% 52.49/52.79 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 52.49/52.79 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 52.49/52.79 3 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c5 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 52.49/52.79 4 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 52.49/52.79 6 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 52.49/52.79 7 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 52.49/52.79 8 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 52.49/52.79 9 multiply(sk_c6,sk_c7) = sk_c5 | inverse(sk_c6) = sk_c5 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 52.49/52.79 11 multiply(sk_c6,sk_c7) = sk_c5 | inverse(sk_c4) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 52.49/52.79 13 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 52.49/52.79 15 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c6) = sk_c5 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 52.49/52.79 18 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 52.49/52.79 19 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 52.49/52.79 20 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 52.49/52.79 21 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c6) = sk_c5 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 52.49/52.79 23 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 52.49/52.79 24 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 52.49/52.79 26 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 52.49/52.79 27 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 52.49/52.79 30 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c6,sk_c5) = sk_c7 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 52.49/52.79 32 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 52.49/52.79 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 52.49/52.79 34 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(D,sk_c7) != sk_c5 | inverse(D) != sk_c7 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 52.49/52.79 50 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 52.49/52.79 53 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 52.49/52.79 56 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 52.49/52.79 57 inverse(sk_c6) = sk_c5 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(9(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79 58 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(9(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79 62 inverse(sk_c4) = sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(11(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79 69 inverse(sk_c6) = sk_c5 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(15(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79 70 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c1,sk_c6)) = multiply(A,sk_c7). [para(15(a,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79 78 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(19(b,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79 80 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5). [para(20(b,1),33(a,2,2)),rewrite([33(8)])].
% 52.49/52.79 85 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(23(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79 88 multiply(sk_c6,sk_c7) = sk_c5 | multiply(A,multiply(sk_c6,sk_c5)) = multiply(A,sk_c7). [para(24(b,1),33(a,2,2)),rewrite([33(9)])].
% 52.49/52.79 93 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(27(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79 99 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(30(a,1),33(a,1,1)),flip(b)].
% 52.49/52.79 103 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(32(b,1),33(a,1,1)),flip(b)].
% 52.49/52.79 131 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7. [para(2(a,1),34(h,1))].
% 52.49/52.79 459 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),56(a,1,2))].
% 52.49/52.79 471 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c1),sk_c7) = sk_c6. [para(15(a,1),56(a,1,2))].
% 52.49/52.79 490 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),identity) = sk_c1. [para(50(b,1),56(a,1,2))].
% 52.49/52.79 491 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(56(a,1),56(a,1,2))].
% 52.49/52.79 492 multiply(A,identity) = A. [back_rewrite(459),rewrite([491(4)])].
% 52.49/52.79 493 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c1. [back_rewrite(490),rewrite([492(8)])].
% 52.49/52.79 495 inverse(identity) = identity. [para(492(a,1),2(a,1))].
% 52.49/52.79 537 inverse(sk_c6) = sk_c5 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(493(b,1),56(a,1,1))].
% 52.49/52.79 546 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c6,sk_c2)) = A. [para(53(b,1),33(a,2,2)),rewrite([33(8),492(10)])].
% 52.49/52.79 547 inverse(sk_c6) = sk_c5 | inverse(sk_c6) = sk_c2. [para(53(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79 570 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c6) = identity. [para(547(b,1),2(a,1,1))].
% 52.49/52.79 571 inverse(sk_c6) = sk_c5 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(547(b,1),56(a,1,1))].
% 52.49/52.79 579 inverse(sk_c6) = sk_c5 | multiply(sk_c5,sk_c1) = sk_c6. [para(50(b,1),57(b,1,2)),rewrite([492(11)]),flip(c),merge(b)].
% 52.49/52.79 602 multiply(A,inverse(A)) = identity. [para(491(a,1),2(a,1))].
% 52.49/52.79 603 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A). [para(3(a,1),491(a,1,1,1))].
% 52.49/52.79 641 multiply(A,multiply(inverse(A),B)) = B. [para(491(a,1),56(a,1))].
% 52.49/52.79 642 inverse(inverse(A)) = A. [para(491(a,1),492(a,1)),rewrite([492(2)]),flip(a)].
% 52.49/52.79 680 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7. [back_rewrite(131),rewrite([642(34)]),xx(i)].
% 52.49/52.79 685 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = identity. [para(4(b,1),602(a,1,2))].
% 52.49/52.79 687 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(7(b,1),602(a,1,2))].
% 52.49/52.79 688 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(8(b,1),602(a,1,2))].
% 52.49/52.79 689 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(602(a,1),33(a,1)),flip(a)].
% 52.49/52.79 709 inverse(sk_c6) = sk_c5 | multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6. [para(21(a,1),58(b,2)),merge(b)].
% 52.49/52.79 776 inverse(sk_c6) = sk_c5 | multiply(A,multiply(sk_c2,sk_c6)) = A. [para(570(b,1),33(a,2,2)),rewrite([33(8),492(10)])].
% 52.49/52.79 793 inverse(sk_c6) = sk_c5 | multiply(sk_c5,multiply(sk_c1,A)) = multiply(sk_c6,A). [para(579(b,1),33(a,1,1)),flip(b)].
% 52.49/52.79 795 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = sk_c1. [para(579(b,1),56(a,1,2))].
% 52.49/52.79 796 inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(685(b,1),13(b,1)),merge(b)].
% 52.49/52.79 805 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6. [para(23(a,1),62(b,2)),merge(b)].
% 52.49/52.79 916 inverse(sk_c2) = sk_c6 | identity = sk_c7. [para(687(b,1),19(b,1)),merge(b)].
% 52.49/52.79 918 identity = sk_c7 | multiply(sk_c6,sk_c2) = identity. [para(916(a,1),2(a,1,1))].
% 52.49/52.79 965 inverse(sk_c2) = sk_c6 | identity = sk_c5. [para(688(b,1),20(b,1)),merge(b)].
% 52.49/52.79 967 identity = sk_c5 | multiply(sk_c6,sk_c2) = identity. [para(965(a,1),2(a,1,1))].
% 52.49/52.79 1014 identity = sk_c5 | multiply(A,multiply(sk_c6,sk_c2)) = A. [para(967(b,1),33(a,2,2)),rewrite([33(7),492(9)])].
% 52.49/52.79 1185 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c2) = sk_c1. [para(53(b,1),69(b,1,2)),rewrite([492(11)]),flip(c),merge(b)].
% 52.49/52.79 1766 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c1) = sk_c2. [para(1185(b,1),56(a,1,2))].
% 52.49/52.79 2546 inverse(sk_c2) = sk_c6 | multiply(A,sk_c7) = A. [para(687(b,1),78(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79 2646 inverse(sk_c2) = sk_c6 | sk_c4 = sk_c5. [para(2546(b,1),20(b,1)),merge(b)].
% 52.49/52.79 2698 sk_c4 = sk_c5 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(2646(a,1),641(a,1,2,1))].
% 52.49/52.79 2845 inverse(sk_c2) = sk_c6 | multiply(A,sk_c5) = A. [para(688(b,1),80(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79 3313 inverse(sk_c2) = sk_c6 | sk_c7 = sk_c6. [para(2845(b,1),18(b,1)),flip(c),merge(b)].
% 52.49/52.79 3374 sk_c7 = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(3313(a,1),641(a,1,2,1))].
% 52.49/52.79 3948 inverse(sk_c4) = sk_c7 | multiply(sk_c2,multiply(sk_c5,multiply(sk_c6,sk_c7))) = multiply(sk_c6,sk_c5). [para(62(b,1),85(b,2)),merge(b)].
% 52.49/52.79 4457 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(a,1),471(b,1,1)),merge(b)].
% 52.49/52.79 4461 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(4457(b,1),56(a,1,2))].
% 52.49/52.79 4615 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c6,sk_c5)) = sk_c5. [para(26(b,1),88(b,2)),merge(b)].
% 52.49/52.79 5095 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(689(a,1),56(a,1,2)),rewrite([492(3)]),flip(a)].
% 52.49/52.79 5184 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(5095(a,1),56(a,1,2)),flip(a)].
% 52.49/52.79 6729 identity = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c7,sk_c2) = sk_c1. [para(918(b,1),93(b,1,2)),rewrite([492(11)]),flip(c)].
% 52.49/52.79 7544 identity = sk_c5 | multiply(inverse(sk_c2),inverse(sk_c6)) = identity. [para(1014(b,1),2(a,1)),rewrite([5184(7)])].
% 52.49/52.79 7725 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c6,inverse(sk_c5)) = sk_c2. [para(602(a,1),99(b,1,2)),rewrite([492(8)]),flip(b)].
% 52.49/52.79 8297 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c1) = sk_c2. [para(493(b,1),1766(b,1,1)),merge(b)].
% 52.49/52.79 8300 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c5,inverse(sk_c7)) = sk_c4. [para(602(a,1),103(b,1,2)),rewrite([492(8)]),flip(b)].
% 52.49/52.79 8368 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c1),sk_c2) = sk_c1. [para(8297(b,1),56(a,1,2))].
% 52.49/52.79 13870 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7. [para(1(a,1),680(e,1)),rewrite([495(14)])].
% 52.49/52.79 14012 multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(A),inverse(B)) != sk_c7 | multiply(B,multiply(A,sk_c6)) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(C,sk_c7) != sk_c5 | inverse(C) != sk_c7. [para(33(a,1),13870(c,1)),rewrite([5184(7)])].
% 52.49/52.79 18363 inverse(sk_c4) = sk_c7 | sk_c7 = sk_c6. [para(805(b,1),3374(b,1)),flip(c),merge(c)].
% 52.49/52.79 18561 inverse(sk_c6) = sk_c5 | multiply(sk_c6,inverse(sk_c1)) = sk_c5. [para(602(a,1),793(b,1,2)),rewrite([492(7)]),flip(b)].
% 52.49/52.79 18632 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c5) = inverse(sk_c1). [para(18561(b,1),571(b,1,2)),merge(b)].
% 52.49/52.79 18633 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = sk_c6. [para(18632(b,1),21(a,1)),merge(c)].
% 52.49/52.79 18647 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c6) = identity. [para(18633(b,1),602(a,1,2))].
% 52.49/52.79 18650 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c2) = sk_c1. [para(18633(b,1),8368(b,1,1)),merge(b)].
% 52.49/52.79 18745 inverse(sk_c6) = sk_c5 | identity = sk_c7. [para(18647(b,1),15(a,1)),merge(c)].
% 52.49/52.79 18748 inverse(sk_c6) = sk_c5 | multiply(A,sk_c7) = A. [para(18647(b,1),70(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79 18751 inverse(sk_c6) = sk_c5 | multiply(inverse(sk_c7),sk_c6) = identity. [para(18647(b,1),603(b,2)),merge(b)].
% 52.49/52.79 18765 identity = sk_c7 | multiply(sk_c6,sk_c5) = identity. [para(18745(a,1),602(a,1,2))].
% 52.49/52.79 19054 identity = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5. [para(18765(b,1),24(b,1)),merge(c)].
% 52.49/52.79 19268 identity = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(19054(b,1),56(a,1,2))].
% 52.49/52.79 19316 inverse(sk_c6) = sk_c5 | multiply(A,sk_c1) = A. [para(18650(b,1),546(b,1,2)),merge(b)].
% 52.49/52.79 19538 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c7) = inverse(sk_c7). [para(18748(b,1),603(b,1)),flip(c),merge(b)].
% 52.49/52.79 19548 inverse(sk_c6) = sk_c5 | multiply(sk_c2,sk_c6) = sk_c6. [para(18748(b,1),709(b,1,2)),merge(b)].
% 52.49/52.79 19901 identity = sk_c7 | multiply(sk_c5,sk_c5) = sk_c7. [para(18745(a,1),19268(b,1,1)),merge(b)].
% 52.49/52.79 19905 identity = sk_c7 | multiply(inverse(sk_c5),inverse(sk_c5)) = inverse(sk_c7). [para(19901(b,1),5184(a,1,1)),flip(b)].
% 52.49/52.79 19917 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = identity. [para(19316(b,1),2(a,1))].
% 52.49/52.79 21839 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7. [para(2(a,1),14012(c,1,2)),rewrite([642(8),492(12)]),flip(c)].
% 52.49/52.79 21842 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(B,multiply(C,sk_c7)) != sk_c5 | multiply(inverse(C),inverse(B)) != sk_c7. [para(33(a,1),21839(i,1)),rewrite([5184(37)])].
% 52.49/52.79 22090 inverse(sk_c6) = sk_c5 | multiply(A,sk_c6) = A. [para(19548(b,1),776(b,1,2)),merge(b)].
% 52.49/52.79 22735 inverse(sk_c6) = sk_c5 | inverse(sk_c5) = sk_c1. [para(22090(b,1),795(b,1)),merge(b)].
% 52.49/52.79 22742 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c7. [para(22090(b,1),4461(b,1)),merge(b)].
% 52.49/52.79 22848 inverse(sk_c6) = sk_c5 | inverse(sk_c1) = sk_c5. [para(22735(b,1),642(a,1,1))].
% 52.49/52.79 22877 inverse(sk_c6) = sk_c5 | identity = sk_c5. [para(22848(b,1),19917(b,1)),flip(c),merge(b)].
% 52.49/52.79 22887 identity = sk_c5 | multiply(inverse(sk_c2),sk_c5) = identity. [para(22877(a,1),7544(b,1,2)),merge(b)].
% 52.49/52.79 23363 inverse(sk_c6) = sk_c5 | multiply(sk_c7,sk_c6) = identity. [para(22742(b,1),18751(b,1,1)),merge(b)].
% 52.49/52.79 23366 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c6. [para(23363(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79 23374 inverse(sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = identity. [para(23366(b,1),2(a,1,1))].
% 52.49/52.79 23401 inverse(sk_c6) = sk_c5 | multiply(A,sk_c5) = A. [para(23374(b,1),58(b,1,2)),rewrite([492(10)]),flip(c),merge(b)].
% 52.49/52.79 23493 inverse(sk_c6) = sk_c5 | multiply(sk_c1,sk_c7) = sk_c5. [para(23401(b,1),537(b,1,2)),merge(b)].
% 52.49/52.79 24262 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | sk_c5 != B | multiply(sk_c7,inverse(B)) != sk_c7. [para(2(a,1),21842(i,1,2)),rewrite([492(32),642(35)]),flip(i)].
% 52.49/52.79 24265 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,A) != sk_c7 | inverse(A) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | sk_c5 != B | multiply(sk_c7,inverse(B)) != sk_c7. [para(642(a,1),24262(b,1,2)),flip(c)].
% 52.49/52.79 24270 multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,A) != sk_c7 | inverse(A) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c5 | multiply(sk_c7,B) != sk_c7. [para(642(a,1),24265(j,1,2)),flip(i)].
% 52.49/52.79 24288 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c5 | multiply(sk_c7,B) != sk_c7. [para(641(a,1),24270(b,1)),rewrite([5184(11),642(11)]),flip(b)].
% 52.49/52.79 24312 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(inverse(B),sk_c7) != sk_c5 | sk_c7 != B. [para(641(a,1),24288(j,1)),rewrite([5184(34),642(34)]),flip(j)].
% 52.49/52.79 24314 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5. [factor(24312,b,j)].
% 52.49/52.79 24498 inverse(sk_c6) = sk_c5 | inverse(sk_c7) = sk_c5. [para(19538(b,1),23493(b,1)),merge(b)].
% 52.49/52.79 24519 inverse(sk_c6) = sk_c5 | multiply(sk_c5,sk_c6) = identity. [para(24498(b,1),18751(b,1,1)),merge(b)].
% 52.49/52.79 24569 inverse(sk_c6) = sk_c5 | inverse(sk_c5) = sk_c6. [para(24519(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79 24591 inverse(sk_c6) = sk_c5. [para(24569(b,1),642(a,1,1)),merge(b)].
% 52.49/52.79 24647 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5. [back_rewrite(24314),rewrite([24591(25)]),xx(g)].
% 52.49/52.79 28497 multiply(sk_c5,sk_c6) = identity. [para(24591(a,1),2(a,1,1))].
% 52.49/52.79 28498 multiply(sk_c5,multiply(sk_c6,A)) = A. [para(24591(a,1),56(a,1,1))].
% 52.49/52.79 28499 inverse(sk_c5) = sk_c6. [para(24591(a,1),642(a,1,1))].
% 52.49/52.79 28500 multiply(sk_c6,sk_c5) = identity. [para(24591(a,1),602(a,1,2))].
% 52.49/52.79 28558 inverse(sk_c4) = sk_c7 | multiply(sk_c2,sk_c7) = identity. [back_rewrite(3948),rewrite([28498(10),28500(10)])].
% 52.49/52.79 28777 identity = sk_c7 | multiply(sk_c6,sk_c6) = inverse(sk_c7). [back_rewrite(19905),rewrite([28499(5),28499(6)])].
% 52.49/52.79 28867 identity = sk_c7 | multiply(sk_c6,sk_c6) = sk_c2. [back_rewrite(7725),rewrite([28500(3),28499(6)])].
% 52.49/52.79 29929 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | identity != sk_c7 | multiply(inverse(A),sk_c7) != sk_c5. [back_rewrite(24647),rewrite([28500(21)]),merge(g)].
% 52.49/52.79 30194 identity = sk_c7 | multiply(sk_c7,sk_c2) = sk_c1. [back_rewrite(6729),rewrite([28500(6)]),merge(b)].
% 52.49/52.79 30213 multiply(sk_c6,sk_c7) = sk_c5 | sk_c4 = sk_c5. [back_rewrite(4615),rewrite([28500(9),492(8)])].
% 52.49/52.79 30579 sk_c4 = sk_c5 | multiply(sk_c2,sk_c5) = sk_c7. [para(30213(a,1),2698(b,1,2)),merge(b)].
% 52.49/52.79 30580 sk_c4 = sk_c5 | multiply(inverse(sk_c7),sk_c5) = sk_c6. [para(30213(a,1),5184(a,1,1)),rewrite([28499(5),24591(8)]),flip(b)].
% 52.49/52.79 31196 inverse(sk_c4) = sk_c7 | inverse(sk_c2) = sk_c7. [para(28558(b,1),56(a,1,2)),rewrite([492(8)])].
% 52.49/52.79 31203 inverse(sk_c2) = sk_c7 | inverse(sk_c7) = sk_c4. [para(31196(a,1),642(a,1,1))].
% 52.49/52.79 31220 inverse(sk_c7) = sk_c4 | identity = sk_c5 | multiply(sk_c7,sk_c5) = identity. [para(31203(a,1),22887(b,1,1))].
% 52.49/52.79 31643 identity = sk_c7 | inverse(sk_c7) = sk_c2. [para(28777(b,1),28867(b,1)),merge(b)].
% 52.49/52.79 31648 identity = sk_c7 | multiply(sk_c7,sk_c2) = identity. [para(31643(b,1),602(a,1,2))].
% 52.49/52.79 31996 identity = sk_c7 | identity = sk_c1. [para(31648(b,1),30194(b,1)),merge(b)].
% 52.49/52.79 31999 identity = sk_c7 | inverse(sk_c1) = identity. [para(31996(b,1),495(a,1,1))].
% 52.49/52.79 32012 identity = sk_c7. [para(31999(b,1),796(a,1)),merge(b),merge(c)].
% 52.49/52.79 32084 inverse(sk_c7) = sk_c4 | sk_c5 = sk_c7 | multiply(sk_c7,sk_c5) = sk_c7. [back_rewrite(31220),rewrite([32012(5),32012(11)]),flip(b)].
% 52.49/52.79 32186 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | sk_c7 != sk_c6 | sk_c5 != sk_c6 | multiply(inverse(A),sk_c7) != sk_c5. [back_rewrite(29929),rewrite([32012(13),32012(19)]),xx(f)].
% 52.49/52.79 33094 multiply(sk_c5,sk_c6) = sk_c7. [back_rewrite(28497),rewrite([32012(4)])].
% 52.49/52.79 33869 inverse(sk_c7) = sk_c7. [back_rewrite(495),rewrite([32012(1),32012(3)])].
% 52.49/52.79 33870 multiply(A,sk_c7) = A. [back_rewrite(492),rewrite([32012(1)])].
% 52.49/52.79 33872 multiply(sk_c7,A) = A. [back_rewrite(1),rewrite([32012(1)])].
% 52.49/52.79 33882 sk_c5 != sk_c6 | sk_c7 != sk_c6. [factor(32186,b,d),rewrite([33870(3),24591(8),33094(9),24591(14),33870(15)]),flip(a),xx(c),xx(e),merge(c)].
% 52.49/52.79 33953 sk_c4 = sk_c7 | sk_c5 = sk_c7. [back_rewrite(32084),rewrite([33869(2),33872(9)]),flip(a),merge(c)].
% 52.49/52.79 33970 sk_c4 = sk_c5 | sk_c5 = sk_c6. [back_rewrite(30580),rewrite([33869(5),33872(6)])].
% 52.49/52.79 34148 multiply(sk_c2,sk_c5) = sk_c6 | sk_c4 = sk_c5. [back_rewrite(8300),rewrite([33869(8),33870(8)]),flip(b)].
% 52.49/52.79 35374 sk_c5 = sk_c6 | sk_c5 = sk_c7. [para(33970(a,1),33953(a,1)),merge(c)].
% 52.49/52.79 35970 sk_c5 = sk_c6 | sk_c7 != sk_c6. [para(35374(b,1),33882(a,1)),merge(c)].
% 52.49/52.79 37860 sk_c4 = sk_c5 | sk_c7 = sk_c6. [para(34148(a,1),30579(b,1)),flip(c),merge(b)].
% 52.49/52.79 37901 sk_c7 = sk_c6. [para(37860(a,1),18363(a,1,1)),rewrite([28499(5)]),flip(b),merge(b),merge(c)].
% 52.49/52.79 38839 sk_c5 = sk_c6. [back_rewrite(35970),rewrite([37901(4)]),xx(b)].
% 52.49/52.79 39328 $F. [back_rewrite(33882),rewrite([38839(1),37901(4)]),xx(a),xx(b)].
% 52.49/52.79
% 52.49/52.79 % SZS output end Refutation
% 52.49/52.79 ============================== end of proof ==========================
% 52.49/52.79
% 52.49/52.79 ============================== STATISTICS ============================
% 52.49/52.79
% 52.49/52.79 Given=5644. Generated=2452782. Kept=39327. proofs=1.
% 52.49/52.79 Usable=518. Sos=1623. Demods=19. Limbo=1427, Disabled=35793. Hints=0.
% 52.49/52.79 Megabytes=32.75.
% 52.49/52.79 User_CPU=50.59, System_CPU=1.24, Wall_clock=52.
% 52.49/52.79
% 52.49/52.79 ============================== end of statistics =====================
% 52.49/52.79
% 52.49/52.79 ============================== end of search =========================
% 52.49/52.79
% 52.49/52.79 THEOREM PROVED
% 52.49/52.79 % SZS status Unsatisfiable
% 52.49/52.79
% 52.49/52.79 Exiting with 1 proof.
% 52.49/52.79
% 52.49/52.79 Process 32019 exit (max_proofs) Mon Jun 13 07:58:17 2022
% 52.49/52.79 Prover9 interrupted
%------------------------------------------------------------------------------