TSTP Solution File: GRP344-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP344-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:18:42 EDT 2022
% Result : Unsatisfiable 9.23s 9.58s
% Output : Refutation 9.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP344-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 04:32:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.23/9.58 ============================== Prover9 ===============================
% 9.23/9.58 Prover9 (32) version 2009-11A, November 2009.
% 9.23/9.58 Process 30128 was started by sandbox on n013.cluster.edu,
% 9.23/9.58 Mon Jun 13 04:32:29 2022
% 9.23/9.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29975_n013.cluster.edu".
% 9.23/9.58 ============================== end of head ===========================
% 9.23/9.58
% 9.23/9.58 ============================== INPUT =================================
% 9.23/9.58
% 9.23/9.58 % Reading from file /tmp/Prover9_29975_n013.cluster.edu
% 9.23/9.58
% 9.23/9.58 set(prolog_style_variables).
% 9.23/9.58 set(auto2).
% 9.23/9.58 % set(auto2) -> set(auto).
% 9.23/9.58 % set(auto) -> set(auto_inference).
% 9.23/9.58 % set(auto) -> set(auto_setup).
% 9.23/9.58 % set(auto_setup) -> set(predicate_elim).
% 9.23/9.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.23/9.58 % set(auto) -> set(auto_limits).
% 9.23/9.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.23/9.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.23/9.58 % set(auto) -> set(auto_denials).
% 9.23/9.58 % set(auto) -> set(auto_process).
% 9.23/9.58 % set(auto2) -> assign(new_constants, 1).
% 9.23/9.58 % set(auto2) -> assign(fold_denial_max, 3).
% 9.23/9.58 % set(auto2) -> assign(max_weight, "200.000").
% 9.23/9.58 % set(auto2) -> assign(max_hours, 1).
% 9.23/9.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.23/9.58 % set(auto2) -> assign(max_seconds, 0).
% 9.23/9.58 % set(auto2) -> assign(max_minutes, 5).
% 9.23/9.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.23/9.58 % set(auto2) -> set(sort_initial_sos).
% 9.23/9.58 % set(auto2) -> assign(sos_limit, -1).
% 9.23/9.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.23/9.58 % set(auto2) -> assign(max_megs, 400).
% 9.23/9.58 % set(auto2) -> assign(stats, some).
% 9.23/9.58 % set(auto2) -> clear(echo_input).
% 9.23/9.58 % set(auto2) -> set(quiet).
% 9.23/9.58 % set(auto2) -> clear(print_initial_clauses).
% 9.23/9.58 % set(auto2) -> clear(print_given).
% 9.23/9.58 assign(lrs_ticks,-1).
% 9.23/9.58 assign(sos_limit,10000).
% 9.23/9.58 assign(order,kbo).
% 9.23/9.58 set(lex_order_vars).
% 9.23/9.58 clear(print_given).
% 9.23/9.58
% 9.23/9.58 % formulas(sos). % not echoed (21 formulas)
% 9.23/9.58
% 9.23/9.58 ============================== end of input ==========================
% 9.23/9.58
% 9.23/9.58 % From the command line: assign(max_seconds, 300).
% 9.23/9.58
% 9.23/9.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.23/9.58
% 9.23/9.58 % Formulas that are not ordinary clauses:
% 9.23/9.58
% 9.23/9.58 ============================== end of process non-clausal formulas ===
% 9.23/9.58
% 9.23/9.58 ============================== PROCESS INITIAL CLAUSES ===============
% 9.23/9.58
% 9.23/9.58 ============================== PREDICATE ELIMINATION =================
% 9.23/9.58
% 9.23/9.58 ============================== end predicate elimination =============
% 9.23/9.58
% 9.23/9.58 Auto_denials: (non-Horn, no changes).
% 9.23/9.58
% 9.23/9.58 Term ordering decisions:
% 9.23/9.58
% 9.23/9.58 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 9.23/9.58 Function symbol KB weights: sk_c6=1. sk_c5=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 9.23/9.58
% 9.23/9.58 ============================== end of process initial clauses ========
% 9.23/9.58
% 9.23/9.58 ============================== CLAUSES FOR SEARCH ====================
% 9.23/9.58
% 9.23/9.58 ============================== end of clauses for search =============
% 9.23/9.58
% 9.23/9.58 ============================== SEARCH ================================
% 9.23/9.58
% 9.23/9.58 % Starting search at 0.01 seconds.
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=44.000, iters=3678
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=39.000, iters=3524
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=37.000, iters=3442
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=36.000, iters=3405
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=35.000, iters=3368
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=34.000, iters=3371
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=33.000, iters=3355
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=32.000, iters=3345
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=31.000, iters=3387
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=30.000, iters=3353
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=29.000, iters=3352
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=28.000, iters=3348
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=27.000, iters=3416
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=26.000, iters=3337
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=25.000, iters=3371
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=24.000, iters=3489
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=23.000, iters=3349
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=22.000, iters=3377
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=21.000, iters=3386
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=20.000, iters=3333
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=19.000, iters=3355
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=18.000, iters=3348
% 9.23/9.58
% 9.23/9.58 Low Water (keep): wt=17.000, iters=3333
% 9.23/9.58
% 9.23/9.58 ============================== PROOF =================================
% 9.23/9.58 % SZS status Unsatisfiable
% 9.23/9.58 % SZS output start Refutation
% 9.23/9.58
% 9.23/9.58 % Proof 1 at 8.40 (+ 0.18) seconds.
% 9.23/9.58 % Length of proof is 111.
% 9.23/9.58 % Level of proof is 28.
% 9.23/9.58 % Maximum clause weight is 42.000.
% 9.23/9.58 % Given clauses 1704.
% 9.23/9.58
% 9.23/9.58 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 9.23/9.58 2 multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 9.23/9.58 3 sk_c5 = multiply(sk_c6,sk_c7). [copy(2),flip(a)].
% 9.23/9.58 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 9.23/9.58 5 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 9.23/9.58 6 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c5 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 9.23/9.58 7 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = inverse(sk_c4). [copy(6),rewrite([3(7)]),flip(b)].
% 9.23/9.58 8 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 9.23/9.58 9 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c5 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 9.23/9.58 10 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c4). [copy(9),rewrite([3(7)]),flip(b)].
% 9.23/9.58 11 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 9.23/9.58 12 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 9.23/9.58 13 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7). [copy(12),rewrite([3(8)])].
% 9.23/9.58 14 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 9.23/9.58 17 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 9.23/9.58 18 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c6) = sk_c5 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 9.23/9.58 19 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7). [copy(18),rewrite([3(8)])].
% 9.23/9.58 20 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 9.23/9.58 21 multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 | inverse(sk_c3) = sk_c6. [copy(20),rewrite([3(2)])].
% 9.23/9.58 22 multiply(sk_c2,sk_c5) = sk_c6 | inverse(sk_c4) = sk_c5 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 9.23/9.58 23 multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c4). [copy(22),rewrite([3(2),3(10)]),flip(b)].
% 9.23/9.58 24 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 9.23/9.58 27 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 9.23/9.58 28 multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7. [copy(27),rewrite([3(2)])].
% 9.23/9.58 29 multiply(sk_c2,sk_c5) = sk_c6 | multiply(sk_c4,sk_c6) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 9.23/9.58 30 multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7). [copy(29),rewrite([3(2),3(11)])].
% 9.23/9.58 31 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 9.23/9.58 32 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(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | inverse(D) != sk_c5 | multiply(D,sk_c6) != sk_c5 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 9.23/9.58 33 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | inverse(D) != multiply(sk_c6,sk_c7) | multiply(sk_c6,sk_c7) != multiply(D,sk_c6). [copy(32),rewrite([3(4),3(18),3(32),3(38)]),flip(i),xx(a)].
% 9.23/9.58 39 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = inverse(sk_c4). [para(7(b,1),13(b,2)),merge(b)].
% 9.23/9.58 40 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c6) = inverse(sk_c4). [para(10(b,1),19(b,2)),merge(b)].
% 9.23/9.58 41 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),31(a,1,1)),rewrite([1(2)]),flip(a)].
% 9.23/9.58 43 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,inverse(sk_c4)). [para(7(b,1),31(a,2,2)),rewrite([31(8)])].
% 9.23/9.58 47 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(11(b,1),31(a,2,2)),rewrite([31(8)])].
% 9.23/9.58 50 inverse(sk_c3) = sk_c6 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(14(a,1),31(a,1,1)),flip(b)].
% 9.23/9.58 55 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(17(b,1),31(a,2,2)),rewrite([31(8)])].
% 9.23/9.58 62 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(24(b,1),31(a,1,1)),flip(b)].
% 9.23/9.58 93 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | inverse(C) != multiply(sk_c6,sk_c7) | multiply(sk_c6,sk_c7) != multiply(C,sk_c6). [para(4(a,1),33(e,1))].
% 9.23/9.58 253 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),41(a,1,2))].
% 9.23/9.58 257 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(11(b,1),41(a,1,2))].
% 9.23/9.58 273 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(41(a,1),41(a,1,2))].
% 9.23/9.58 274 multiply(A,identity) = A. [back_rewrite(253),rewrite([273(4)])].
% 9.23/9.58 277 inverse(identity) = identity. [para(274(a,1),4(a,1))].
% 9.23/9.58 318 multiply(A,inverse(A)) = identity. [para(273(a,1),4(a,1))].
% 9.23/9.58 334 multiply(A,multiply(inverse(A),B)) = B. [para(273(a,1),41(a,1))].
% 9.23/9.58 335 inverse(inverse(A)) = A. [para(273(a,1),274(a,1)),rewrite([274(2)]),flip(a)].
% 9.23/9.58 359 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,multiply(sk_c6,sk_c7)) != sk_c6 | identity != sk_c7 | inverse(C) != multiply(sk_c6,sk_c7) | multiply(sk_c6,sk_c7) != multiply(C,sk_c6). [back_rewrite(93),rewrite([335(22)]),xx(f)].
% 9.23/9.58 362 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = identity. [para(5(b,1),318(a,1,2))].
% 9.23/9.58 363 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(8(b,1),318(a,1,2))].
% 9.23/9.58 364 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(318(a,1),31(a,1)),flip(a)].
% 9.23/9.58 855 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c6. [para(5(b,1),257(b,1,1)),merge(b)].
% 9.23/9.58 862 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6. [para(855(b,1),7(b,1)),flip(c),merge(b)].
% 9.23/9.58 906 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = identity. [para(862(b,1),318(a,1,2))].
% 9.23/9.58 1079 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = identity. [para(906(b,1),13(b,1)),flip(c),merge(b)].
% 9.23/9.58 1081 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = identity. [para(906(b,1),39(b,1)),flip(c),merge(b)].
% 9.23/9.58 1098 inverse(sk_c1) = sk_c7 | multiply(A,sk_c7) = A. [para(362(b,1),47(b,1,2)),rewrite([274(10)]),flip(c),merge(b)].
% 9.23/9.58 1270 inverse(sk_c1) = sk_c7 | multiply(sk_c4,A) = A. [para(1081(b,1),41(a,1,1)),rewrite([1(8)])].
% 9.23/9.58 1956 inverse(sk_c1) = sk_c7 | multiply(A,inverse(sk_c4)) = A. [para(1079(b,1),43(b,1,2)),rewrite([274(10)]),flip(c),merge(b)].
% 9.23/9.58 2272 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),A) = A. [para(1270(b,1),41(a,1,2))].
% 9.23/9.58 3238 inverse(sk_c2) = sk_c6 | multiply(A,sk_c7) = A. [para(363(b,1),55(b,1,2)),rewrite([274(10)]),flip(c),merge(b)].
% 9.23/9.58 3701 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6. [para(3238(b,1),10(b,1)),flip(c),merge(b)].
% 9.23/9.58 4077 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c6) = identity. [para(3701(b,1),318(a,1,2))].
% 9.23/9.58 4870 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = identity. [para(4077(b,1),40(b,1)),flip(c),merge(b)].
% 9.23/9.58 5114 inverse(sk_c2) = sk_c6 | multiply(sk_c4,A) = A. [para(4870(b,1),41(a,1,1)),rewrite([1(8)])].
% 9.23/9.58 5381 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c3,multiply(sk_c6,inverse(sk_c7))) = identity. [para(318(a,1),62(b,2))].
% 9.23/9.58 5947 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c4),A) = A. [para(5114(b,1),41(a,1,2))].
% 9.23/9.58 6402 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(364(a,1),41(a,1,2)),rewrite([274(3)]),flip(a)].
% 9.23/9.58 6415 inverse(sk_c3) = sk_c6 | multiply(sk_c7,inverse(multiply(sk_c1,sk_c6))) = identity. [para(364(a,1),50(b,1)),flip(b)].
% 9.23/9.58 6508 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(6402(a,1),41(a,1,2)),flip(a)].
% 9.23/9.58 6610 inverse(sk_c3) = sk_c6 | multiply(sk_c7,multiply(inverse(sk_c6),inverse(sk_c1))) = identity. [back_rewrite(6415),rewrite([6508(9)])].
% 9.23/9.58 9236 inverse(sk_c1) = sk_c7 | multiply(A,sk_c6) = A. [para(862(b,1),1956(b,1,2)),merge(b)].
% 9.23/9.58 9563 inverse(sk_c1) = sk_c7 | identity = sk_c3. [para(9236(b,1),362(b,1)),flip(c),merge(b)].
% 9.23/9.58 9594 identity = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(9563(a,1),318(a,1,2))].
% 9.23/9.58 10069 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c7. [para(2272(b,1),1098(b,1)),flip(c),merge(b)].
% 9.23/9.58 10078 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c7. [para(10069(b,1),39(b,2)),merge(b)].
% 9.23/9.58 10357 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c6. [para(10078(b,1),41(a,1,2))].
% 9.23/9.58 11687 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c7. [para(5947(b,1),3238(b,1)),flip(c),merge(b)].
% 9.23/9.58 11696 inverse(sk_c2) = sk_c6 | sk_c7 = sk_c6. [para(11687(b,1),3701(b,1)),merge(b)].
% 9.23/9.58 11716 sk_c7 = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(11696(a,1),334(a,1,2,1))].
% 9.23/9.58 12991 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(10069(b,1),10357(b,1,1)),merge(b)].
% 9.23/9.58 13013 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(12991(b,1),41(a,1,2))].
% 9.23/9.58 13684 sk_c7 = sk_c6 | inverse(sk_c3) = sk_c6. [para(11716(b,1),21(a,1)),merge(b)].
% 9.23/9.58 13685 sk_c7 = sk_c6 | multiply(sk_c6,sk_c7) = inverse(sk_c4). [para(11716(b,1),23(a,1)),merge(b)].
% 9.23/9.58 13686 sk_c7 = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7. [para(11716(b,1),28(a,1)),merge(b)].
% 9.23/9.58 13687 sk_c7 = sk_c6 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7). [para(11716(b,1),30(a,1)),merge(b)].
% 9.23/9.58 13709 sk_c7 = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(13684(b,1),318(a,1,2))].
% 9.23/9.58 13761 sk_c7 = sk_c6 | identity = sk_c7. [para(13709(b,1),13686(b,1)),merge(b)].
% 9.23/9.58 13763 sk_c7 = sk_c6 | multiply(A,sk_c7) = A. [para(13761(b,1),274(a,1,2))].
% 9.23/9.58 14099 sk_c7 = sk_c6 | inverse(sk_c4) = sk_c6. [para(13685(b,1),13763(b,1)),merge(b)].
% 9.23/9.58 14103 sk_c7 = sk_c6 | multiply(sk_c4,sk_c6) = identity. [para(14099(b,1),318(a,1,2))].
% 9.23/9.58 14159 sk_c7 = sk_c6 | multiply(sk_c4,sk_c6) = sk_c7. [para(13761(b,1),14103(b,2)),merge(b)].
% 9.23/9.58 14447 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | inverse(B) != multiply(sk_c6,sk_c7) | multiply(sk_c6,sk_c7) != multiply(B,sk_c6). [para(1(a,1),359(d,1)),rewrite([277(9)])].
% 9.23/9.58 14472 inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | multiply(sk_c6,sk_c7) != identity. [para(1(a,1),14447(g,2)),rewrite([277(20)]),flip(f),merge(g)].
% 9.23/9.58 14475 multiply(inverse(A),inverse(B)) != sk_c7 | multiply(B,multiply(A,sk_c6)) != sk_c7 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | multiply(sk_c6,sk_c7) != identity. [para(31(a,1),14472(b,1)),rewrite([6508(2)])].
% 9.23/9.58 14476 multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | multiply(sk_c6,sk_c7) != identity. [para(4(a,1),14475(b,1,2)),rewrite([335(3),274(7)]),flip(b)].
% 9.23/9.58 14478 multiply(sk_c6,A) != sk_c7 | inverse(A) != sk_c7 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | multiply(sk_c6,sk_c7) != identity. [para(335(a,1),14476(a,1,2)),flip(b)].
% 9.23/9.58 14494 multiply(inverse(sk_c7),sk_c6) != sk_c7 | identity != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | identity != sk_c7 | multiply(sk_c6,sk_c7) != identity. [resolve(14478,a,334,a),rewrite([6508(5),335(5)])].
% 9.23/9.58 16460 sk_c7 = sk_c6 | multiply(sk_c4,sk_c6) = sk_c6. [para(13763(b,1),13687(b,2)),merge(b)].
% 9.23/9.58 16476 sk_c7 = sk_c6. [para(16460(b,1),14159(b,1)),flip(c),merge(b),merge(c)].
% 9.23/9.58 17364 identity != sk_c6 | multiply(sk_c6,sk_c6) != sk_c6 | multiply(sk_c6,sk_c6) != identity. [back_rewrite(14494),rewrite([16476(1),4(4),16476(2),16476(8),16476(13),16476(16)]),merge(b),merge(d)].
% 9.23/9.58 17791 inverse(sk_c1) = sk_c6 | identity = sk_c6. [back_rewrite(13013),rewrite([16476(3),16476(5),4(8),16476(6)])].
% 9.23/9.58 19250 identity = sk_c3 | multiply(sk_c1,sk_c6) = identity. [back_rewrite(9594),rewrite([16476(5)])].
% 9.23/9.58 20292 inverse(sk_c3) = sk_c6 | inverse(sk_c1) = identity. [back_rewrite(6610),rewrite([16476(5),334(11)])].
% 9.23/9.58 20462 multiply(sk_c1,sk_c6) = sk_c6 | identity = sk_c3. [back_rewrite(5381),rewrite([16476(4),16476(8),318(10),274(8)]),flip(b)].
% 9.23/9.58 23416 identity = sk_c3 | identity = sk_c6. [para(20462(a,1),19250(b,1)),flip(c),merge(b)].
% 9.23/9.58 23520 identity = sk_c6 | inverse(sk_c3) = identity. [para(23416(a,1),277(a,1,1))].
% 9.23/9.58 23576 identity = sk_c6 | inverse(sk_c1) = identity. [para(23520(b,1),20292(a,1)),merge(b)].
% 9.23/9.58 23697 identity = sk_c6. [para(23576(b,1),17791(a,1)),merge(b),merge(c)].
% 9.23/9.58 25139 multiply(sk_c6,sk_c6) != sk_c6. [back_rewrite(17364),rewrite([23697(1),23697(12)]),xx(a),merge(b)].
% 9.23/9.58 25164 multiply(A,sk_c6) = A. [back_rewrite(274),rewrite([23697(1)])].
% 9.23/9.58 25165 $F. [resolve(25164,a,25139,a)].
% 9.23/9.58
% 9.23/9.58 % SZS output end Refutation
% 9.23/9.58 ============================== end of proof ==========================
% 9.23/9.58
% 9.23/9.58 ============================== STATISTICS ============================
% 9.23/9.58
% 9.23/9.58 Given=1704. Generated=335928. Kept=25152. proofs=1.
% 9.23/9.58 Usable=76. Sos=1382. Demods=14. Limbo=1467, Disabled=22247. Hints=0.
% 9.23/9.58 Megabytes=21.38.
% 9.23/9.58 User_CPU=8.40, System_CPU=0.18, Wall_clock=9.
% 9.23/9.58
% 9.23/9.58 ============================== end of statistics =====================
% 9.23/9.58
% 9.23/9.58 ============================== end of search =========================
% 9.23/9.58
% 9.23/9.58 THEOREM PROVED
% 9.23/9.58 % SZS status Unsatisfiable
% 9.23/9.58
% 9.23/9.58 Exiting with 1 proof.
% 9.23/9.58
% 9.23/9.58 Process 30128 exit (max_proofs) Mon Jun 13 04:32:38 2022
% 9.23/9.58 Prover9 interrupted
%------------------------------------------------------------------------------