TSTP Solution File: GRP321-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP321-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:18:37 EDT 2022
% Result : Unsatisfiable 186.81s 187.11s
% Output : Refutation 186.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP321-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.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 06:52:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.15/6.43 ============================== Prover9 ===============================
% 6.15/6.43 Prover9 (32) version 2009-11A, November 2009.
% 6.15/6.43 Process 21351 was started by sandbox2 on n009.cluster.edu,
% 6.15/6.43 Mon Jun 13 06:52:53 2022
% 6.15/6.43 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21198_n009.cluster.edu".
% 6.15/6.43 ============================== end of head ===========================
% 6.15/6.43
% 6.15/6.43 ============================== INPUT =================================
% 6.15/6.43
% 6.15/6.43 % Reading from file /tmp/Prover9_21198_n009.cluster.edu
% 6.15/6.43
% 6.15/6.43 set(prolog_style_variables).
% 6.15/6.43 set(auto2).
% 6.15/6.43 % set(auto2) -> set(auto).
% 6.15/6.43 % set(auto) -> set(auto_inference).
% 6.15/6.43 % set(auto) -> set(auto_setup).
% 6.15/6.43 % set(auto_setup) -> set(predicate_elim).
% 6.15/6.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.15/6.43 % set(auto) -> set(auto_limits).
% 6.15/6.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.15/6.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.15/6.43 % set(auto) -> set(auto_denials).
% 6.15/6.43 % set(auto) -> set(auto_process).
% 6.15/6.43 % set(auto2) -> assign(new_constants, 1).
% 6.15/6.43 % set(auto2) -> assign(fold_denial_max, 3).
% 6.15/6.43 % set(auto2) -> assign(max_weight, "200.000").
% 6.15/6.43 % set(auto2) -> assign(max_hours, 1).
% 6.15/6.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.15/6.43 % set(auto2) -> assign(max_seconds, 0).
% 6.15/6.43 % set(auto2) -> assign(max_minutes, 5).
% 6.15/6.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.15/6.43 % set(auto2) -> set(sort_initial_sos).
% 6.15/6.43 % set(auto2) -> assign(sos_limit, -1).
% 6.15/6.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.15/6.43 % set(auto2) -> assign(max_megs, 400).
% 6.15/6.43 % set(auto2) -> assign(stats, some).
% 6.15/6.43 % set(auto2) -> clear(echo_input).
% 6.15/6.43 % set(auto2) -> set(quiet).
% 6.15/6.43 % set(auto2) -> clear(print_initial_clauses).
% 6.15/6.43 % set(auto2) -> clear(print_given).
% 6.15/6.43 assign(lrs_ticks,-1).
% 6.15/6.43 assign(sos_limit,10000).
% 6.15/6.43 assign(order,kbo).
% 6.15/6.43 set(lex_order_vars).
% 6.15/6.43 clear(print_given).
% 6.15/6.43
% 6.15/6.43 % formulas(sos). % not echoed (34 formulas)
% 6.15/6.43
% 6.15/6.43 ============================== end of input ==========================
% 6.15/6.43
% 6.15/6.43 % From the command line: assign(max_seconds, 300).
% 6.15/6.43
% 6.15/6.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.15/6.43
% 6.15/6.43 % Formulas that are not ordinary clauses:
% 6.15/6.43
% 6.15/6.43 ============================== end of process non-clausal formulas ===
% 6.15/6.43
% 6.15/6.43 ============================== PROCESS INITIAL CLAUSES ===============
% 6.15/6.43
% 6.15/6.43 ============================== PREDICATE ELIMINATION =================
% 6.15/6.43
% 6.15/6.43 ============================== end predicate elimination =============
% 6.15/6.43
% 6.15/6.43 Auto_denials: (non-Horn, no changes).
% 6.15/6.43
% 6.15/6.43 Term ordering decisions:
% 6.15/6.43
% 6.15/6.43 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 6.15/6.43 Function symbol KB weights: sk_c7=1. sk_c8=1. sk_c6=1. sk_c4=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. identity=1. multiply=1. inverse=0.
% 6.15/6.43
% 6.15/6.43 ============================== end of process initial clauses ========
% 6.15/6.43
% 6.15/6.43 ============================== CLAUSES FOR SEARCH ====================
% 6.15/6.43
% 6.15/6.43 ============================== end of clauses for search =============
% 6.15/6.43
% 6.15/6.43 ============================== SEARCH ================================
% 6.15/6.43
% 6.15/6.43 % Starting search at 0.02 seconds.
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=53.000, iters=3577
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=49.000, iters=3415
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=48.000, iters=3333
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=46.000, iters=3436
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=45.000, iters=3346
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=44.000, iters=3345
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=43.000, iters=3525
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=42.000, iters=3481
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=41.000, iters=3513
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=40.000, iters=3380
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=39.000, iters=3341
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=37.000, iters=3375
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=36.000, iters=3414
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=35.000, iters=3341
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=34.000, iters=3360
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=33.000, iters=3343
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=32.000, iters=3358
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=31.000, iters=3340
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=30.000, iters=3345
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=29.000, iters=3351
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=26.000, iters=3344
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=23.000, iters=3335
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=17.000, iters=3371
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=16.000, iters=3434
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=15.000, iters=3352
% 6.15/6.43
% 6.15/6.43 Low Water (keep): wt=14.000, iters=3336
% 6.15/6.43
% 6.15/6.43 Low Water (displace): id=3597, wt=57.000
% 186.81/187.11
% 186.81/187.11 Low Water (displace): id=16194, wt=13.000
% 186.81/187.11
% 186.81/187.11 Low Water (displace): id=16308, wt=12.000
% 186.81/187.11
% 186.81/187.11 Low Water (keep): wt=13.000, iters=3420
% 186.81/187.11
% 186.81/187.11 Low Water (displace): id=16440, wt=11.000
% 186.81/187.11
% 186.81/187.11 Low Water (displace): id=16550, wt=10.000
% 186.81/187.11
% 186.81/187.11 Low Water (keep): wt=12.000, iters=3334
% 186.81/187.11
% 186.81/187.11 Low Water (keep): wt=11.000, iters=3333
% 186.81/187.11
% 186.81/187.11 ============================== PROOF =================================
% 186.81/187.11 % SZS status Unsatisfiable
% 186.81/187.11 % SZS output start Refutation
% 186.81/187.11
% 186.81/187.11 % Proof 1 at 180.95 (+ 5.18) seconds.
% 186.81/187.11 % Length of proof is 279.
% 186.81/187.11 % Level of proof is 50.
% 186.81/187.11 % Maximum clause weight is 51.000.
% 186.81/187.11 % Given clauses 9958.
% 186.81/187.11
% 186.81/187.11 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 186.81/187.11 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 186.81/187.11 3 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 186.81/187.11 4 inverse(sk_c1) = sk_c7 | inverse(sk_c5) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 186.81/187.11 5 inverse(sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 186.81/187.11 6 inverse(sk_c2) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 186.81/187.11 7 multiply(sk_c7,sk_c8) = sk_c6 | inverse(sk_c4) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 186.81/187.11 8 multiply(sk_c7,sk_c8) = sk_c6 | inverse(sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 186.81/187.11 9 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 186.81/187.11 10 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 186.81/187.11 11 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 186.81/187.11 12 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 186.81/187.11 13 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 186.81/187.11 14 multiply(sk_c8,sk_c3) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 186.81/187.11 15 multiply(sk_c8,sk_c3) = sk_c7 | inverse(sk_c5) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 186.81/187.11 16 multiply(sk_c2,sk_c8) = sk_c3 | inverse(sk_c4) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 186.81/187.11 17 multiply(sk_c2,sk_c8) = sk_c3 | inverse(sk_c5) = sk_c7 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 186.81/187.11 18 inverse(sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 186.81/187.11 19 inverse(sk_c2) = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 186.81/187.11 20 inverse(sk_c2) = sk_c8 | multiply(sk_c6,sk_c7) = sk_c8 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 186.81/187.11 21 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 186.81/187.11 22 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 186.81/187.11 24 multiply(sk_c1,sk_c7) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 186.81/187.11 25 multiply(sk_c1,sk_c7) = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 186.81/187.11 26 multiply(sk_c1,sk_c7) = sk_c8 | multiply(sk_c6,sk_c7) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 186.81/187.11 27 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 186.81/187.11 30 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c4,sk_c8) = sk_c7 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 186.81/187.11 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 186.81/187.11 34 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(D,sk_c8) != sk_c7 | inverse(D) != sk_c8 | multiply(E,sk_c7) != sk_c6 | inverse(E) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 186.81/187.11 62 inverse(sk_c4) = sk_c8 | multiply(sk_c7,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 186.81/187.11 64 inverse(sk_c4) = sk_c8 | multiply(sk_c8,sk_c2) = identity. [para(5(a,1),2(a,1,1))].
% 186.81/187.11 65 inverse(sk_c5) = sk_c7 | multiply(sk_c8,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 186.81/187.11 66 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 186.81/187.11 67 inverse(sk_c4) = sk_c8 | multiply(sk_c7,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(7(a,1),33(a,1,1)),flip(b)].
% 186.81/187.11 69 inverse(sk_c5) = sk_c7 | multiply(sk_c7,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(8(a,1),33(a,1,1)),flip(b)].
% 186.81/187.11 70 inverse(sk_c5) = sk_c7 | multiply(A,multiply(sk_c7,sk_c8)) = multiply(A,sk_c6). [para(8(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 72 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c8). [para(9(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 73 inverse(sk_c5) = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(10(a,1),33(a,1,1)),flip(b)].
% 186.81/187.11 74 inverse(sk_c5) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c8). [para(10(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 75 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(11(b,1),33(a,1,1)),flip(b)].
% 186.81/187.11 76 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c7). [para(11(b,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 78 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c5,sk_c7)) = multiply(A,sk_c6). [para(12(b,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 79 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(13(b,1),33(a,1,1)),flip(b)].
% 186.81/187.11 82 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,sk_c7). [para(14(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 84 inverse(sk_c5) = sk_c7 | multiply(A,multiply(sk_c8,sk_c3)) = multiply(A,sk_c7). [para(15(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 86 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(16(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 88 inverse(sk_c5) = sk_c7 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(17(a,1),33(a,2,2)),rewrite([33(8)])].
% 186.81/187.11 89 inverse(sk_c2) = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(18(b,1),33(a,1,1)),flip(b)].
% 186.81/187.11 93 inverse(sk_c2) = sk_c8 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(20(b,1),33(a,1,1)),flip(b)].
% 186.81/187.11 114 multiply(sk_c4,sk_c8) = sk_c7 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(30(a,1),33(a,2,2)),rewrite([33(9)])].
% 186.81/187.11 146 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(D,sk_c7) != sk_c6 | inverse(D) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(2(a,1),34(b,1))].
% 186.81/187.11 294 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [factor(146,e,g),merge(g)].
% 186.81/187.11 989 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),66(a,1,2))].
% 186.81/187.11 990 inverse(sk_c5) = sk_c7 | multiply(sk_c7,multiply(sk_c1,A)) = A. [para(4(a,1),66(a,1,1))].
% 186.81/187.11 1020 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c7),identity) = sk_c1. [para(62(b,1),66(a,1,2))].
% 186.81/187.11 1021 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(66(a,1),66(a,1,2))].
% 186.81/187.11 1022 multiply(A,identity) = A. [back_rewrite(989),rewrite([1021(4)])].
% 186.81/187.11 1023 inverse(sk_c4) = sk_c8 | inverse(sk_c7) = sk_c1. [back_rewrite(1020),rewrite([1022(8)])].
% 186.81/187.11 1036 inverse(identity) = identity. [para(1022(a,1),2(a,1))].
% 186.81/187.11 1114 inverse(sk_c7) = sk_c1 | multiply(sk_c8,sk_c4) = identity. [para(1023(a,1),2(a,1,1))].
% 186.81/187.11 1129 inverse(sk_c4) = sk_c8 | inverse(sk_c8) = sk_c2. [para(64(b,1),66(a,1,2)),rewrite([1022(8)])].
% 186.81/187.11 1141 inverse(sk_c5) = sk_c7 | inverse(sk_c8) = sk_c2. [para(65(b,1),66(a,1,2)),rewrite([1022(8)])].
% 186.81/187.11 1153 inverse(sk_c4) = sk_c8 | multiply(sk_c6,sk_c2) = sk_c7. [para(64(b,1),67(b,1,2)),rewrite([1022(11)]),flip(c),merge(b)].
% 186.81/187.11 1179 multiply(A,inverse(A)) = identity. [para(1021(a,1),2(a,1))].
% 186.81/187.11 1181 inverse(sk_c5) = sk_c7 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A). [para(4(a,1),1021(a,1,1,1))].
% 186.81/187.11 1236 multiply(A,multiply(inverse(A),B)) = B. [para(1021(a,1),66(a,1))].
% 186.81/187.11 1237 inverse(inverse(A)) = A. [para(1021(a,1),1022(a,1)),rewrite([1022(2)]),flip(a)].
% 186.81/187.11 1238 inverse(sk_c7) = sk_c1 | multiply(inverse(sk_c8),A) = multiply(sk_c4,A). [para(1023(a,1),1021(a,1,1,1))].
% 186.81/187.11 1296 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [back_rewrite(294),rewrite([1237(11)]),xx(c)].
% 186.81/187.11 1306 inverse(sk_c8) = sk_c2 | inverse(sk_c8) = sk_c4. [para(1129(a,1),1237(a,1,1))].
% 186.81/187.11 1307 inverse(sk_c8) = sk_c2 | inverse(sk_c7) = sk_c5. [para(1141(a,1),1237(a,1,1))].
% 186.81/187.11 1308 inverse(sk_c4) = sk_c8 | multiply(sk_c1,sk_c7) = identity. [para(3(a,1),1179(a,1,2))].
% 186.81/187.11 1309 inverse(sk_c5) = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(4(a,1),1179(a,1,2))].
% 186.81/187.11 1310 inverse(sk_c4) = sk_c8 | multiply(sk_c2,sk_c8) = identity. [para(5(a,1),1179(a,1,2))].
% 186.81/187.11 1311 inverse(sk_c5) = sk_c7 | multiply(sk_c2,sk_c8) = identity. [para(6(a,1),1179(a,1,2))].
% 186.81/187.11 1312 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1179(a,1),33(a,1)),flip(a)].
% 186.81/187.11 1407 inverse(sk_c5) = sk_c7 | multiply(sk_c6,sk_c2) = sk_c7. [para(65(b,1),69(b,1,2)),rewrite([1022(11)]),flip(c),merge(b)].
% 186.81/187.11 1473 inverse(sk_c7) = sk_c1 | multiply(A,multiply(sk_c8,sk_c4)) = A. [para(1114(b,1),33(a,2,2)),rewrite([33(8),1022(10)])].
% 186.81/187.11 1496 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c6),sk_c7) = sk_c2. [para(1153(b,1),66(a,1,2))].
% 186.81/187.11 1543 inverse(sk_c4) = sk_c8 | identity = sk_c8. [para(1308(b,1),9(a,1)),merge(c)].
% 186.81/187.11 1549 identity = sk_c8 | multiply(sk_c4,sk_c8) = identity. [para(1543(a,1),1179(a,1,2))].
% 186.81/187.11 1550 identity = sk_c8 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(1543(a,1),1236(a,1,2,1))].
% 186.81/187.11 1579 inverse(sk_c4) = sk_c8 | multiply(A,sk_c8) = A. [para(1308(b,1),72(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 1625 identity = sk_c8 | multiply(A,multiply(sk_c4,sk_c8)) = A. [para(1549(b,1),33(a,2,2)),rewrite([33(7),1022(9)])].
% 186.81/187.11 1626 inverse(sk_c5) = sk_c7 | identity = sk_c8. [para(1309(b,1),10(a,1)),merge(c)].
% 186.81/187.11 1629 identity = sk_c8 | multiply(sk_c7,sk_c5) = identity. [para(1626(a,1),2(a,1,1))].
% 186.81/187.11 1630 identity = sk_c8 | multiply(sk_c7,multiply(sk_c5,A)) = A. [para(1626(a,1),66(a,1,1))].
% 186.81/187.11 1631 identity = sk_c8 | inverse(sk_c7) = sk_c5. [para(1626(a,1),1237(a,1,1))].
% 186.81/187.11 1632 identity = sk_c8 | multiply(sk_c5,sk_c7) = identity. [para(1626(a,1),1179(a,1,2))].
% 186.81/187.11 1690 identity = sk_c8 | multiply(A,multiply(sk_c7,sk_c5)) = A. [para(1629(b,1),33(a,2,2)),rewrite([33(7),1022(9)])].
% 186.81/187.11 1724 inverse(sk_c5) = sk_c7 | multiply(A,sk_c8) = A. [para(1309(b,1),74(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 1826 inverse(sk_c1) = sk_c7 | multiply(sk_c7,inverse(sk_c8)) = sk_c4. [para(1179(a,1),75(b,1,2)),rewrite([1022(7)]),flip(b)].
% 186.81/187.11 1875 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),multiply(sk_c4,sk_c8)) = identity. [para(2(a,1),76(b,2))].
% 186.81/187.11 2035 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),multiply(sk_c5,sk_c7)) = identity. [para(2(a,1),78(b,2))].
% 186.81/187.11 2184 inverse(sk_c5) = sk_c7 | multiply(inverse(sk_c6),sk_c7) = sk_c2. [para(1407(b,1),66(a,1,2))].
% 186.81/187.11 2414 inverse(sk_c4) = sk_c8 | inverse(sk_c8) = identity. [para(1579(b,1),2(a,1))].
% 186.81/187.11 2938 inverse(sk_c8) = identity | inverse(sk_c8) = sk_c4. [para(2414(a,1),1237(a,1,1))].
% 186.81/187.11 3108 inverse(sk_c8) = sk_c4 | multiply(sk_c8,A) = A. [para(2938(a,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 3284 inverse(sk_c5) = sk_c7 | inverse(sk_c8) = identity. [para(1724(b,1),2(a,1))].
% 186.81/187.11 3285 inverse(sk_c5) = sk_c7 | sk_c6 = sk_c7. [para(1724(b,1),8(a,1)),flip(b),merge(c)].
% 186.81/187.11 3368 sk_c6 = sk_c7 | inverse(sk_c7) = sk_c5. [para(3285(a,1),1237(a,1,1))].
% 186.81/187.11 3560 inverse(sk_c8) = identity | inverse(sk_c7) = sk_c5. [para(3284(a,1),1237(a,1,1))].
% 186.81/187.11 3610 inverse(sk_c4) = sk_c8 | multiply(A,sk_c3) = A. [para(1310(b,1),86(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 3817 inverse(sk_c7) = sk_c5 | multiply(sk_c8,A) = A. [para(3560(a,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 4251 inverse(sk_c8) = sk_c4 | multiply(inverse(sk_c8),A) = A. [para(3108(b,1),66(a,1,2))].
% 186.81/187.11 4314 inverse(sk_c5) = sk_c7 | multiply(A,sk_c3) = A. [para(1311(b,1),88(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 4428 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = identity. [para(3610(b,1),2(a,1))].
% 186.81/187.11 4468 inverse(sk_c2) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c4. [para(1179(a,1),89(b,1,2)),rewrite([1022(7)]),flip(b)].
% 186.81/187.11 4566 inverse(sk_c4) = sk_c8 | multiply(sk_c3,A) = A. [para(4428(b,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 4715 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c8),A) = A. [para(3817(b,1),66(a,1,2))].
% 186.81/187.11 4769 inverse(sk_c5) = sk_c7 | inverse(sk_c3) = identity. [para(4314(b,1),2(a,1))].
% 186.81/187.11 4950 inverse(sk_c5) = sk_c7 | multiply(sk_c3,A) = A. [para(4769(b,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 5056 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c3),A) = A. [para(4566(b,1),66(a,1,2))].
% 186.81/187.11 5182 inverse(sk_c2) = sk_c8 | multiply(sk_c8,inverse(sk_c7)) = sk_c6. [para(1179(a,1),93(b,1,2)),rewrite([1022(7)]),flip(b)].
% 186.81/187.11 5344 inverse(sk_c5) = sk_c7 | multiply(inverse(sk_c3),A) = A. [para(4950(b,1),66(a,1,2))].
% 186.81/187.11 6056 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1312(a,1),66(a,1,2)),rewrite([1022(3)]),flip(a)].
% 186.81/187.11 6150 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(6056(a,1),66(a,1,2)),flip(a)].
% 186.81/187.11 7629 identity = sk_c8 | multiply(inverse(sk_c5),inverse(sk_c7)) = identity. [para(1690(b,1),2(a,1)),rewrite([6150(7)])].
% 186.81/187.11 8120 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(1826(b,1),79(b,1,2)),rewrite([1179(15)]),merge(b)].
% 186.81/187.11 8125 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c4. [para(8120(b,1),66(a,1,2)),rewrite([1022(8)])].
% 186.81/187.11 8129 inverse(sk_c6) = sk_c4 | inverse(sk_c7) = sk_c1. [para(8125(a,1),1237(a,1,1))].
% 186.81/187.11 8286 inverse(sk_c7) = sk_c1 | multiply(sk_c4,sk_c6) = identity. [para(8129(a,1),2(a,1,1))].
% 186.81/187.11 10351 inverse(sk_c8) = sk_c4 | multiply(sk_c2,A) = A. [para(1306(a,1),4251(b,1,1)),merge(b)].
% 186.81/187.11 10398 inverse(sk_c8) = sk_c4 | inverse(sk_c2) = identity. [para(10351(b,1),1179(a,1))].
% 186.81/187.11 10517 inverse(sk_c2) = sk_c8 | multiply(sk_c6,sk_c4) = identity. [para(4468(b,1),93(b,1,2)),rewrite([1179(15)]),merge(b)].
% 186.81/187.11 10525 inverse(sk_c2) = sk_c8 | inverse(sk_c6) = sk_c4. [para(10517(b,1),66(a,1,2)),rewrite([1022(8)])].
% 186.81/187.11 10540 inverse(sk_c6) = sk_c4 | multiply(sk_c8,sk_c2) = identity. [para(10525(a,1),2(a,1,1))].
% 186.81/187.11 10601 inverse(sk_c6) = sk_c4 | identity = sk_c8 | sk_c2 = sk_c4. [para(10540(b,1),1550(b,1,2)),rewrite([1022(10)]),flip(c)].
% 186.81/187.11 10822 inverse(sk_c7) = sk_c5 | multiply(sk_c2,A) = A. [para(1307(a,1),4715(b,1,1)),merge(b)].
% 186.81/187.11 10847 inverse(sk_c7) = sk_c5 | inverse(sk_c2) = identity. [para(10822(b,1),1179(a,1))].
% 186.81/187.11 10972 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(A,multiply(B,sk_c8)) != sk_c7 | multiply(inverse(B),inverse(A)) != sk_c8 | multiply(C,sk_c7) != sk_c6 | inverse(C) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(33(a,1),1296(d,1)),rewrite([6150(20)])].
% 186.81/187.11 10986 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = sk_c8. [para(5056(b,1),1579(b,1)),flip(c),merge(b)].
% 186.81/187.11 10995 inverse(sk_c4) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(10986(b,1),2(a,1,1))].
% 186.81/187.11 11033 inverse(sk_c4) = sk_c8 | identity = sk_c7. [para(10995(b,1),14(a,1)),merge(c)].
% 186.81/187.11 11037 inverse(sk_c4) = sk_c8 | multiply(A,sk_c7) = A. [para(10995(b,1),82(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 11051 identity = sk_c7 | inverse(sk_c8) = sk_c4. [para(11033(a,1),1237(a,1,1))].
% 186.81/187.11 11052 identity = sk_c7 | multiply(sk_c4,sk_c8) = identity. [para(11033(a,1),1179(a,1,2))].
% 186.81/187.11 11084 identity = sk_c7 | inverse(sk_c2) = sk_c8. [para(11052(b,1),18(b,1)),merge(c)].
% 186.81/187.11 11085 identity = sk_c7 | multiply(sk_c7,sk_c8) = sk_c6. [para(11052(b,1),21(b,1)),merge(c)].
% 186.81/187.11 11086 identity = sk_c7 | multiply(sk_c8,sk_c3) = sk_c7. [para(11052(b,1),27(b,1)),merge(c)].
% 186.81/187.11 11107 identity = sk_c7 | inverse(sk_c8) = sk_c2. [para(11084(b,1),1237(a,1,1))].
% 186.81/187.11 11127 identity = sk_c7 | sk_c2 = sk_c4. [para(11107(b,1),11051(b,1)),merge(b)].
% 186.81/187.11 11132 sk_c2 = sk_c4 | inverse(sk_c7) = identity. [para(11127(a,1),1036(a,1,1))].
% 186.81/187.11 11234 sk_c2 = sk_c4 | inverse(sk_c7) = sk_c7. [para(11127(a,1),11132(b,2)),merge(b)].
% 186.81/187.11 11235 sk_c2 = sk_c4 | multiply(sk_c7,sk_c7) = identity. [para(11234(b,1),2(a,1,1))].
% 186.81/187.11 11255 identity = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(11085(b,1),66(a,1,2))].
% 186.81/187.11 11274 identity = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c3. [para(11086(b,1),66(a,1,2))].
% 186.81/187.11 11770 inverse(sk_c4) = sk_c8 | inverse(sk_c7) = identity. [para(11037(b,1),2(a,1))].
% 186.81/187.11 11783 inverse(sk_c4) = sk_c8 | inverse(sk_c6) = sk_c2. [para(11037(b,1),1496(b,1)),merge(b)].
% 186.81/187.11 11825 inverse(sk_c7) = identity | multiply(sk_c4,sk_c8) = identity. [para(11770(a,1),1179(a,1,2))].
% 186.81/187.11 11831 inverse(sk_c6) = sk_c2 | inverse(sk_c8) = sk_c4. [para(11783(a,1),1237(a,1,1))].
% 186.81/187.11 11923 inverse(sk_c8) = sk_c4 | inverse(sk_c2) = sk_c6. [para(11831(a,1),1237(a,1,1))].
% 186.81/187.11 11940 inverse(sk_c8) = sk_c4 | identity = sk_c6. [para(11923(b,1),10398(b,1)),flip(c),merge(b)].
% 186.81/187.11 12618 identity = sk_c7 | multiply(sk_c2,sk_c7) = sk_c3. [para(11107(b,1),11274(b,1,1)),merge(b)].
% 186.81/187.11 12629 identity = sk_c7 | multiply(inverse(sk_c2),sk_c3) = sk_c7. [para(12618(b,1),66(a,1,2))].
% 186.81/187.11 13066 identity = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7 | sk_c8 = sk_c7. [para(12629(b,1),114(b,2)),rewrite([66(14)])].
% 186.81/187.11 13298 inverse(sk_c5) = sk_c7 | inverse(sk_c3) = sk_c8. [para(5344(b,1),1724(b,1)),flip(c),merge(b)].
% 186.81/187.11 13303 inverse(sk_c5) = sk_c7 | multiply(sk_c8,sk_c3) = identity. [para(13298(b,1),2(a,1,1))].
% 186.81/187.11 13353 inverse(sk_c5) = sk_c7 | multiply(A,sk_c7) = A. [para(13303(b,1),84(b,1,2)),rewrite([1022(10)]),flip(c),merge(b)].
% 186.81/187.11 13772 inverse(sk_c5) = sk_c7 | inverse(sk_c7) = identity. [para(13353(b,1),2(a,1))].
% 186.81/187.11 13785 inverse(sk_c5) = sk_c7 | inverse(sk_c6) = sk_c2. [para(13353(b,1),2184(b,1)),merge(b)].
% 186.81/187.11 13790 inverse(sk_c5) = sk_c7 | inverse(sk_c3) = sk_c7. [para(13353(b,1),5344(b,1)),merge(b)].
% 186.81/187.11 13828 inverse(sk_c7) = identity | inverse(sk_c7) = sk_c5. [para(13772(a,1),1237(a,1,1))].
% 186.81/187.11 13835 inverse(sk_c6) = sk_c2 | inverse(sk_c7) = sk_c5. [para(13785(a,1),1237(a,1,1))].
% 186.81/187.11 13840 inverse(sk_c5) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(13790(b,1),2(a,1,1))].
% 186.81/187.11 13848 inverse(sk_c5) = sk_c7 | multiply(sk_c7,A) = A. [para(13790(b,1),5344(b,1,1)),merge(b)].
% 186.81/187.11 13905 inverse(sk_c7) = sk_c5 | multiply(sk_c7,A) = A. [para(13828(a,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 13913 inverse(sk_c7) = sk_c5 | inverse(sk_c2) = sk_c6. [para(13835(a,1),1237(a,1,1))].
% 186.81/187.11 13927 inverse(sk_c7) = sk_c5 | identity = sk_c6. [para(13913(b,1),10847(b,1)),flip(c),merge(b)].
% 186.81/187.11 13930 identity = sk_c6 | multiply(sk_c5,sk_c7) = identity. [para(13927(a,1),2(a,1,1))].
% 186.81/187.11 13989 identity = sk_c6 | inverse(sk_c2) = sk_c8. [para(13930(b,1),19(b,1)),merge(c)].
% 186.81/187.11 13990 identity = sk_c6 | multiply(sk_c7,sk_c8) = sk_c6. [para(13930(b,1),22(b,1)),merge(c)].
% 186.81/187.11 14001 identity = sk_c6 | inverse(sk_c8) = sk_c2. [para(13989(b,1),1237(a,1,1))].
% 186.81/187.11 14171 identity = sk_c6 | sk_c2 = sk_c4. [para(14001(b,1),11940(a,1)),merge(c)].
% 186.81/187.11 14175 sk_c2 = sk_c4 | inverse(sk_c6) = identity. [para(14171(a,1),1036(a,1,1))].
% 186.81/187.11 14470 identity = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(13990(b,1),66(a,1,2))].
% 186.81/187.11 15170 inverse(sk_c5) = sk_c7 | multiply(sk_c8,sk_c3) = sk_c1. [para(13840(b,1),73(b,1,2)),rewrite([1022(11)]),flip(c),merge(b)].
% 186.81/187.11 15418 identity = sk_c6 | multiply(sk_c5,sk_c6) = sk_c8. [para(13927(a,1),14470(b,1,1)),merge(b)].
% 186.81/187.11 15422 identity = sk_c6 | multiply(inverse(sk_c5),sk_c8) = sk_c6. [para(15418(b,1),66(a,1,2))].
% 186.81/187.11 15673 inverse(sk_c5) = sk_c7 | sk_c1 = sk_c7. [para(15170(b,1),15(a,1)),merge(c)].
% 186.81/187.11 15683 sk_c1 = sk_c7 | inverse(sk_c7) = sk_c5. [para(15673(a,1),1237(a,1,1))].
% 186.81/187.11 15691 sk_c1 = sk_c7 | inverse(sk_c2) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c6. [para(15683(b,1),5182(b,1,2))].
% 186.81/187.11 15814 multiply(sk_c6,sk_c7) = sk_c8 | multiply(inverse(sk_c7),inverse(sk_c1)) = inverse(sk_c8). [para(26(a,1),6150(a,1,1)),flip(b)].
% 186.81/187.11 16055 identity = sk_c7 | multiply(inverse(sk_c6),sk_c7) = inverse(sk_c8). [para(11255(b,1),6150(a,1,1)),rewrite([1237(10)]),flip(b)].
% 186.81/187.11 17104 identity = sk_c8 | sk_c2 = sk_c4 | identity = sk_c4. [para(10601(a,1),14175(b,1)),flip(d),merge(c)].
% 186.81/187.11 17111 identity = sk_c8 | sk_c2 = sk_c4 | inverse(sk_c4) = identity. [para(17104(c,1),1036(a,1,1))].
% 186.81/187.11 22274 identity = sk_c7 | multiply(sk_c6,inverse(sk_c8)) = sk_c7. [para(16055(b,1),66(a,1,2)),rewrite([1237(6)])].
% 186.81/187.11 25039 identity = sk_c8 | sk_c2 = sk_c4. [para(17111(c,1),1543(a,1)),merge(c),merge(d)].
% 186.81/187.11 25063 sk_c2 = sk_c4 | multiply(sk_c7,sk_c7) = sk_c8. [para(25039(a,1),11235(b,2)),merge(b)].
% 186.81/187.11 31467 inverse(sk_c5) = sk_c7 | multiply(sk_c1,A) = A. [para(990(b,1),13848(b,1)),flip(c),merge(b)].
% 186.81/187.11 31504 inverse(sk_c5) = sk_c7 | multiply(inverse(sk_c1),A) = A. [para(31467(b,1),66(a,1,2))].
% 186.81/187.11 31858 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | sk_c7 != A | multiply(sk_c8,inverse(A)) != sk_c8 | multiply(B,sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(2(a,1),10972(d,1,2)),rewrite([1022(15),1237(18)]),flip(d)].
% 186.81/187.11 31861 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | sk_c7 != A | multiply(sk_c8,inverse(A)) != sk_c8 | multiply(B,multiply(C,sk_c7)) != sk_c6 | multiply(inverse(C),inverse(B)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(33(a,1),31858(f,1)),rewrite([6150(27)])].
% 186.81/187.11 32494 inverse(sk_c5) = sk_c7 | multiply(sk_c1,sk_c6) = sk_c8. [para(1181(b,1),70(b,2)),rewrite([66(14)]),flip(c),merge(b)].
% 186.81/187.11 32512 inverse(sk_c5) = sk_c7 | multiply(inverse(sk_c1),sk_c8) = sk_c6. [para(32494(b,1),66(a,1,2))].
% 186.81/187.11 32564 inverse(sk_c7) = sk_c1 | multiply(inverse(sk_c8),sk_c6) = identity. [para(8286(b,1),1238(b,2)),merge(b)].
% 186.81/187.11 34751 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | sk_c7 != A | multiply(sk_c8,inverse(A)) != sk_c8 | sk_c6 != B | multiply(sk_c7,inverse(B)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(2(a,1),31861(f,1,2)),rewrite([1022(22),1237(25)]),flip(f)].
% 186.81/187.11 34774 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | sk_c6 != B | multiply(sk_c7,inverse(B)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(1237(a,1),34751(e,1,2)),flip(d)].
% 186.81/187.11 34780 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | inverse(B) != sk_c6 | multiply(sk_c7,B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(1237(a,1),34774(g,1,2)),flip(f)].
% 186.81/187.11 34781 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),sk_c8) != sk_c7 | sk_c8 != A | sk_c6 != B | multiply(sk_c7,inverse(B)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(1236(a,1),34774(e,1)),rewrite([6150(17),1237(17)]),flip(e)].
% 186.81/187.11 34803 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | sk_c6 != C | multiply(sk_c7,inverse(C)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(6150(a,1),34781(d,1,1)),rewrite([33(18)]),flip(e)].
% 186.81/187.11 35702 inverse(sk_c5) = sk_c7 | inverse(sk_c1) = sk_c6. [para(32512(b,1),1724(b,1)),flip(c),merge(b)].
% 186.81/187.11 35722 inverse(sk_c5) = sk_c7 | multiply(sk_c6,A) = A. [para(35702(b,1),31504(b,1,1)),merge(b)].
% 186.81/187.11 35820 inverse(sk_c5) = sk_c7 | inverse(sk_c6) = identity. [para(35722(b,1),1179(a,1))].
% 186.81/187.11 35825 inverse(sk_c6) = identity | multiply(sk_c5,sk_c7) = identity. [para(35820(a,1),1179(a,1,2))].
% 186.81/187.11 36027 multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | multiply(C,D) != sk_c6 | multiply(sk_c7,multiply(inverse(D),inverse(C))) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c8. [para(6150(a,1),34803(g,1,2)),flip(f)].
% 186.81/187.11 36940 inverse(sk_c7) = identity | inverse(sk_c1) = sk_c7. [para(11825(b,1),1875(b,1,2)),rewrite([1022(12)]),merge(c)].
% 186.81/187.11 36963 inverse(sk_c7) = identity | inverse(sk_c7) = sk_c1. [para(36940(b,1),1237(a,1,1))].
% 186.81/187.11 36965 inverse(sk_c7) = sk_c1 | multiply(sk_c7,A) = A. [para(36963(a,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 37590 inverse(sk_c6) = identity | inverse(sk_c1) = sk_c7. [para(35825(b,1),2035(b,1,2)),rewrite([1022(12)]),merge(c)].
% 186.81/187.11 37596 inverse(sk_c6) = identity | inverse(sk_c7) = sk_c1. [para(37590(b,1),1237(a,1,1))].
% 186.81/187.11 37598 inverse(sk_c7) = sk_c1 | multiply(sk_c6,A) = A. [para(37596(a,1),66(a,1,1)),rewrite([1(8)])].
% 186.81/187.11 37704 inverse(sk_c7) = sk_c1 | multiply(sk_c8,sk_c4) = sk_c6. [para(37598(b,1),1473(b,1)),merge(b)].
% 186.81/187.11 37837 inverse(sk_c7) = sk_c1 | multiply(A,sk_c6) = A. [para(37704(b,1),1473(b,1,2)),merge(b)].
% 186.81/187.11 37898 inverse(sk_c7) = sk_c1 | inverse(sk_c8) = identity. [para(37837(b,1),32564(b,1)),merge(b)].
% 186.81/187.11 37899 inverse(sk_c7) = sk_c1 | identity = sk_c8. [para(37898(b,1),2(a,1,1)),rewrite([1(7)]),flip(b)].
% 186.81/187.11 37912 identity = sk_c8 | multiply(sk_c1,sk_c7) = identity. [para(37899(a,1),2(a,1,1))].
% 186.81/187.11 37919 identity = sk_c8 | multiply(sk_c4,sk_c8) = sk_c7. [para(37912(b,1),24(a,1)),merge(b)].
% 186.81/187.11 37920 identity = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6. [para(37912(b,1),25(a,1)),merge(b)].
% 186.81/187.11 37921 identity = sk_c8 | multiply(sk_c6,sk_c7) = sk_c8. [para(37912(b,1),26(a,1)),merge(b)].
% 186.81/187.11 37933 identity = sk_c8 | identity = sk_c7. [para(37919(b,1),1549(b,1)),flip(c),merge(b)].
% 186.81/187.11 37935 identity = sk_c8 | multiply(A,sk_c7) = A. [para(37919(b,1),1625(b,1,2)),merge(b)].
% 186.81/187.11 37941 identity = sk_c7 | inverse(sk_c8) = identity. [para(37933(a,1),1036(a,1,1))].
% 186.81/187.11 37973 identity = sk_c7 | identity = sk_c4. [para(37941(b,1),11051(b,1)),merge(b)].
% 186.81/187.11 37985 identity = sk_c7 | sk_c6 = sk_c7. [para(37941(b,1),22274(b,1,2)),rewrite([1022(9)]),merge(b)].
% 186.81/187.11 38022 identity = sk_c7 | sk_c4 = sk_c8. [para(37973(b,1),37933(a,1)),merge(c)].
% 186.81/187.11 38066 sk_c6 = sk_c7 | inverse(sk_c7) = identity. [para(37985(a,1),1036(a,1,1))].
% 186.81/187.11 38081 sk_c4 = sk_c8 | inverse(sk_c7) = identity. [para(38022(a,1),1036(a,1,1))].
% 186.81/187.11 38320 sk_c6 = sk_c7 | identity = sk_c5. [para(38066(b,1),3368(b,1)),merge(b)].
% 186.81/187.11 38445 sk_c4 = sk_c8 | inverse(sk_c7) = sk_c7. [para(38022(a,1),38081(b,2)),merge(b)].
% 186.81/187.11 38673 sk_c4 = sk_c8 | multiply(sk_c7,sk_c7) = identity. [para(38445(b,1),2(a,1,1))].
% 186.81/187.11 38773 identity = sk_c8 | identity = sk_c6. [para(37920(b,1),1632(b,1)),flip(c),merge(b)].
% 186.81/187.11 38784 identity = sk_c8 | inverse(sk_c6) = identity. [para(38773(b,1),1036(a,1,1))].
% 186.81/187.11 38792 identity = sk_c8 | sk_c6 = sk_c7. [para(38773(b,1),37985(a,1)),merge(c)].
% 186.81/187.11 38823 sk_c6 = sk_c7 | sk_c5 = sk_c8. [para(38792(a,1),38320(b,1)),flip(c),merge(b)].
% 186.81/187.11 38842 sk_c6 = sk_c7 | identity = sk_c6. [para(38823(b,1),15422(b,1,1,1)),rewrite([2(10)]),merge(c)].
% 186.81/187.11 38883 sk_c6 = sk_c7. [para(38842(b,1),37985(a,1)),merge(b),merge(c)].
% 186.81/187.11 38897 identity = sk_c8 | inverse(sk_c7) = identity. [back_rewrite(38784),rewrite([38883(4)])].
% 186.81/187.11 39002 identity = sk_c8 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(37921),rewrite([38883(4)])].
% 186.81/187.11 39755 multiply(sk_c7,sk_c8) != sk_c7 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | multiply(C,D) != sk_c7 | multiply(sk_c7,multiply(inverse(D),inverse(C))) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(36027),rewrite([38883(4),38883(25),38883(34)])].
% 186.81/187.11 40368 multiply(sk_c7,sk_c8) != sk_c7 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | inverse(B) != sk_c7 | multiply(sk_c7,B) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(34780),rewrite([38883(4),38883(22),38883(28)])].
% 186.81/187.11 42669 multiply(sk_c7,sk_c7) = sk_c8 | multiply(inverse(sk_c7),inverse(sk_c1)) = inverse(sk_c8). [back_rewrite(15814),rewrite([38883(1)])].
% 186.81/187.11 42722 sk_c1 = sk_c7 | inverse(sk_c2) = sk_c8 | multiply(sk_c8,sk_c5) = sk_c7. [back_rewrite(15691),rewrite([38883(11)])].
% 186.81/187.11 46295 multiply(sk_c7,sk_c8) != sk_c7 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | multiply(sk_c7,multiply(inverse(sk_c8),multiply(B,A))) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [factor(39755,d,f),rewrite([6150(28),1237(28),1237(29),33(28)])].
% 186.81/187.11 46312 multiply(sk_c7,sk_c8) != sk_c7 | identity != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | multiply(sk_c7,A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [factor(40368,d,f)].
% 186.81/187.11 46461 identity = sk_c8 | identity = sk_c5. [para(38897(b,1),1631(b,1)),merge(b)].
% 186.81/187.11 46464 identity = sk_c8 | inverse(sk_c5) = identity. [para(38897(b,1),7629(b,1,2)),rewrite([1022(10)]),merge(b)].
% 186.81/187.11 46700 identity = sk_c8 | inverse(sk_c5) = sk_c5. [para(46461(b,1),46464(b,2)),merge(b)].
% 186.81/187.11 46840 identity = sk_c8 | multiply(sk_c5,inverse(sk_c7)) = identity. [para(46700(b,1),7629(b,1,1)),merge(b)].
% 186.81/187.11 47380 identity = sk_c8 | sk_c8 = sk_c7. [para(39002(b,1),37935(b,1)),merge(b)].
% 186.81/187.11 47382 identity = sk_c8 | sk_c4 = sk_c8. [para(39002(b,1),38673(b,1)),flip(c),merge(c)].
% 186.81/187.11 47416 sk_c8 = sk_c7 | sk_c4 = sk_c8. [para(47380(a,1),38022(a,1)),merge(b)].
% 186.81/187.11 47508 sk_c4 = sk_c8 | multiply(sk_c7,sk_c7) = sk_c8. [para(47382(a,1),38673(b,2)),merge(b)].
% 186.81/187.11 49206 identity = sk_c8 | inverse(sk_c7) = sk_c7. [para(46840(b,1),1630(b,1,2)),rewrite([1022(9)]),flip(c),merge(b)].
% 186.81/187.11 49210 identity = sk_c8 | multiply(sk_c7,sk_c7) = identity. [para(49206(b,1),2(a,1,1))].
% 186.81/187.11 49222 identity = sk_c8. [para(49210(b,1),39002(b,1)),merge(b),merge(c)].
% 186.81/187.11 49724 multiply(sk_c7,sk_c8) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | multiply(sk_c7,A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(46312),rewrite([49222(6)]),xx(b)].
% 186.81/187.11 49735 multiply(sk_c7,sk_c8) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c8)) != sk_c7 | multiply(B,A) != sk_c8 | multiply(sk_c7,multiply(inverse(sk_c8),multiply(B,A))) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(46295),rewrite([49222(6)]),xx(b)].
% 186.81/187.11 50794 sk_c8 = sk_c7 | multiply(sk_c4,sk_c8) = sk_c7. [back_rewrite(13066),rewrite([49222(1)]),merge(c)].
% 186.81/187.11 50981 inverse(sk_c8) = sk_c8. [back_rewrite(1036),rewrite([49222(1),49222(3)])].
% 186.81/187.11 50982 multiply(A,sk_c8) = A. [back_rewrite(1022),rewrite([49222(1)])].
% 186.81/187.11 50984 multiply(sk_c8,A) = A. [back_rewrite(1),rewrite([49222(1)])].
% 186.81/187.11 51013 sk_c8 != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [factor(49724,a,e),rewrite([50982(3),50984(6),50981(8),50982(12)]),xx(a),xx(b),xx(d)].
% 186.81/187.11 51014 multiply(inverse(sk_c7),inverse(sk_c7)) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7. [factor(49735,d,f),rewrite([50982(3),50984(6),50982(12),50981(21),50984(24)]),xx(a),xx(b)].
% 186.81/187.11 51104 multiply(sk_c7,sk_c7) = sk_c8 | multiply(inverse(sk_c7),inverse(sk_c1)) = sk_c8. [back_rewrite(42669),rewrite([50981(12)])].
% 186.81/187.11 51165 sk_c8 = sk_c7 | sk_c4 = sk_c7. [back_rewrite(50794),rewrite([50982(6)])].
% 186.81/187.11 51698 sk_c1 = sk_c7 | inverse(sk_c2) = sk_c8 | sk_c5 = sk_c7. [back_rewrite(42722),rewrite([50984(10)])].
% 186.81/187.11 51810 sk_c8 != sk_c7 | sk_c4 = sk_c8. [resolve(51013,b,47508,b)].
% 186.81/187.11 51814 sk_c8 != sk_c7 | sk_c2 = sk_c4. [resolve(51013,b,25063,b)].
% 186.81/187.11 51818 inverse(sk_c7) = sk_c5 | sk_c8 != sk_c7. [para(13905(b,1),51013(b,1)),flip(c),merge(c)].
% 186.81/187.11 51819 inverse(sk_c7) = sk_c1 | sk_c8 != sk_c7. [para(36965(b,1),51013(b,1)),flip(c),merge(c)].
% 186.81/187.11 52385 sk_c8 = sk_c7. [para(51165(b,1),47416(b,1)),flip(c),merge(b),merge(c)].
% 186.81/187.11 52668 inverse(sk_c7) = sk_c1. [back_rewrite(51819),rewrite([52385(5)]),xx(b)].
% 186.81/187.11 52669 sk_c1 = sk_c5. [back_rewrite(51818),rewrite([52668(2),52385(4)]),xx(b)].
% 186.81/187.11 52672 sk_c2 = sk_c4. [back_rewrite(51814),rewrite([52385(1)]),xx(a)].
% 186.81/187.11 52674 sk_c4 = sk_c7. [back_rewrite(51810),rewrite([52385(1),52385(5)]),xx(a)].
% 186.81/187.11 52692 sk_c5 = sk_c7. [back_rewrite(51698),rewrite([52669(1),52672(4),52674(4),52668(5),52669(4),52385(5)]),merge(b),merge(c)].
% 186.81/187.11 52754 multiply(sk_c7,sk_c7) = sk_c7. [back_rewrite(51104),rewrite([52385(4),52668(7),52669(6),52692(6),52669(7),52692(7),52668(8),52669(7),52692(7),52385(9)]),merge(b)].
% 186.81/187.11 52777 $F. [back_rewrite(51014),rewrite([52668(2),52669(1),52692(1),52668(3),52669(2),52692(2),52754(3),52754(6),52385(5),52754(10),52754(9)]),xx(a),xx(b),xx(c)].
% 186.81/187.11
% 186.81/187.11 % SZS output end Refutation
% 186.81/187.11 ============================== end of proof ==========================
% 186.81/187.11
% 186.81/187.11 ============================== STATISTICS ============================
% 186.81/187.11
% 186.81/187.11 Given=9958. Generated=10211153. Kept=52776. proofs=1.
% 186.81/187.11 Usable=849. Sos=1430. Demods=22. Limbo=392, Disabled=50139. Hints=0.
% 186.81/187.11 Megabytes=41.91.
% 186.81/187.11 User_CPU=180.95, System_CPU=5.18, Wall_clock=186.
% 186.81/187.11
% 186.81/187.11 ============================== end of statistics =====================
% 186.81/187.11
% 186.81/187.11 ============================== end of search =========================
% 186.81/187.11
% 186.81/187.11 THEOREM PROVED
% 186.81/187.11 % SZS status Unsatisfiable
% 186.81/187.11
% 186.81/187.11 Exiting with 1 proof.
% 186.81/187.11
% 186.81/187.11 Process 21351 exit (max_proofs) Mon Jun 13 06:55:59 2022
% 186.81/187.11 Prover9 interrupted
%------------------------------------------------------------------------------