TSTP Solution File: GRP359-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP359-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 104.97s 105.23s
% Output : Refutation 104.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP359-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Mon Jun 13 13:52:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 104.97/105.23 ============================== Prover9 ===============================
% 104.97/105.23 Prover9 (32) version 2009-11A, November 2009.
% 104.97/105.23 Process 20003 was started by sandbox2 on n027.cluster.edu,
% 104.97/105.23 Mon Jun 13 13:52:47 2022
% 104.97/105.23 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19849_n027.cluster.edu".
% 104.97/105.23 ============================== end of head ===========================
% 104.97/105.23
% 104.97/105.23 ============================== INPUT =================================
% 104.97/105.23
% 104.97/105.23 % Reading from file /tmp/Prover9_19849_n027.cluster.edu
% 104.97/105.23
% 104.97/105.23 set(prolog_style_variables).
% 104.97/105.23 set(auto2).
% 104.97/105.23 % set(auto2) -> set(auto).
% 104.97/105.23 % set(auto) -> set(auto_inference).
% 104.97/105.23 % set(auto) -> set(auto_setup).
% 104.97/105.23 % set(auto_setup) -> set(predicate_elim).
% 104.97/105.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 104.97/105.23 % set(auto) -> set(auto_limits).
% 104.97/105.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 104.97/105.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 104.97/105.23 % set(auto) -> set(auto_denials).
% 104.97/105.23 % set(auto) -> set(auto_process).
% 104.97/105.23 % set(auto2) -> assign(new_constants, 1).
% 104.97/105.23 % set(auto2) -> assign(fold_denial_max, 3).
% 104.97/105.23 % set(auto2) -> assign(max_weight, "200.000").
% 104.97/105.23 % set(auto2) -> assign(max_hours, 1).
% 104.97/105.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 104.97/105.23 % set(auto2) -> assign(max_seconds, 0).
% 104.97/105.23 % set(auto2) -> assign(max_minutes, 5).
% 104.97/105.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 104.97/105.23 % set(auto2) -> set(sort_initial_sos).
% 104.97/105.23 % set(auto2) -> assign(sos_limit, -1).
% 104.97/105.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 104.97/105.23 % set(auto2) -> assign(max_megs, 400).
% 104.97/105.23 % set(auto2) -> assign(stats, some).
% 104.97/105.23 % set(auto2) -> clear(echo_input).
% 104.97/105.23 % set(auto2) -> set(quiet).
% 104.97/105.23 % set(auto2) -> clear(print_initial_clauses).
% 104.97/105.23 % set(auto2) -> clear(print_given).
% 104.97/105.23 assign(lrs_ticks,-1).
% 104.97/105.23 assign(sos_limit,10000).
% 104.97/105.23 assign(order,kbo).
% 104.97/105.23 set(lex_order_vars).
% 104.97/105.23 clear(print_given).
% 104.97/105.23
% 104.97/105.23 % formulas(sos). % not echoed (34 formulas)
% 104.97/105.23
% 104.97/105.23 ============================== end of input ==========================
% 104.97/105.23
% 104.97/105.23 % From the command line: assign(max_seconds, 300).
% 104.97/105.23
% 104.97/105.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 104.97/105.23
% 104.97/105.23 % Formulas that are not ordinary clauses:
% 104.97/105.23
% 104.97/105.23 ============================== end of process non-clausal formulas ===
% 104.97/105.23
% 104.97/105.23 ============================== PROCESS INITIAL CLAUSES ===============
% 104.97/105.23
% 104.97/105.23 ============================== PREDICATE ELIMINATION =================
% 104.97/105.23
% 104.97/105.23 ============================== end predicate elimination =============
% 104.97/105.23
% 104.97/105.23 Auto_denials: (non-Horn, no changes).
% 104.97/105.23
% 104.97/105.23 Term ordering decisions:
% 104.97/105.23
% 104.97/105.23 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 104.97/105.23 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.
% 104.97/105.23
% 104.97/105.23 ============================== end of process initial clauses ========
% 104.97/105.23
% 104.97/105.23 ============================== CLAUSES FOR SEARCH ====================
% 104.97/105.23
% 104.97/105.23 ============================== end of clauses for search =============
% 104.97/105.23
% 104.97/105.23 ============================== SEARCH ================================
% 104.97/105.23
% 104.97/105.23 % Starting search at 0.02 seconds.
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=38.000, iters=3555
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=37.000, iters=3540
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=36.000, iters=3358
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=35.000, iters=3333
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=34.000, iters=3362
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=33.000, iters=3339
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=32.000, iters=3340
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=31.000, iters=3421
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=30.000, iters=3382
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=29.000, iters=3403
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=28.000, iters=3395
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=27.000, iters=3371
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=26.000, iters=3398
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=25.000, iters=3351
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=23.000, iters=3432
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=17.000, iters=3362
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=16.000, iters=3498
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=15.000, iters=3341
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=14.000, iters=3344
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=13.000, iters=3460
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=12.000, iters=3787
% 104.97/105.23
% 104.97/105.23 Low Water (keep): wt=11.000, iters=3463
% 104.97/105.23
% 104.97/105.23 ============================== PROOF =================================
% 104.97/105.23 % SZS status Unsatisfiable
% 104.97/105.23 % SZS output start Refutation
% 104.97/105.23
% 104.97/105.23 % Proof 1 at 101.20 (+ 3.09) seconds.
% 104.97/105.23 % Length of proof is 169.
% 104.97/105.23 % Level of proof is 34.
% 104.97/105.23 % Maximum clause weight is 51.000.
% 104.97/105.23 % Given clauses 9649.
% 104.97/105.23
% 104.97/105.23 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 104.97/105.23 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 104.97/105.23 3 inverse(sk_c8) = sk_c6 | inverse(sk_c3) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 104.97/105.23 4 inverse(sk_c8) = sk_c6 | inverse(sk_c4) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 104.97/105.23 5 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 104.97/105.23 6 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 104.97/105.23 7 multiply(sk_c7,sk_c6) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 104.97/105.23 9 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 104.97/105.23 10 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 104.97/105.23 11 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 104.97/105.23 12 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 104.97/105.23 13 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 104.97/105.23 14 multiply(sk_c8,sk_c2) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 104.97/105.23 15 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c3) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 104.97/105.23 16 multiply(sk_c1,sk_c8) = sk_c2 | inverse(sk_c4) = sk_c8 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 104.97/105.23 18 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 104.97/105.23 19 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 104.97/105.23 20 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 104.97/105.23 22 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 104.97/105.23 27 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 104.97/105.23 28 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 104.97/105.23 31 multiply(sk_c1,sk_c8) = sk_c2 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 104.97/105.23 32 multiply(sk_c1,sk_c8) = sk_c2 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 104.97/105.23 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 104.97/105.23 34 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != 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].
% 104.97/105.23 38 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8. [factor(34,d,j),merge(i),merge(j)].
% 104.97/105.23 42 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(B,sk_c8) != sk_c7. [factor(38,e,h)].
% 104.97/105.23 44 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 104.97/105.23 45 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 104.97/105.23 46 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 104.97/105.23 47 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 104.97/105.23 48 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 104.97/105.23 49 inverse(sk_c3) = sk_c8 | multiply(sk_c7,multiply(sk_c6,A)) = multiply(sk_c8,A). [para(7(a,1),33(a,1,1)),flip(b)].
% 104.97/105.23 54 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)])].
% 104.97/105.23 56 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)])].
% 104.97/105.23 60 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)])].
% 104.97/105.23 61 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c2,A)) = multiply(sk_c7,A). [para(13(a,1),33(a,1,1)),flip(b)].
% 104.97/105.23 65 inverse(sk_c3) = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c2,A). [para(15(a,1),33(a,1,1)),flip(b)].
% 104.97/105.23 68 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c2). [para(16(a,1),33(a,2,2)),rewrite([33(8)])].
% 104.97/105.23 71 inverse(sk_c1) = sk_c8 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(18(b,1),33(a,1,1)),flip(b)].
% 104.97/105.23 73 inverse(sk_c1) = sk_c8 | multiply(sk_c8,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(19(b,1),33(a,1,1)),flip(b)].
% 104.97/105.23 75 inverse(sk_c1) = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c5,A). [para(20(b,1),33(a,1,1)),flip(b)].
% 104.97/105.23 76 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(20(b,1),33(a,2,2)),rewrite([33(8)])].
% 104.97/105.23 80 multiply(sk_c7,sk_c6) = sk_c8 | multiply(A,multiply(sk_c3,sk_c8)) = multiply(A,sk_c7). [para(22(b,1),33(a,2,2)),rewrite([33(9)])].
% 104.97/105.23 92 multiply(sk_c8,sk_c2) = sk_c7 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(28(b,1),33(a,2,2)),rewrite([33(9)])].
% 104.97/105.23 98 multiply(sk_c8,sk_c5) = sk_c7 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c2). [para(31(a,1),33(a,2,2)),rewrite([33(9)])].
% 104.97/105.23 100 multiply(sk_c1,sk_c8) = sk_c2 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c5). [para(32(b,1),33(a,2,2)),rewrite([33(9)])].
% 104.97/105.23 218 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,identity). [para(44(b,1),33(a,2,2)),rewrite([33(8)])].
% 104.97/105.23 232 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),48(a,1,2))].
% 104.97/105.23 240 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),sk_c7) = sk_c5. [para(11(b,1),48(a,1,2))].
% 104.97/105.23 263 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),identity) = sk_c3. [para(44(b,1),48(a,1,2))].
% 104.97/105.23 264 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(48(a,1),48(a,1,2))].
% 104.97/105.23 265 multiply(A,identity) = A. [back_rewrite(232),rewrite([264(4)])].
% 104.97/105.23 266 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c3. [back_rewrite(263),rewrite([265(8)])].
% 104.97/105.23 270 inverse(sk_c8) = sk_c6 | multiply(A,multiply(sk_c8,sk_c3)) = A. [back_rewrite(218),rewrite([265(10)])].
% 104.97/105.23 273 inverse(identity) = identity. [para(265(a,1),2(a,1))].
% 104.97/105.23 292 inverse(sk_c8) = sk_c6 | multiply(sk_c3,sk_c8) = identity. [para(266(b,1),2(a,1,1))].
% 104.97/105.23 295 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c4. [para(45(b,1),48(a,1,2)),rewrite([265(8)])].
% 104.97/105.23 296 inverse(sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = identity. [para(295(b,1),2(a,1,1))].
% 104.97/105.23 312 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c8,sk_c3)) = A. [para(46(b,1),33(a,2,2)),rewrite([33(8),265(10)])].
% 104.97/105.23 336 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c8,sk_c4)) = A. [para(47(b,1),33(a,2,2)),rewrite([33(8),265(10)])].
% 104.97/105.23 344 inverse(sk_c3) = sk_c8 | multiply(sk_c7,multiply(sk_c6,sk_c2)) = sk_c7. [para(13(a,1),49(b,2)),merge(b)].
% 104.97/105.23 402 multiply(A,inverse(A)) = identity. [para(264(a,1),2(a,1))].
% 104.97/105.23 405 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c8),A) = multiply(sk_c3,A). [para(5(b,1),264(a,1,1,1))].
% 104.97/105.23 412 multiply(A,multiply(inverse(A),B)) = B. [para(264(a,1),48(a,1))].
% 104.97/105.23 413 inverse(inverse(A)) = A. [para(264(a,1),265(a,1)),rewrite([265(2)]),flip(a)].
% 104.97/105.23 459 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c8) = identity. [para(6(b,1),402(a,1,2))].
% 104.97/105.23 460 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(402(a,1),33(a,1)),flip(a)].
% 104.97/105.23 467 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(sk_c8),sk_c7) != multiply(A,sk_c8) | inverse(A) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,sk_c8) != sk_c7. [resolve(412,a,42,c),flip(c)].
% 104.97/105.23 788 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(A,multiply(B,sk_c8)) != multiply(inverse(sk_c8),sk_c7) | inverse(multiply(A,B)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,multiply(B,sk_c8)) != sk_c7. [para(33(a,1),467(c,2)),rewrite([33(29)]),flip(c)].
% 104.97/105.23 898 inverse(sk_c8) = sk_c6 | multiply(A,sk_c7) = A. [para(292(b,1),56(b,1,2)),rewrite([265(10)]),flip(c),merge(b)].
% 104.97/105.23 1382 inverse(sk_c8) = sk_c6 | multiply(A,sk_c5) = A. [para(296(b,1),60(b,1,2)),rewrite([265(10)]),flip(c),merge(b)].
% 104.97/105.23 1499 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c2,sk_c6)) = sk_c8. [para(7(a,1),61(b,2)),merge(b)].
% 104.97/105.23 2127 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = identity. [para(898(b,1),2(a,1))].
% 104.97/105.23 2368 inverse(sk_c8) = sk_c6 | multiply(sk_c7,A) = A. [para(2127(b,1),48(a,1,1)),rewrite([1(8)])].
% 104.97/105.23 2660 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = identity. [para(1382(b,1),2(a,1))].
% 104.97/105.23 2661 inverse(sk_c8) = sk_c6 | sk_c7 = sk_c8. [para(1382(b,1),11(b,1)),flip(c),merge(b)].
% 104.97/105.23 2846 inverse(sk_c8) = sk_c6 | multiply(sk_c5,A) = A. [para(2660(b,1),48(a,1,1)),rewrite([1(8)])].
% 104.97/105.23 2861 inverse(sk_c4) = sk_c8 | multiply(sk_c8,multiply(sk_c1,sk_c8)) = sk_c7. [para(14(a,1),68(b,2)),merge(b)].
% 104.97/105.23 3414 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c7),A) = A. [para(2368(b,1),48(a,1,2))].
% 104.97/105.23 3668 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c5),A) = A. [para(2846(b,1),48(a,1,2))].
% 104.97/105.23 4229 inverse(sk_c1) = sk_c8 | multiply(sk_c7,inverse(sk_c5)) = sk_c8. [para(402(a,1),73(b,1,2)),rewrite([265(7)]),flip(b)].
% 104.97/105.23 4569 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c3) = sk_c4. [para(46(b,1),75(b,1,2)),rewrite([265(11)]),flip(c),merge(b)].
% 104.97/105.23 4628 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c5),sk_c4) = sk_c3. [para(4569(b,1),48(a,1,2))].
% 104.97/105.23 4650 inverse(sk_c8) = sk_c6 | inverse(sk_c8) = sk_c5. [para(240(b,1),898(b,1)),flip(c),merge(b)].
% 104.97/105.23 4662 inverse(sk_c1) = sk_c8 | multiply(A,sk_c5) = A. [para(459(b,1),76(b,1,2)),rewrite([265(10)]),flip(c),merge(b)].
% 104.97/105.23 4747 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c8. [para(4650(b,1),413(a,1,1))].
% 104.97/105.23 5223 multiply(sk_c7,sk_c6) = sk_c8 | multiply(inverse(multiply(sk_c3,sk_c8)),sk_c7) = identity. [para(80(b,1),2(a,1))].
% 104.97/105.23 5282 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = identity. [para(4662(b,1),2(a,1))].
% 104.97/105.23 5283 inverse(sk_c1) = sk_c8 | sk_c7 = sk_c8. [para(4662(b,1),19(b,1)),flip(c),merge(b)].
% 104.97/105.23 5308 sk_c7 = sk_c8 | inverse(sk_c8) = sk_c1. [para(5283(a,1),413(a,1,1))].
% 104.97/105.23 5309 sk_c7 = sk_c8 | multiply(sk_c1,sk_c8) = identity. [para(5283(a,1),402(a,1,2))].
% 104.97/105.23 5310 sk_c7 = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = A. [para(5283(a,1),412(a,1,2,1))].
% 104.97/105.23 5336 sk_c7 = sk_c8 | sk_c1 = sk_c6. [para(5308(b,1),2661(a,1)),merge(c)].
% 104.97/105.23 5427 sk_c7 = sk_c8 | multiply(A,multiply(sk_c1,sk_c8)) = A. [para(5309(b,1),33(a,2,2)),rewrite([33(7),265(9)])].
% 104.97/105.23 6016 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(sk_c8),sk_c7) != A | inverse(multiply(A,inverse(sk_c8))) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | sk_c7 != A. [para(2(a,1),788(c,1,2)),rewrite([265(11),2(29),265(27)]),flip(c),flip(f)].
% 104.97/105.23 6606 multiply(sk_c8,sk_c2) = sk_c7 | multiply(sk_c8,multiply(sk_c4,sk_c8)) = sk_c7. [para(27(b,1),92(b,2)),merge(b)].
% 104.97/105.23 8367 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(460(a,1),48(a,1,2)),rewrite([265(3)]),flip(a)].
% 104.97/105.23 8565 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(8367(a,1),48(a,1,2)),flip(a)].
% 104.97/105.23 8837 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(sk_c8),sk_c7) != A | multiply(sk_c8,inverse(A)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | sk_c7 != A. [back_rewrite(6016),rewrite([8565(18),413(17)])].
% 104.97/105.23 8846 multiply(sk_c7,sk_c6) = sk_c8 | multiply(inverse(sk_c8),multiply(inverse(sk_c3),sk_c7)) = identity. [back_rewrite(5223),rewrite([8565(9),33(12)])].
% 104.97/105.23 9114 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | inverse(A) != multiply(inverse(sk_c8),sk_c7) | multiply(sk_c8,A) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | inverse(A) != sk_c7. [para(413(a,1),8837(d,1,2)),flip(c),flip(f)].
% 104.97/105.23 9132 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(sk_c8),sk_c7) != multiply(inverse(A),sk_c8) | sk_c8 != A | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(A),sk_c8) != sk_c7. [para(412(a,1),9114(d,1)),rewrite([8565(13),413(13),8565(28),413(28)]),flip(c),flip(d)].
% 104.97/105.23 10017 inverse(sk_c8) = sk_c6 | multiply(sk_c8,A) = A. [para(4747(b,1),3668(b,1,1)),merge(b)].
% 104.97/105.23 10076 inverse(sk_c8) = sk_c6 | multiply(inverse(sk_c8),A) = A. [para(10017(b,1),48(a,1,2))].
% 104.97/105.23 11843 inverse(sk_c8) = sk_c6 | multiply(A,sk_c3) = A. [para(10017(b,1),270(b,1,2)),merge(b)].
% 104.97/105.23 11865 inverse(sk_c8) = sk_c6 | multiply(A,sk_c8) = A. [para(11843(b,1),270(b,1,2)),merge(b)].
% 104.97/105.23 12654 inverse(sk_c3) = sk_c8 | multiply(sk_c6,sk_c2) = identity. [para(344(b,1),48(a,1,2)),rewrite([2(8)]),flip(b)].
% 104.97/105.23 12817 inverse(sk_c1) = sk_c8 | multiply(sk_c7,A) = A. [para(71(b,1),405(b,2)),rewrite([48(13)]),flip(c),merge(b)].
% 104.97/105.23 13322 inverse(sk_c8) = sk_c6 | inverse(sk_c7) = sk_c8. [para(11865(b,1),3414(b,1)),merge(b)].
% 104.97/105.23 13327 inverse(sk_c8) = sk_c6 | multiply(sk_c8,sk_c7) = identity. [para(13322(b,1),2(a,1,1))].
% 104.97/105.23 14263 inverse(sk_c3) = sk_c8 | inverse(sk_c6) = sk_c2. [para(12654(b,1),48(a,1,2)),rewrite([265(8)])].
% 104.97/105.23 14276 inverse(sk_c6) = sk_c2 | inverse(sk_c8) = sk_c3. [para(14263(a,1),413(a,1,1))].
% 104.97/105.23 14285 inverse(sk_c8) = sk_c3 | multiply(sk_c2,sk_c6) = identity. [para(14276(a,1),2(a,1,1))].
% 104.97/105.23 14318 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c8. [para(12817(b,1),4229(b,1)),merge(b)].
% 104.97/105.23 14327 inverse(sk_c1) = sk_c8 | identity = sk_c8. [para(14318(b,1),5282(b,1)),flip(c),merge(b)].
% 104.97/105.23 14328 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c4) = sk_c3. [para(14318(b,1),4628(b,1,1)),merge(b)].
% 104.97/105.23 14438 inverse(sk_c8) = sk_c6 | multiply(A,sk_c6) = A. [para(13327(b,1),54(b,1,2)),rewrite([265(10)]),flip(c),merge(b)].
% 104.97/105.23 14819 inverse(sk_c1) = sk_c8 | multiply(A,sk_c3) = A. [para(14328(b,1),336(b,1,2)),merge(b)].
% 104.97/105.23 15145 inverse(sk_c1) = sk_c8 | multiply(A,sk_c8) = A. [para(14819(b,1),312(b,1,2)),merge(b)].
% 104.97/105.23 15366 inverse(sk_c1) = sk_c8 | inverse(sk_c8) = identity. [para(15145(b,1),2(a,1))].
% 104.97/105.23 15422 inverse(sk_c8) = identity | multiply(sk_c1,sk_c8) = identity. [para(15366(a,1),402(a,1,2))].
% 104.97/105.23 16245 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != multiply(inverse(sk_c8),sk_c7) | multiply(B,A) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7. [para(8565(a,1),9132(c,2,1)),rewrite([33(18),8565(29),33(32)]),flip(c),flip(d)].
% 104.97/105.23 17115 inverse(sk_c8) = sk_c3 | multiply(inverse(sk_c6),inverse(sk_c2)) = identity. [para(14285(b,1),8565(a,1,1)),rewrite([273(6)]),flip(b)].
% 104.97/105.23 17288 inverse(sk_c8) = identity | multiply(inverse(sk_c8),inverse(sk_c1)) = identity. [para(15422(b,1),8565(a,1,1)),rewrite([273(6)]),flip(b)].
% 104.97/105.23 17443 multiply(sk_c7,sk_c6) != sk_c8 | inverse(sk_c8) != sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != multiply(inverse(sk_c8),sk_c7) | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7. [factor(16245,a,d)].
% 104.97/105.23 18519 inverse(sk_c8) = sk_c6. [para(10076(b,1),14438(b,1)),flip(c),merge(b),merge(c)].
% 104.97/105.23 19149 multiply(sk_c7,sk_c6) != sk_c8 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != multiply(sk_c6,sk_c7) | multiply(sk_c8,sk_c7) != sk_c6 | multiply(inverse(sk_c6),multiply(inverse(sk_c7),sk_c8)) != sk_c7. [back_rewrite(17443),rewrite([18519(7),18519(17)]),xx(b)].
% 104.97/105.23 19273 identity = sk_c6 | multiply(sk_c6,inverse(sk_c1)) = identity. [back_rewrite(17288),rewrite([18519(2),18519(5)]),flip(a)].
% 104.97/105.23 19400 sk_c3 = sk_c6 | multiply(inverse(sk_c6),inverse(sk_c2)) = identity. [back_rewrite(17115),rewrite([18519(2)]),flip(a)].
% 104.97/105.23 21708 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c6,multiply(inverse(sk_c3),sk_c7)) = identity. [back_rewrite(8846),rewrite([18519(7)])].
% 104.97/105.23 23618 multiply(sk_c6,sk_c8) = identity. [para(18519(a,1),2(a,1,1))].
% 104.97/105.23 23619 multiply(sk_c6,multiply(sk_c8,A)) = A. [para(18519(a,1),48(a,1,1))].
% 104.97/105.23 23620 inverse(sk_c6) = sk_c8. [para(18519(a,1),413(a,1,1))].
% 104.97/105.23 23621 multiply(sk_c8,sk_c6) = identity. [para(18519(a,1),402(a,1,2))].
% 104.97/105.23 23703 sk_c3 = sk_c6 | multiply(sk_c8,inverse(sk_c2)) = identity. [back_rewrite(19400),rewrite([23620(5)])].
% 104.97/105.23 23716 multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != multiply(sk_c6,sk_c7) | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,multiply(inverse(sk_c7),sk_c8)) != sk_c7. [back_rewrite(19149),rewrite([23620(7),23620(22)])].
% 104.97/105.23 25932 inverse(sk_c3) = sk_c8 | multiply(sk_c2,sk_c6) = identity. [para(1499(b,1),48(a,1,2)),rewrite([18519(6),23618(7)]),flip(b)].
% 104.97/105.23 26481 inverse(sk_c3) = sk_c8 | identity = sk_c1. [para(25932(b,1),65(b,2)),rewrite([23621(12),265(11)]),flip(c),merge(b)].
% 104.97/105.23 26485 identity = sk_c1 | sk_c3 = sk_c6. [para(26481(a,1),413(a,1,1)),rewrite([18519(5)]),flip(b)].
% 104.97/105.23 26491 sk_c3 = sk_c6 | inverse(sk_c1) = identity. [para(26485(a,1),273(a,1,1))].
% 104.97/105.23 26520 sk_c3 = sk_c6 | identity = sk_c8. [para(26491(b,1),14327(a,1)),merge(c)].
% 104.97/105.23 26526 sk_c3 = sk_c6 | identity = sk_c6. [para(26491(b,1),19273(b,1,2)),rewrite([265(9)]),flip(c),merge(c)].
% 104.97/105.23 26530 sk_c3 = sk_c6 | multiply(sk_c8,A) = A. [para(26520(b,1),1(a,1,1))].
% 104.97/105.23 26601 sk_c3 = sk_c6 | inverse(sk_c2) = identity. [para(26530(b,1),23703(b,1)),merge(b)].
% 104.97/105.23 26613 sk_c3 = sk_c6 | inverse(sk_c2) = sk_c8. [para(26520(b,1),26601(b,2)),merge(b)].
% 104.97/105.23 26636 sk_c3 = sk_c6 | multiply(sk_c8,sk_c8) = identity. [para(26613(b,1),23703(b,1,2)),merge(b)].
% 104.97/105.23 26694 sk_c3 = sk_c6 | multiply(sk_c8,sk_c8) = sk_c6. [para(26526(b,1),26636(b,2)),merge(b)].
% 104.97/105.23 27145 sk_c7 = sk_c8 | inverse(sk_c4) = sk_c8. [para(5336(b,1),2861(b,1,2,1)),rewrite([23618(11),265(10)]),flip(c),merge(c)].
% 104.97/105.23 27150 sk_c7 = sk_c8 | sk_c4 = sk_c6. [para(27145(b,1),413(a,1,1)),rewrite([18519(5)]),flip(b)].
% 104.97/105.23 27152 sk_c7 = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(27145(b,1),412(a,1,2,1))].
% 104.97/105.23 30277 sk_c7 = sk_c8 | multiply(sk_c8,sk_c2) = sk_c7. [para(27150(b,1),6606(b,1,2,1)),rewrite([23618(12),265(11)]),flip(c),merge(c)].
% 104.97/105.23 30285 sk_c7 = sk_c8 | multiply(sk_c1,sk_c7) = sk_c2. [para(30277(b,1),5310(b,1,2)),merge(b)].
% 104.97/105.23 30289 sk_c7 = sk_c8 | multiply(inverse(sk_c1),sk_c2) = sk_c7. [para(30285(b,1),48(a,1,2))].
% 104.97/105.23 30293 sk_c7 = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7. [para(30289(b,1),98(b,2)),rewrite([48(14)]),flip(c),merge(c)].
% 104.97/105.23 32698 sk_c7 = sk_c8 | multiply(sk_c4,sk_c7) = sk_c5. [para(30293(b,1),27152(b,1,2)),merge(b)].
% 104.97/105.23 32708 sk_c7 = sk_c8 | multiply(inverse(sk_c4),sk_c5) = sk_c7. [para(32698(b,1),48(a,1,2))].
% 104.97/105.23 32718 sk_c7 = sk_c8 | multiply(sk_c1,sk_c8) = sk_c2. [para(32708(b,1),100(b,2)),rewrite([48(14)]),flip(c),merge(c)].
% 104.97/105.23 32742 sk_c7 = sk_c8 | multiply(A,sk_c2) = A. [para(32718(b,1),5427(b,1,2)),merge(b)].
% 104.97/105.23 32782 sk_c7 = sk_c8. [para(32742(b,1),30277(b,1)),flip(c),merge(b),merge(c)].
% 104.97/105.23 35209 identity != sk_c8 | multiply(sk_c8,sk_c8) != sk_c6. [back_rewrite(23716),rewrite([32782(1),23621(3),32782(5),18519(6),23618(7),265(6),32782(6),23618(7),32782(8),32782(13),18519(14),23618(15),265(14),32782(13)]),flip(b),xx(d),merge(b)].
% 104.97/105.23 35279 identity = sk_c8 | multiply(sk_c6,multiply(inverse(sk_c3),sk_c8)) = identity. [back_rewrite(21708),rewrite([32782(1),23621(3),32782(7)])].
% 104.97/105.23 36030 identity != sk_c8 | sk_c3 = sk_c6. [resolve(35209,b,26694,b)].
% 104.97/105.23 36453 sk_c3 = sk_c6. [resolve(36030,a,26520,b),merge(b)].
% 104.97/105.23 36598 identity = sk_c8. [back_rewrite(35279),rewrite([36453(5),23620(6),23619(8)]),flip(b),merge(b)].
% 104.97/105.23 36658 multiply(sk_c8,sk_c8) != sk_c6. [back_rewrite(35209),rewrite([36598(1)]),xx(a)].
% 104.97/105.23 36669 sk_c6 = sk_c8. [back_rewrite(273),rewrite([36598(1),18519(2),36598(2)])].
% 104.97/105.23 36670 multiply(A,sk_c8) = A. [back_rewrite(265),rewrite([36598(1)])].
% 104.97/105.23 36686 $F. [back_rewrite(36658),rewrite([36670(3),36669(2)]),xx(a)].
% 104.97/105.23
% 104.97/105.23 % SZS output end Refutation
% 104.97/105.23 ============================== end of proof ==========================
% 104.97/105.23
% 104.97/105.23 ============================== STATISTICS ============================
% 104.97/105.23
% 104.97/105.23 Given=9649. Generated=5949976. Kept=36685. proofs=1.
% 104.97/105.23 Usable=10. Sos=57. Demods=20. Limbo=17, Disabled=36635. Hints=0.
% 104.97/105.23 Megabytes=30.97.
% 104.97/105.23 User_CPU=101.20, System_CPU=3.09, Wall_clock=105.
% 104.97/105.23
% 104.97/105.23 ============================== end of statistics =====================
% 104.97/105.23
% 104.97/105.23 ============================== end of search =========================
% 104.97/105.23
% 104.97/105.23 THEOREM PROVED
% 104.97/105.23 % SZS status Unsatisfiable
% 104.97/105.23
% 104.97/105.23 Exiting with 1 proof.
% 104.97/105.23
% 104.97/105.23 Process 20003 exit (max_proofs) Mon Jun 13 13:54:32 2022
% 104.97/105.23 Prover9 interrupted
%------------------------------------------------------------------------------