TSTP Solution File: GRP233-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP233-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:18:15 EDT 2022
% Result : Unsatisfiable 37.09s 37.37s
% Output : Refutation 37.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP233-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 01:12:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 37.09/37.37 ============================== Prover9 ===============================
% 37.09/37.37 Prover9 (32) version 2009-11A, November 2009.
% 37.09/37.37 Process 18537 was started by sandbox2 on n020.cluster.edu,
% 37.09/37.37 Tue Jun 14 01:12:50 2022
% 37.09/37.37 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18384_n020.cluster.edu".
% 37.09/37.37 ============================== end of head ===========================
% 37.09/37.37
% 37.09/37.37 ============================== INPUT =================================
% 37.09/37.37
% 37.09/37.37 % Reading from file /tmp/Prover9_18384_n020.cluster.edu
% 37.09/37.37
% 37.09/37.37 set(prolog_style_variables).
% 37.09/37.37 set(auto2).
% 37.09/37.37 % set(auto2) -> set(auto).
% 37.09/37.37 % set(auto) -> set(auto_inference).
% 37.09/37.37 % set(auto) -> set(auto_setup).
% 37.09/37.37 % set(auto_setup) -> set(predicate_elim).
% 37.09/37.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 37.09/37.37 % set(auto) -> set(auto_limits).
% 37.09/37.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 37.09/37.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 37.09/37.37 % set(auto) -> set(auto_denials).
% 37.09/37.37 % set(auto) -> set(auto_process).
% 37.09/37.37 % set(auto2) -> assign(new_constants, 1).
% 37.09/37.37 % set(auto2) -> assign(fold_denial_max, 3).
% 37.09/37.37 % set(auto2) -> assign(max_weight, "200.000").
% 37.09/37.37 % set(auto2) -> assign(max_hours, 1).
% 37.09/37.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 37.09/37.37 % set(auto2) -> assign(max_seconds, 0).
% 37.09/37.37 % set(auto2) -> assign(max_minutes, 5).
% 37.09/37.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 37.09/37.37 % set(auto2) -> set(sort_initial_sos).
% 37.09/37.37 % set(auto2) -> assign(sos_limit, -1).
% 37.09/37.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 37.09/37.37 % set(auto2) -> assign(max_megs, 400).
% 37.09/37.37 % set(auto2) -> assign(stats, some).
% 37.09/37.37 % set(auto2) -> clear(echo_input).
% 37.09/37.37 % set(auto2) -> set(quiet).
% 37.09/37.37 % set(auto2) -> clear(print_initial_clauses).
% 37.09/37.37 % set(auto2) -> clear(print_given).
% 37.09/37.37 assign(lrs_ticks,-1).
% 37.09/37.37 assign(sos_limit,10000).
% 37.09/37.37 assign(order,kbo).
% 37.09/37.37 set(lex_order_vars).
% 37.09/37.37 clear(print_given).
% 37.09/37.37
% 37.09/37.37 % formulas(sos). % not echoed (34 formulas)
% 37.09/37.37
% 37.09/37.37 ============================== end of input ==========================
% 37.09/37.37
% 37.09/37.37 % From the command line: assign(max_seconds, 300).
% 37.09/37.37
% 37.09/37.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 37.09/37.37
% 37.09/37.37 % Formulas that are not ordinary clauses:
% 37.09/37.37
% 37.09/37.37 ============================== end of process non-clausal formulas ===
% 37.09/37.37
% 37.09/37.37 ============================== PROCESS INITIAL CLAUSES ===============
% 37.09/37.37
% 37.09/37.37 ============================== PREDICATE ELIMINATION =================
% 37.09/37.37
% 37.09/37.37 ============================== end predicate elimination =============
% 37.09/37.37
% 37.09/37.37 Auto_denials: (non-Horn, no changes).
% 37.09/37.37
% 37.09/37.37 Term ordering decisions:
% 37.09/37.37
% 37.09/37.37 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 37.09/37.37 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c4=1. sk_c5=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. identity=1. multiply=1. inverse=0.
% 37.09/37.37
% 37.09/37.37 ============================== end of process initial clauses ========
% 37.09/37.37
% 37.09/37.37 ============================== CLAUSES FOR SEARCH ====================
% 37.09/37.37
% 37.09/37.37 ============================== end of clauses for search =============
% 37.09/37.37
% 37.09/37.37 ============================== SEARCH ================================
% 37.09/37.37
% 37.09/37.37 % Starting search at 0.02 seconds.
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=34.000, iters=3526
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=33.000, iters=3362
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=32.000, iters=3339
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=31.000, iters=3400
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=30.000, iters=3334
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=29.000, iters=3333
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=28.000, iters=3340
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=27.000, iters=3345
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=26.000, iters=3340
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=25.000, iters=3335
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=24.000, iters=3382
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=23.000, iters=3343
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=20.000, iters=3394
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=19.000, iters=3336
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=16.000, iters=3333
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=15.000, iters=3341
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=14.000, iters=3385
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=13.000, iters=3336
% 37.09/37.37
% 37.09/37.37 Low Water (keep): wt=12.000, iters=3340
% 37.09/37.37
% 37.09/37.37 ============================== PROOF =================================
% 37.09/37.37 % SZS status Unsatisfiable
% 37.09/37.37 % SZS output start Refutation
% 37.09/37.37
% 37.09/37.37 % Proof 1 at 35.29 (+ 1.03) seconds.
% 37.09/37.37 % Length of proof is 218.
% 37.09/37.37 % Level of proof is 38.
% 37.09/37.37 % Maximum clause weight is 50.000.
% 37.09/37.37 % Given clauses 4903.
% 37.09/37.37
% 37.09/37.37 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 37.09/37.37 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 37.09/37.37 3 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 37.09/37.37 4 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 37.09/37.37 5 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 37.09/37.37 6 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 37.09/37.37 7 inverse(sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 37.09/37.37 9 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 37.09/37.37 10 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 37.09/37.37 11 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 37.09/37.37 12 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 37.09/37.37 13 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c5) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 37.09/37.37 14 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 37.09/37.37 15 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 37.09/37.37 16 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 37.09/37.37 17 multiply(sk_c8,sk_c3) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 37.09/37.37 19 multiply(sk_c2,sk_c8) = sk_c3 | inverse(sk_c4) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 37.09/37.37 22 inverse(sk_c2) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 37.09/37.37 23 inverse(sk_c2) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 37.09/37.37 24 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 37.09/37.37 26 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 37.09/37.37 27 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 37.09/37.37 28 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 37.09/37.37 29 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 37.09/37.37 30 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 37.09/37.37 31 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 37.09/37.37 32 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 37.09/37.37 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 37.09/37.37 34 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8 | multiply(sk_c8,E) != sk_c7 | multiply(F,sk_c8) != E | inverse(F) != sk_c8 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 37.09/37.37 40 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8. [factor(34,e,j),merge(i),merge(j)].
% 37.09/37.37 56 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 37.09/37.37 57 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = identity. [para(4(b,1),2(a,1,1))].
% 37.09/37.37 62 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 37.09/37.37 63 inverse(sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(9(b,1),33(a,1,1)),flip(b)].
% 37.09/37.37 64 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c8). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 66 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 68 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(11(b,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 70 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c7). [para(12(a,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 76 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(15(b,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 79 inverse(sk_c4) = sk_c8 | multiply(sk_c8,multiply(sk_c3,A)) = multiply(sk_c7,A). [para(17(a,1),33(a,1,1)),flip(b)].
% 37.09/37.37 84 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(19(a,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 92 inverse(sk_c2) = sk_c8 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(23(b,1),33(a,2,2)),rewrite([33(8)])].
% 37.09/37.37 93 multiply(sk_c4,sk_c7) = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(24(a,1),33(a,1,1)),flip(b)].
% 37.09/37.37 101 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c8,multiply(sk_c3,A)) = multiply(sk_c7,A). [para(28(a,1),33(a,1,1)),flip(b)].
% 37.09/37.37 108 multiply(sk_c8,sk_c6) = sk_c7 | multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3). [para(31(a,1),33(a,2,2)),rewrite([33(9)])].
% 37.09/37.37 130 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [resolve(40,e,2,a)].
% 37.09/37.37 136 inverse(sk_c8) != sk_c7 | sk_c7 != sk_c8 | inverse(identity) != sk_c8 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8. [para(1(a,1),40(b,1)),flip(b)].
% 37.09/37.37 139 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8. [para(2(a,1),40(b,1))].
% 37.09/37.37 225 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [factor(130,e,f)].
% 37.09/37.37 248 inverse(sk_c8) != sk_c7 | sk_c7 != sk_c8 | inverse(identity) != sk_c8 | multiply(sk_c8,A) != sk_c7 | sk_c8 != A | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [factor(136,c,f),rewrite([1(18)])].
% 37.09/37.37 252 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,A) != sk_c7 | identity != A | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [factor(139,c,f),rewrite([2(20)])].
% 37.09/37.37 385 inverse(sk_c8) != sk_c7 | sk_c7 != sk_c8 | inverse(identity) != sk_c8 | multiply(sk_c8,A) != sk_c7 | sk_c8 != A. [factor(248,c,f),rewrite([1(20)]),merge(f)].
% 37.09/37.37 386 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8. [factor(252,b,e)].
% 37.09/37.37 480 inverse(sk_c8) = sk_c7 | multiply(sk_c8,multiply(sk_c4,A)) = A. [para(56(b,1),33(a,1,1)),rewrite([1(6)]),flip(b)].
% 37.09/37.37 488 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),62(a,1,2))].
% 37.09/37.37 495 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(10(b,1),62(a,1,2))].
% 37.09/37.37 511 multiply(sk_c5,sk_c8) = sk_c6 | multiply(inverse(sk_c1),sk_c7) = sk_c8. [para(26(a,1),62(a,1,2))].
% 37.09/37.37 519 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),identity) = sk_c4. [para(56(b,1),62(a,1,2))].
% 37.09/37.37 520 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(62(a,1),62(a,1,2))].
% 37.09/37.37 521 multiply(A,identity) = A. [back_rewrite(488),rewrite([520(4)])].
% 37.09/37.37 522 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c4. [back_rewrite(519),rewrite([521(8)])].
% 37.09/37.37 525 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | sk_c7 != sk_c8 | inverse(inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [back_rewrite(225),rewrite([521(14)]),flip(d)].
% 37.09/37.37 529 inverse(identity) = identity. [para(521(a,1),2(a,1))].
% 37.09/37.37 535 inverse(sk_c8) != sk_c7 | sk_c7 != sk_c8 | identity != sk_c8. [para(521(a,1),385(d,1)),rewrite([529(9)]),flip(d),flip(e),merge(d),merge(e)].
% 37.09/37.37 545 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c5. [para(57(b,1),62(a,1,2)),rewrite([521(8)])].
% 37.09/37.37 547 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = identity. [para(545(b,1),2(a,1,1))].
% 37.09/37.37 549 inverse(sk_c8) = sk_c7 | sk_c5 = sk_c4. [para(545(b,1),522(b,1)),merge(b)].
% 37.09/37.37 552 sk_c5 = sk_c4 | multiply(sk_c7,sk_c8) = identity. [para(549(a,1),2(a,1,1))].
% 37.09/37.37 570 sk_c5 = sk_c4 | inverse(sk_c7) = sk_c8. [para(552(b,1),62(a,1,2)),rewrite([521(7)])].
% 37.09/37.37 574 sk_c5 = sk_c4 | multiply(sk_c8,sk_c7) = identity. [para(570(b,1),2(a,1,1))].
% 37.09/37.37 649 sk_c5 = sk_c4 | inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8. [para(574(b,1),386(d,1)),merge(e)].
% 37.09/37.37 651 sk_c5 = sk_c4 | inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [factor(649,d,e)].
% 37.09/37.37 668 multiply(A,inverse(A)) = identity. [para(520(a,1),2(a,1))].
% 37.09/37.37 693 multiply(A,multiply(inverse(A),B)) = B. [para(520(a,1),62(a,1))].
% 37.09/37.37 694 inverse(inverse(A)) = A. [para(520(a,1),521(a,1)),rewrite([521(2)]),flip(a)].
% 37.09/37.37 705 sk_c5 = sk_c4 | inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [back_rewrite(651),rewrite([694(13)]),xx(d)].
% 37.09/37.37 720 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [back_rewrite(525),rewrite([694(17)]),xx(e)].
% 37.09/37.37 728 inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(sk_c8,A) != sk_c7 | identity != A | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8. [back_rewrite(252),rewrite([694(10)]),xx(c)].
% 37.09/37.37 735 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c4),multiply(sk_c8,A)) = multiply(sk_c7,A). [para(63(b,1),62(a,1,2))].
% 37.09/37.37 741 inverse(sk_c4) = sk_c8 | multiply(sk_c1,sk_c8) = identity. [para(5(a,1),668(a,1,2))].
% 37.09/37.37 742 inverse(sk_c5) = sk_c8 | multiply(sk_c1,sk_c8) = identity. [para(6(a,1),668(a,1,2))].
% 37.09/37.37 743 inverse(sk_c4) = sk_c8 | multiply(sk_c2,sk_c8) = identity. [para(7(a,1),668(a,1,2))].
% 37.09/37.37 745 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(668(a,1),33(a,1)),flip(a)].
% 37.09/37.37 755 inverse(sk_c8) = sk_c7 | multiply(sk_c8,inverse(sk_c7)) = sk_c4. [para(668(a,1),63(b,1,2)),rewrite([521(7)]),flip(b)].
% 37.09/37.37 874 inverse(sk_c8) != sk_c7 | multiply(A,multiply(B,sk_c8)) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(33(a,1),720(b,1))].
% 37.09/37.37 940 inverse(sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8. [para(9(b,1),66(b,2)),merge(b)].
% 37.09/37.37 962 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8. [para(668(a,1),728(c,1)),flip(d),merge(c)].
% 37.09/37.37 967 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(multiply(A,B)) != sk_c8 | multiply(A,multiply(B,sk_c7)) != sk_c8. [para(33(a,1),962(e,1))].
% 37.09/37.37 998 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(multiply(A,inverse(sk_c7))) != sk_c8 | sk_c8 != A. [para(2(a,1),967(e,1,2)),rewrite([521(19)]),flip(e)].
% 37.09/37.37 1005 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(multiply(A,multiply(B,inverse(sk_c7)))) != sk_c8 | multiply(A,B) != sk_c8. [para(33(a,1),998(d,1,1)),flip(e)].
% 37.09/37.37 1092 inverse(sk_c8) = sk_c7 | multiply(A,sk_c6) = A. [para(547(b,1),68(b,1,2)),rewrite([521(10)]),flip(c),merge(b)].
% 37.09/37.37 1151 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(multiply(A,multiply(B,multiply(C,inverse(sk_c7))))) != sk_c8 | multiply(A,multiply(B,C)) != sk_c8. [para(33(a,1),1005(d,1,1,2))].
% 37.09/37.37 1303 inverse(sk_c4) = sk_c8 | identity = sk_c7. [para(741(b,1),12(a,1)),merge(c)].
% 37.09/37.37 1305 inverse(sk_c4) = sk_c8 | multiply(A,sk_c7) = A. [para(741(b,1),70(b,1,2)),rewrite([521(10)]),flip(c),merge(b)].
% 37.09/37.37 1393 inverse(sk_c8) != sk_c7 | multiply(A,multiply(B,multiply(C,sk_c8))) != sk_c7 | inverse(multiply(A,multiply(B,C))) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(33(a,1),874(b,1,2))].
% 37.09/37.37 1425 identity = sk_c7 | inverse(sk_c8) = sk_c4. [para(1303(a,1),694(a,1,1))].
% 37.09/37.37 1482 inverse(sk_c5) = sk_c8 | identity = sk_c7. [para(742(b,1),13(a,1)),merge(c)].
% 37.09/37.37 1489 identity = sk_c7 | inverse(sk_c8) = sk_c5. [para(1482(a,1),694(a,1,1))].
% 37.09/37.37 1501 identity = sk_c7 | sk_c5 = sk_c4. [para(1489(b,1),1425(b,1)),merge(b)].
% 37.09/37.37 1505 sk_c5 = sk_c4 | inverse(sk_c7) = identity. [para(1501(a,1),529(a,1,1))].
% 37.09/37.37 1668 sk_c5 = sk_c4 | identity = sk_c8. [para(1505(b,1),570(b,1)),merge(b)].
% 37.09/37.37 1679 sk_c5 = sk_c4 | inverse(sk_c8) = identity. [para(1668(b,1),529(a,1,1))].
% 37.09/37.37 1798 sk_c5 = sk_c4 | inverse(sk_c8) = sk_c8. [para(1668(b,1),1679(b,2)),merge(b)].
% 37.09/37.37 1799 sk_c5 = sk_c4 | multiply(sk_c8,sk_c8) = identity. [para(1798(b,1),2(a,1,1))].
% 37.09/37.37 2019 inverse(sk_c1) = sk_c8 | multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8. [para(14(b,1),76(b,2)),merge(b)].
% 37.09/37.37 2222 sk_c5 = sk_c4 | multiply(sk_c8,sk_c8) = sk_c7. [para(1501(a,1),1799(b,2)),merge(b)].
% 37.09/37.37 2392 sk_c5 = sk_c4 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(2222(b,1),62(a,1,2))].
% 37.09/37.37 2623 inverse(sk_c4) = sk_c8 | multiply(sk_c7,inverse(sk_c3)) = sk_c8. [para(668(a,1),79(b,1,2)),rewrite([521(7)]),flip(b)].
% 37.09/37.37 3645 inverse(sk_c4) = sk_c8 | multiply(A,sk_c3) = A. [para(743(b,1),84(b,1,2)),rewrite([521(10)]),flip(c),merge(b)].
% 37.09/37.37 4664 inverse(sk_c8) = sk_c7 | inverse(sk_c6) = identity. [para(1092(b,1),2(a,1))].
% 37.09/37.37 4873 inverse(sk_c8) = sk_c7 | multiply(sk_c6,A) = A. [para(4664(b,1),62(a,1,1)),rewrite([1(8)])].
% 37.09/37.37 5027 inverse(sk_c2) = sk_c8 | multiply(sk_c8,multiply(sk_c5,sk_c8)) = sk_c7. [para(22(b,1),92(b,2)),merge(b)].
% 37.09/37.37 5050 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(A) != sk_c8 | multiply(A,multiply(inverse(multiply(B,inverse(sk_c7))),B)) != sk_c8. [para(2(a,1),1151(d,1,1,2)),rewrite([521(13)])].
% 37.09/37.37 5058 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | inverse(multiply(sk_c8,inverse(sk_c7))) != sk_c8. [resolve(5050,e,693,a)].
% 37.09/37.37 5184 multiply(sk_c4,sk_c7) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c1. [para(668(a,1),93(b,1,2)),rewrite([521(8)]),flip(b)].
% 37.09/37.37 5988 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = identity. [para(3645(b,1),2(a,1))].
% 37.09/37.37 6093 inverse(sk_c4) = sk_c8 | multiply(sk_c3,A) = A. [para(5988(b,1),62(a,1,1)),rewrite([1(8)])].
% 37.09/37.37 6209 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,multiply(inverse(sk_c3),A)) = multiply(sk_c8,A). [para(693(a,1),101(b,1,2)),flip(b)].
% 37.09/37.37 6498 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c6),A) = A. [para(4873(b,1),62(a,1,2))].
% 37.09/37.37 6673 inverse(sk_c8) != sk_c7 | sk_c7 != A | inverse(multiply(A,multiply(inverse(multiply(B,sk_c8)),B))) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(2(a,1),1393(b,1,2)),rewrite([521(6)]),flip(b)].
% 37.09/37.37 6731 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c3),A) = A. [para(6093(b,1),62(a,1,2))].
% 37.09/37.37 6810 inverse(sk_c8) != sk_c7 | sk_c7 != A | inverse(multiply(A,multiply(inverse(multiply(B,multiply(C,sk_c8))),multiply(B,C)))) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(33(a,1),6673(c,1,1,2,1,1))].
% 37.09/37.37 7029 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c8,multiply(sk_c2,sk_c8)) = sk_c7. [para(28(a,1),108(b,2)),merge(b)].
% 37.09/37.37 7195 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c6. [para(522(b,1),495(b,1,1)),merge(b)].
% 37.09/37.37 7200 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c7. [para(7195(b,1),62(a,1,2))].
% 37.09/37.37 11746 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(745(a,1),62(a,1,2)),rewrite([521(3)]),flip(a)].
% 37.09/37.37 12105 multiply(sk_c5,sk_c8) = sk_c6 | multiply(sk_c8,inverse(sk_c7)) = inverse(sk_c1). [para(26(a,1),11746(a,1,2,1))].
% 37.09/37.37 12106 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c7,inverse(sk_c8)) = inverse(sk_c4). [para(27(b,1),11746(a,1,2,1))].
% 37.09/37.37 12120 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(11746(a,1),62(a,1,2)),flip(a)].
% 37.09/37.37 12199 inverse(sk_c8) != sk_c7 | sk_c7 != A | multiply(sk_c8,inverse(A)) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(11746(a,1),6810(c,1,1,2,2)),rewrite([12120(8),33(11),693(12),12120(10),694(10),33(11),668(10),521(10),12120(10),694(9)])].
% 37.09/37.37 13015 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(sk_c8) != identity | multiply(sk_c7,inverse(sk_c8)) != sk_c8. [back_rewrite(5058),rewrite([12120(16),694(14)])].
% 37.09/37.37 13293 inverse(sk_c8) != sk_c7 | inverse(A) != sk_c7 | multiply(sk_c8,A) != sk_c8 | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(694(a,1),12199(c,1,2)),flip(b)].
% 37.09/37.37 13335 inverse(sk_c8) != sk_c7 | multiply(inverse(A),sk_c8) != sk_c7 | sk_c8 != A | sk_c7 != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [para(693(a,1),13293(c,1)),rewrite([12120(8),694(8)]),flip(c)].
% 37.09/37.37 14162 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = sk_c7. [para(6731(b,1),1305(b,1)),flip(c),merge(b)].
% 37.09/37.37 14174 inverse(sk_c4) = sk_c8 | multiply(sk_c7,A) = A. [para(14162(b,1),6731(b,1,1)),merge(b)].
% 37.09/37.37 14222 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = sk_c8. [para(14174(b,1),2623(b,1)),merge(b)].
% 37.09/37.37 14226 inverse(sk_c4) = sk_c8 | identity = sk_c8. [para(14222(b,1),5988(b,1)),flip(c),merge(b)].
% 37.09/37.37 14232 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(14226(a,1),694(a,1,1))].
% 37.09/37.37 14930 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c7. [para(7200(b,1),1092(b,1)),flip(c),merge(b)].
% 37.09/37.37 14934 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(14930(b,1),668(a,1,2))].
% 37.09/37.37 14942 inverse(sk_c8) = sk_c7 | identity = sk_c8. [para(14934(b,1),9(b,1)),merge(b)].
% 37.09/37.37 14944 inverse(sk_c8) = sk_c7 | multiply(A,sk_c8) = A. [para(14934(b,1),64(b,1,2)),rewrite([521(10)]),flip(c),merge(b)].
% 37.09/37.37 14967 identity = sk_c8 | sk_c4 = sk_c7. [para(14942(a,1),14232(b,1)),flip(c),merge(b)].
% 37.09/37.37 15577 inverse(sk_c8) = sk_c7 | inverse(sk_c6) = sk_c8. [para(14944(b,1),6498(b,1)),merge(b)].
% 37.09/37.37 15699 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = identity. [para(15577(b,1),2(a,1,1))].
% 37.09/37.37 16431 inverse(sk_c8) = sk_c7 | identity = sk_c7. [para(15699(b,1),10(b,1)),merge(b)].
% 37.09/37.37 16434 inverse(sk_c8) = sk_c7 | multiply(A,sk_c7) = A. [para(15699(b,1),66(b,1,2)),rewrite([521(10)]),flip(c),merge(b)].
% 37.09/37.37 16444 identity = sk_c7 | sk_c4 = sk_c7. [para(16431(a,1),1425(b,1)),flip(c),merge(b)].
% 37.09/37.37 16448 sk_c4 = sk_c7 | inverse(sk_c7) = identity. [para(16444(a,1),529(a,1,1))].
% 37.09/37.37 16930 sk_c4 = sk_c7 | inverse(sk_c7) = sk_c7. [para(16444(a,1),16448(b,2)),merge(b)].
% 37.09/37.37 17194 sk_c4 = sk_c7 | multiply(sk_c7,sk_c7) = identity. [para(16930(b,1),2(a,1,1))].
% 37.09/37.37 17527 sk_c4 = sk_c7 | multiply(sk_c7,sk_c7) = sk_c8. [para(14967(a,1),17194(b,2)),merge(b)].
% 37.09/37.37 18535 inverse(sk_c8) = sk_c7 | inverse(sk_c6) = sk_c7. [para(16434(b,1),6498(b,1)),merge(b)].
% 37.09/37.37 18625 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = sk_c6. [para(18535(b,1),694(a,1,1))].
% 37.09/37.37 18653 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = sk_c4. [para(18625(b,1),755(b,1,2)),merge(b)].
% 37.09/37.37 18938 sk_c5 = sk_c4 | inverse(sk_c8) != sk_c7 | identity != sk_c7. [resolve(705,d,2392,b),merge(d)].
% 37.09/37.37 20503 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c4) = sk_c8. [para(18653(b,1),940(b,1,2)),merge(b)].
% 37.09/37.37 20512 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c8) = sk_c4. [para(20503(b,1),480(b,1,2)),merge(b)].
% 37.09/37.37 20522 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c8) = identity. [para(20512(b,1),735(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 37.09/37.37 20536 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = sk_c8. [para(20522(b,1),62(a,1,2)),rewrite([521(8)])].
% 37.09/37.37 20542 inverse(sk_c8) = sk_c7. [para(20536(b,1),694(a,1,1)),merge(b)].
% 37.09/37.37 21137 sk_c5 = sk_c4 | identity != sk_c7. [back_rewrite(18938),rewrite([20542(5)]),xx(b)].
% 37.09/37.37 22026 multiply(inverse(A),sk_c8) != sk_c7 | sk_c8 != A | sk_c7 != sk_c8 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(13335),rewrite([20542(2),20542(15)]),xx(a)].
% 37.09/37.37 22191 identity != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(13015),rewrite([20542(2),20542(8),20542(12)]),flip(c),xx(a),merge(b)].
% 37.09/37.37 22690 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c7,sk_c7) = inverse(sk_c4). [back_rewrite(12106),rewrite([20542(8)])].
% 37.09/37.37 23195 multiply(sk_c4,sk_c7) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c1. [back_rewrite(5184),rewrite([20542(8)])].
% 37.09/37.37 23947 sk_c7 != sk_c8 | identity != sk_c8. [back_rewrite(535),rewrite([20542(2)]),xx(a)].
% 37.09/37.37 24255 multiply(sk_c7,sk_c8) = identity. [para(20542(a,1),2(a,1,1))].
% 37.09/37.37 24256 multiply(sk_c7,multiply(sk_c8,A)) = A. [para(20542(a,1),62(a,1,1))].
% 37.09/37.37 24257 inverse(sk_c7) = sk_c8. [para(20542(a,1),694(a,1,1))].
% 37.09/37.37 24258 multiply(sk_c8,sk_c7) = identity. [para(20542(a,1),668(a,1,2))].
% 37.09/37.37 24418 multiply(sk_c5,sk_c8) = sk_c6 | multiply(sk_c8,sk_c8) = inverse(sk_c1). [back_rewrite(12105),rewrite([24257(8)])].
% 37.09/37.37 24525 identity != sk_c7 | sk_c4 = sk_c7. [resolve(22191,b,17527,b)].
% 37.09/37.37 24548 sk_c5 = sk_c4. [resolve(21137,b,1501,a),merge(b)].
% 37.09/37.37 24559 multiply(sk_c4,sk_c8) = sk_c6 | multiply(sk_c8,sk_c8) = inverse(sk_c1). [back_rewrite(24418),rewrite([24548(1)])].
% 37.09/37.37 24810 inverse(sk_c2) = sk_c8 | multiply(sk_c8,multiply(sk_c4,sk_c8)) = sk_c7. [back_rewrite(5027),rewrite([24548(6)])].
% 37.09/37.37 24843 multiply(sk_c4,sk_c8) = sk_c6 | multiply(inverse(sk_c1),sk_c7) = sk_c8. [back_rewrite(511),rewrite([24548(1)])].
% 37.09/37.37 24856 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(32),rewrite([24548(6)])].
% 37.09/37.37 24857 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(29),rewrite([24548(6)])].
% 37.09/37.37 24859 inverse(sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(23),rewrite([24548(5)])].
% 37.09/37.37 24860 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(16),rewrite([24548(5)])].
% 37.09/37.37 24881 sk_c4 = sk_c7. [resolve(24525,a,16444,a),merge(b)].
% 37.09/37.37 24882 inverse(sk_c1) = sk_c8 | identity = sk_c6. [back_rewrite(24860),rewrite([24881(5),24255(7)])].
% 37.09/37.37 24883 inverse(sk_c2) = sk_c8 | identity = sk_c6. [back_rewrite(24859),rewrite([24881(5),24255(7)])].
% 37.09/37.37 24885 multiply(sk_c8,sk_c3) = sk_c7 | identity = sk_c6. [back_rewrite(24857),rewrite([24881(6),24255(8)])].
% 37.09/37.37 24886 multiply(sk_c2,sk_c8) = sk_c3 | identity = sk_c6. [back_rewrite(24856),rewrite([24881(6),24255(8)])].
% 37.09/37.37 24897 identity = sk_c6 | multiply(inverse(sk_c1),sk_c7) = sk_c8. [back_rewrite(24843),rewrite([24881(1),24255(3)])].
% 37.09/37.37 24924 inverse(sk_c2) = sk_c8 | sk_c7 = sk_c8. [back_rewrite(24810),rewrite([24881(6),24255(8),521(7)]),flip(b)].
% 37.09/37.37 25094 identity = sk_c6 | multiply(sk_c8,sk_c8) = inverse(sk_c1). [back_rewrite(24559),rewrite([24881(1),24255(3)])].
% 37.09/37.37 25211 multiply(sk_c7,sk_c7) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c1. [back_rewrite(23195),rewrite([24881(1)])].
% 37.09/37.37 25222 multiply(sk_c8,sk_c3) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(22690),rewrite([24881(9),24257(10)])].
% 37.09/37.37 25256 inverse(sk_c1) = sk_c8 | sk_c6 = sk_c8. [back_rewrite(2019),rewrite([24881(5),24256(9)])].
% 37.09/37.37 25275 multiply(sk_c2,sk_c8) = sk_c3 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(30),rewrite([24881(6)])].
% 37.09/37.37 25317 identity = sk_c6 | multiply(sk_c2,sk_c8) = identity. [para(24883(a,1),668(a,1,2))].
% 37.09/37.37 25363 sk_c7 = sk_c8 | sk_c2 = sk_c7. [para(24924(a,1),694(a,1,1)),rewrite([20542(5)]),flip(b)].
% 37.09/37.37 25409 sk_c6 = sk_c8 | multiply(sk_c8,sk_c1) = identity. [para(25256(a,1),2(a,1,1))].
% 37.09/37.37 25647 multiply(sk_c8,sk_c8) != sk_c7 | sk_c7 != sk_c8 | multiply(sk_c7,sk_c7) != sk_c8. [para(24257(a,1),22026(a,1,1)),flip(b),merge(c)].
% 37.09/37.37 25885 identity = sk_c6 | identity = sk_c3. [para(25317(b,1),24886(a,1)),merge(c)].
% 37.09/37.37 25887 identity = sk_c6 | multiply(A,sk_c3) = A. [para(25885(b,1),521(a,1,2))].
% 37.09/37.37 26549 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,multiply(inverse(sk_c3),multiply(sk_c2,sk_c8))) = multiply(sk_c8,sk_c3). [para(108(b,1),6209(b,2)),merge(b)].
% 37.09/37.37 26716 identity = sk_c6 | sk_c7 = sk_c8. [para(25887(b,1),24885(a,1)),flip(b),merge(c)].
% 37.09/37.37 26820 sk_c7 = sk_c8 | multiply(A,sk_c6) = A. [para(26716(a,1),521(a,1,2))].
% 37.09/37.37 28543 identity = sk_c6 | identity = sk_c8. [para(24882(a,1),24897(b,1,1)),rewrite([24258(9)]),merge(b)].
% 37.09/37.37 28558 identity = sk_c8 | sk_c6 = sk_c8 | multiply(sk_c8,sk_c1) = sk_c6. [para(28543(a,1),25409(b,2))].
% 37.09/37.37 29030 identity = sk_c6 | multiply(sk_c8,sk_c8) = sk_c8. [para(24882(a,1),25094(b,2)),merge(b)].
% 37.09/37.37 29052 sk_c7 = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7. [para(25363(b,1),7029(b,1,2,1)),rewrite([24255(12),521(11)]),flip(c),merge(c)].
% 37.09/37.37 29100 sk_c7 = sk_c8. [para(29052(b,1),26820(b,1)),merge(b),merge(c)].
% 37.09/37.37 30125 multiply(sk_c8,sk_c6) = sk_c8 | multiply(sk_c8,multiply(inverse(sk_c3),multiply(sk_c2,sk_c8))) = multiply(sk_c8,sk_c3). [back_rewrite(26549),rewrite([29100(4),29100(6)])].
% 37.09/37.37 30531 multiply(sk_c8,sk_c8) != sk_c8. [back_rewrite(25647),rewrite([29100(4),29100(6),29100(9),29100(10)]),xx(b),merge(b)].
% 37.09/37.37 30734 multiply(sk_c2,sk_c8) = sk_c3. [back_rewrite(25275),rewrite([29100(6),29100(7)]),unit_del(b,30531)].
% 37.09/37.37 30763 multiply(sk_c8,sk_c3) = sk_c8. [back_rewrite(25222),rewrite([29100(4),29100(6),29100(7)]),unit_del(b,30531)].
% 37.09/37.37 30769 multiply(sk_c8,sk_c8) = sk_c1. [back_rewrite(25211),rewrite([29100(1),29100(2),29100(6),29100(7)]),unit_del(a,30531)].
% 37.09/37.37 30895 identity = sk_c1. [back_rewrite(24258),rewrite([29100(2),30769(3)]),flip(a)].
% 37.09/37.37 30919 sk_c1 != sk_c8. [back_rewrite(23947),rewrite([29100(1),30895(4)]),xx(a)].
% 37.09/37.37 31017 sk_c1 = sk_c6. [back_unit_del(29030),rewrite([30895(1),30769(6)]),unit_del(b,30919)].
% 37.09/37.37 31071 multiply(sk_c8,sk_c6) = sk_c8. [back_rewrite(30125),rewrite([30734(11),2(10),30895(7),31017(7),30763(11)]),merge(b)].
% 37.09/37.37 31090 sk_c6 = sk_c8. [back_unit_del(28558),rewrite([30895(1),31017(1),31017(8),31071(9)]),flip(c),merge(b),merge(c)].
% 37.09/37.37 31095 $F. [back_rewrite(30531),rewrite([30769(3),31017(1),31090(1)]),xx(a)].
% 37.09/37.37
% 37.09/37.37 % SZS output end Refutation
% 37.09/37.37 ============================== end of proof ==========================
% 37.09/37.37
% 37.09/37.37 ============================== STATISTICS ============================
% 37.09/37.37
% 37.09/37.37 Given=4903. Generated=1952745. Kept=31094. proofs=1.
% 37.09/37.37 Usable=48. Sos=359. Demods=33. Limbo=326, Disabled=30395. Hints=0.
% 37.09/37.37 Megabytes=22.27.
% 37.09/37.37 User_CPU=35.29, System_CPU=1.03, Wall_clock=37.
% 37.09/37.37
% 37.09/37.37 ============================== end of statistics =====================
% 37.09/37.37
% 37.09/37.37 ============================== end of search =========================
% 37.09/37.37
% 37.09/37.37 THEOREM PROVED
% 37.09/37.37 % SZS status Unsatisfiable
% 37.09/37.37
% 37.09/37.37 Exiting with 1 proof.
% 37.09/37.37
% 37.09/37.37 Process 18537 exit (max_proofs) Tue Jun 14 01:13:27 2022
% 37.09/37.37 Prover9 interrupted
%------------------------------------------------------------------------------