TSTP Solution File: GRP223-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP223-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:18:13 EDT 2022
% Result : Unsatisfiable 38.54s 38.83s
% Output : Refutation 38.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP223-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 07:27:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 23.53/23.80 ============================== Prover9 ===============================
% 23.53/23.80 Prover9 (32) version 2009-11A, November 2009.
% 23.53/23.80 Process 18212 was started by sandbox on n018.cluster.edu,
% 23.53/23.80 Tue Jun 14 07:27:44 2022
% 23.53/23.80 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18058_n018.cluster.edu".
% 23.53/23.80 ============================== end of head ===========================
% 23.53/23.80
% 23.53/23.80 ============================== INPUT =================================
% 23.53/23.80
% 23.53/23.80 % Reading from file /tmp/Prover9_18058_n018.cluster.edu
% 23.53/23.80
% 23.53/23.80 set(prolog_style_variables).
% 23.53/23.80 set(auto2).
% 23.53/23.80 % set(auto2) -> set(auto).
% 23.53/23.80 % set(auto) -> set(auto_inference).
% 23.53/23.80 % set(auto) -> set(auto_setup).
% 23.53/23.80 % set(auto_setup) -> set(predicate_elim).
% 23.53/23.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 23.53/23.80 % set(auto) -> set(auto_limits).
% 23.53/23.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 23.53/23.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 23.53/23.80 % set(auto) -> set(auto_denials).
% 23.53/23.80 % set(auto) -> set(auto_process).
% 23.53/23.80 % set(auto2) -> assign(new_constants, 1).
% 23.53/23.80 % set(auto2) -> assign(fold_denial_max, 3).
% 23.53/23.80 % set(auto2) -> assign(max_weight, "200.000").
% 23.53/23.80 % set(auto2) -> assign(max_hours, 1).
% 23.53/23.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 23.53/23.80 % set(auto2) -> assign(max_seconds, 0).
% 23.53/23.80 % set(auto2) -> assign(max_minutes, 5).
% 23.53/23.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 23.53/23.80 % set(auto2) -> set(sort_initial_sos).
% 23.53/23.80 % set(auto2) -> assign(sos_limit, -1).
% 23.53/23.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 23.53/23.80 % set(auto2) -> assign(max_megs, 400).
% 23.53/23.80 % set(auto2) -> assign(stats, some).
% 23.53/23.80 % set(auto2) -> clear(echo_input).
% 23.53/23.80 % set(auto2) -> set(quiet).
% 23.53/23.80 % set(auto2) -> clear(print_initial_clauses).
% 23.53/23.80 % set(auto2) -> clear(print_given).
% 23.53/23.80 assign(lrs_ticks,-1).
% 23.53/23.80 assign(sos_limit,10000).
% 23.53/23.80 assign(order,kbo).
% 23.53/23.80 set(lex_order_vars).
% 23.53/23.80 clear(print_given).
% 23.53/23.80
% 23.53/23.80 % formulas(sos). % not echoed (34 formulas)
% 23.53/23.80
% 23.53/23.80 ============================== end of input ==========================
% 23.53/23.80
% 23.53/23.80 % From the command line: assign(max_seconds, 300).
% 23.53/23.80
% 23.53/23.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 23.53/23.80
% 23.53/23.80 % Formulas that are not ordinary clauses:
% 23.53/23.80
% 23.53/23.80 ============================== end of process non-clausal formulas ===
% 23.53/23.80
% 23.53/23.80 ============================== PROCESS INITIAL CLAUSES ===============
% 23.53/23.80
% 23.53/23.80 ============================== PREDICATE ELIMINATION =================
% 23.53/23.80
% 23.53/23.80 ============================== end predicate elimination =============
% 23.53/23.80
% 23.53/23.80 Auto_denials: (non-Horn, no changes).
% 23.53/23.80
% 23.53/23.80 Term ordering decisions:
% 23.53/23.80
% 23.53/23.80 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 23.53/23.80 Function symbol KB weights: sk_c9=1. sk_c8=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c6=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 23.53/23.80
% 23.53/23.80 ============================== end of process initial clauses ========
% 23.53/23.80
% 23.53/23.80 ============================== CLAUSES FOR SEARCH ====================
% 23.53/23.80
% 23.53/23.80 ============================== end of clauses for search =============
% 23.53/23.80
% 23.53/23.80 ============================== SEARCH ================================
% 23.53/23.80
% 23.53/23.80 % Starting search at 0.02 seconds.
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=39.000, iters=3414
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=36.000, iters=3386
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=35.000, iters=3483
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=34.000, iters=3481
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=33.000, iters=3336
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=32.000, iters=3350
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=31.000, iters=3379
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=30.000, iters=3408
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=29.000, iters=3426
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=28.000, iters=3341
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=27.000, iters=3339
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=26.000, iters=3381
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=25.000, iters=3351
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=24.000, iters=3343
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=23.000, iters=3352
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=22.000, iters=3353
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=21.000, iters=3345
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=20.000, iters=3355
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=19.000, iters=3333
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=18.000, iters=3394
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=17.000, iters=3362
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=16.000, iters=3355
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=15.000, iters=3346
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=14.000, iters=3362
% 23.53/23.80
% 23.53/23.80 Low Water (keep): wt=13.000, iters=3335
% 23.53/23.80
% 23.53/23.80 Low Water (displace): id=3499, wt=45.000
% 38.54/38.83
% 38.54/38.83 Low Water (displace): id=25488, wt=12.000
% 38.54/38.83
% 38.54/38.83 Low Water (displace): id=25843, wt=11.000
% 38.54/38.83
% 38.54/38.83 ============================== PROOF =================================
% 38.54/38.83 % SZS status Unsatisfiable
% 38.54/38.83 % SZS output start Refutation
% 38.54/38.83
% 38.54/38.83 % Proof 1 at 36.61 (+ 1.20) seconds.
% 38.54/38.83 % Length of proof is 248.
% 38.54/38.83 % Level of proof is 35.
% 38.54/38.83 % Maximum clause weight is 51.000.
% 38.54/38.83 % Given clauses 4712.
% 38.54/38.83
% 38.54/38.83 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 38.54/38.83 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 38.54/38.83 3 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 38.54/38.83 4 inverse(sk_c1) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 38.54/38.83 5 inverse(sk_c2) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 38.54/38.83 6 inverse(sk_c2) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 38.54/38.83 7 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 38.54/38.83 8 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 38.54/38.83 9 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 38.54/38.83 10 inverse(sk_c1) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 38.54/38.83 11 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 38.54/38.83 12 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 38.54/38.83 13 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c4) = sk_c5 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 38.54/38.83 14 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c6) = sk_c9 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 38.54/38.83 15 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c4) = sk_c5 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 38.54/38.83 16 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c6) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 38.54/38.83 17 inverse(sk_c2) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 38.54/38.83 19 inverse(sk_c2) = sk_c9 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 38.54/38.83 20 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 38.54/38.83 21 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 38.54/38.83 24 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 38.54/38.83 27 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 38.54/38.83 28 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 38.54/38.83 29 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 38.54/38.83 31 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 38.54/38.83 32 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 38.54/38.83 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 38.54/38.83 34 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(D,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9 | multiply(sk_c9,F) != sk_c8 | multiply(V6,sk_c9) != F | inverse(V6) != sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 38.54/38.83 38 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(D,A) != sk_c9 | inverse(D) != A | multiply(sk_c9,E) != sk_c8 | multiply(F,sk_c9) != E | inverse(F) != sk_c9. [factor(34,b,h)].
% 38.54/38.83 41 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(D,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9. [factor(34,d,j),merge(i),merge(j)].
% 38.54/38.83 49 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(D,A) != sk_c9 | inverse(D) != A. [factor(38,d,i),merge(h),merge(i)].
% 38.54/38.83 66 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 38.54/38.83 68 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c4) = identity. [para(5(b,1),2(a,1,1))].
% 38.54/38.83 70 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 38.54/38.83 71 inverse(sk_c1) = sk_c9 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c9,A). [para(7(b,1),33(a,1,1)),flip(b)].
% 38.54/38.83 72 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c9). [para(7(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 73 inverse(sk_c1) = sk_c9 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(8(b,1),33(a,1,1)),flip(b)].
% 38.54/38.83 76 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c9,sk_c7)) = multiply(A,sk_c8). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 78 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c6,sk_c9)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 81 inverse(sk_c6) = sk_c9 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(12(a,1),33(a,1,1)),flip(b)].
% 38.54/38.83 84 inverse(sk_c4) = sk_c5 | multiply(A,multiply(sk_c9,sk_c3)) = multiply(A,sk_c8). [para(13(a,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 85 inverse(sk_c6) = sk_c9 | multiply(sk_c9,multiply(sk_c3,A)) = multiply(sk_c8,A). [para(14(a,1),33(a,1,1)),flip(b)].
% 38.54/38.83 86 inverse(sk_c6) = sk_c9 | multiply(A,multiply(sk_c9,sk_c3)) = multiply(A,sk_c8). [para(14(a,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 89 inverse(sk_c6) = sk_c9 | multiply(sk_c2,multiply(sk_c9,A)) = multiply(sk_c3,A). [para(16(a,1),33(a,1,1)),flip(b)].
% 38.54/38.83 92 inverse(sk_c2) = sk_c9 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c9). [para(17(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 98 inverse(sk_c2) = sk_c9 | multiply(A,multiply(sk_c6,sk_c9)) = multiply(A,sk_c7). [para(20(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 105 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c6,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(24(b,1),33(a,1,1)),flip(b)].
% 38.54/38.83 114 multiply(sk_c9,sk_c3) = sk_c8 | multiply(A,multiply(sk_c6,sk_c9)) = multiply(A,sk_c7). [para(28(b,1),33(a,2,2)),rewrite([33(9)])].
% 38.54/38.83 119 multiply(sk_c9,sk_c7) = sk_c8 | multiply(sk_c2,multiply(sk_c9,A)) = multiply(sk_c3,A). [para(31(a,1),33(a,1,1)),flip(b)].
% 38.54/38.83 145 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [resolve(41,d,2,a)].
% 38.54/38.83 173 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | identity != B | inverse(inverse(sk_c9)) != sk_c9 | multiply(C,D) != sk_c9 | inverse(C) != D | multiply(D,sk_c8) != sk_c9. [para(2(a,1),41(d,1))].
% 38.54/38.83 174 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | identity != sk_c9 | inverse(inverse(D)) != D | multiply(D,sk_c8) != sk_c9. [para(2(a,1),41(f,1))].
% 38.54/38.83 393 inverse(inverse(sk_c9)) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [factor(173,a,e)].
% 38.54/38.83 401 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | identity != sk_c9 | inverse(inverse(A)) != A. [factor(174,b,h)].
% 38.54/38.83 889 inverse(sk_c1) = sk_c9 | multiply(sk_c5,multiply(sk_c4,A)) = A. [para(66(b,1),33(a,1,1)),rewrite([1(6)]),flip(b)].
% 38.54/38.83 890 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c5,sk_c4)) = multiply(A,identity). [para(66(b,1),33(a,2,2)),rewrite([33(8)])].
% 38.54/38.83 905 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),70(a,1,2))].
% 38.54/38.83 906 inverse(sk_c1) = sk_c9 | multiply(sk_c9,multiply(sk_c6,A)) = A. [para(4(b,1),70(a,1,1))].
% 38.54/38.83 941 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(70(a,1),70(a,1,2))].
% 38.54/38.83 945 multiply(A,identity) = A. [back_rewrite(905),rewrite([941(4)])].
% 38.54/38.83 947 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c5,sk_c4)) = A. [back_rewrite(890),rewrite([945(10)])].
% 38.54/38.83 966 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(inverse(sk_c9)) != sk_c9 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [back_rewrite(145),rewrite([945(10)]),flip(c)].
% 38.54/38.83 972 inverse(identity) = identity. [para(945(a,1),2(a,1))].
% 38.54/38.83 1064 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c4. [para(68(b,1),70(a,1,2)),rewrite([945(8)])].
% 38.54/38.83 1099 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c9) = multiply(sk_c9,sk_c8). [para(8(b,1),71(b,1,2)),merge(b)].
% 38.54/38.83 1145 multiply(A,inverse(A)) = identity. [para(941(a,1),2(a,1))].
% 38.54/38.83 1180 multiply(A,multiply(inverse(A),B)) = B. [para(941(a,1),70(a,1))].
% 38.54/38.83 1181 inverse(inverse(A)) = A. [para(941(a,1),945(a,1)),rewrite([945(2)]),flip(a)].
% 38.54/38.83 1186 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [back_rewrite(966),rewrite([1181(13)]),xx(d)].
% 38.54/38.83 1214 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | identity != sk_c9. [back_rewrite(401),rewrite([1181(22)]),xx(g)].
% 38.54/38.83 1220 multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [back_rewrite(393),rewrite([1181(3)]),xx(a)].
% 38.54/38.83 1229 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c5) = identity. [para(3(b,1),1145(a,1,2))].
% 38.54/38.83 1230 inverse(sk_c1) = sk_c9 | multiply(sk_c6,sk_c9) = identity. [para(4(b,1),1145(a,1,2))].
% 38.54/38.83 1231 inverse(sk_c2) = sk_c9 | multiply(sk_c4,sk_c5) = identity. [para(5(b,1),1145(a,1,2))].
% 38.54/38.83 1232 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c9) = identity. [para(6(b,1),1145(a,1,2))].
% 38.54/38.83 1233 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1145(a,1),33(a,1)),flip(a)].
% 38.54/38.83 1254 inverse(sk_c5) = sk_c4 | multiply(sk_c2,sk_c9) = identity. [para(1064(a,1),1145(a,1,2))].
% 38.54/38.83 1311 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != multiply(B,sk_c9) | inverse(B) != sk_c9 | multiply(C,A) != sk_c9 | inverse(C) != A. [resolve(1180,a,49,c),flip(c)].
% 38.54/38.83 1697 inverse(sk_c1) = sk_c9 | identity = sk_c9. [para(1229(b,1),7(b,1)),merge(b)].
% 38.54/38.83 1699 inverse(sk_c1) = sk_c9 | multiply(A,sk_c9) = A. [para(1229(b,1),72(b,1,2)),rewrite([945(10)]),flip(c),merge(b)].
% 38.54/38.83 1702 identity = sk_c9 | inverse(sk_c9) = sk_c1. [para(1697(a,1),1181(a,1,1))].
% 38.54/38.83 1704 identity = sk_c9 | multiply(sk_c1,multiply(sk_c9,A)) = A. [para(1697(a,1),1180(a,1,2,1))].
% 38.54/38.83 1775 inverse(sk_c1) = sk_c9 | identity = sk_c7. [para(1230(b,1),10(b,1)),merge(b)].
% 38.54/38.83 1899 identity = sk_c7 | inverse(sk_c9) = sk_c1. [para(1775(a,1),1181(a,1,1))].
% 38.54/38.83 1901 identity = sk_c7 | multiply(sk_c1,multiply(sk_c9,A)) = A. [para(1775(a,1),1180(a,1,2,1))].
% 38.54/38.83 1971 inverse(sk_c1) = sk_c9 | multiply(A,sk_c7) = A. [para(1230(b,1),78(b,1,2)),rewrite([945(10)]),flip(c),merge(b)].
% 38.54/38.83 2006 inverse(sk_c2) = sk_c9 | identity = sk_c9. [para(1231(b,1),17(b,1)),merge(b)].
% 38.54/38.83 2010 identity = sk_c9 | inverse(sk_c9) = sk_c2. [para(2006(a,1),1181(a,1,1))].
% 38.54/38.83 2019 identity = sk_c9 | sk_c2 = sk_c1. [para(2010(b,1),1702(b,1)),merge(b)].
% 38.54/38.83 2024 sk_c2 = sk_c1 | inverse(sk_c9) = identity. [para(2019(a,1),972(a,1,1))].
% 38.54/38.83 2120 sk_c2 = sk_c1 | inverse(sk_c9) = sk_c9. [para(2019(a,1),2024(b,2)),merge(b)].
% 38.54/38.83 2122 sk_c2 = sk_c1 | multiply(sk_c9,sk_c9) = identity. [para(2120(b,1),2(a,1,1))].
% 38.54/38.83 2582 inverse(sk_c2) = sk_c9 | identity = sk_c7. [para(1232(b,1),20(b,1)),merge(b)].
% 38.54/38.83 2590 identity = sk_c7 | inverse(sk_c9) = sk_c2. [para(2582(a,1),1181(a,1,1))].
% 38.54/38.83 2602 identity = sk_c7 | sk_c2 = sk_c1. [para(2590(b,1),1899(b,1)),merge(b)].
% 38.54/38.83 2632 sk_c2 = sk_c1 | multiply(sk_c9,sk_c9) = sk_c7. [para(2602(a,1),2122(b,2)),merge(b)].
% 38.54/38.83 3001 inverse(sk_c4) = sk_c5 | multiply(sk_c1,multiply(sk_c9,sk_c3)) = sk_c9. [para(11(a,1),84(b,2)),merge(b)].
% 38.54/38.83 3286 sk_c2 = sk_c1 | multiply(inverse(sk_c9),sk_c7) = sk_c9. [para(2632(b,1),70(a,1,2))].
% 38.54/38.83 3496 inverse(sk_c6) = sk_c9 | multiply(sk_c1,multiply(sk_c9,sk_c3)) = sk_c9. [para(12(a,1),86(b,2)),merge(b)].
% 38.54/38.83 3572 inverse(sk_c5) = sk_c4 | identity = sk_c3 | inverse(sk_c4) = sk_c5. [para(1254(b,1),15(a,1))].
% 38.54/38.83 3954 inverse(sk_c1) = sk_c9 | sk_c7 = sk_c6. [para(1699(b,1),10(b,1)),flip(c),merge(b)].
% 38.54/38.83 4032 sk_c7 = sk_c6 | inverse(sk_c9) = sk_c1. [para(3954(a,1),1181(a,1,1))].
% 38.54/38.83 4055 inverse(sk_c6) = sk_c9 | multiply(sk_c3,inverse(sk_c9)) = sk_c2. [para(1145(a,1),89(b,1,2)),rewrite([945(7)]),flip(b)].
% 38.54/38.83 4620 inverse(sk_c1) = sk_c9 | inverse(sk_c7) = identity. [para(1971(b,1),2(a,1))].
% 38.54/38.83 4677 inverse(sk_c2) = sk_c9 | multiply(A,sk_c9) = A. [para(1231(b,1),92(b,1,2)),rewrite([945(10)]),flip(c),merge(b)].
% 38.54/38.83 4899 inverse(sk_c1) = sk_c9 | multiply(sk_c7,A) = A. [para(4620(b,1),70(a,1,1)),rewrite([1(8)])].
% 38.54/38.83 5770 inverse(sk_c2) = sk_c9 | sk_c7 = sk_c6. [para(4677(b,1),20(b,1)),flip(c),merge(b)].
% 38.54/38.83 5802 sk_c7 = sk_c6 | multiply(sk_c2,sk_c9) = identity. [para(5770(a,1),1145(a,1,2))].
% 38.54/38.83 6171 inverse(sk_c2) = sk_c9 | multiply(A,sk_c7) = A. [para(1232(b,1),98(b,1,2)),rewrite([945(10)]),flip(c),merge(b)].
% 38.54/38.83 6650 sk_c7 = sk_c6 | identity = sk_c3 | inverse(sk_c6) = sk_c9. [para(5802(b,1),16(a,1))].
% 38.54/38.83 6726 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | sk_c9 != B | inverse(B) != identity. [para(1(a,1),1186(f,1)),rewrite([945(12)]),flip(d),merge(f)].
% 38.54/38.83 6898 inverse(multiply(A,B)) != sk_c9 | multiply(A,multiply(B,sk_c8)) != sk_c9 | sk_c8 != sk_c9 | sk_c9 != C | inverse(C) != identity. [para(33(a,1),6726(b,1))].
% 38.54/38.83 7261 inverse(multiply(A,inverse(sk_c8))) != sk_c9 | sk_c9 != A | sk_c8 != sk_c9 | sk_c9 != B | inverse(B) != identity. [para(2(a,1),6898(b,1,2)),rewrite([945(8)]),flip(b)].
% 38.54/38.83 7272 inverse(multiply(A,inverse(sk_c8))) != sk_c9 | sk_c9 != A | sk_c8 != sk_c9 | inverse(A) != identity. [factor(7261,b,d)].
% 38.54/38.83 7361 inverse(multiply(A,multiply(B,inverse(sk_c8)))) != sk_c9 | multiply(A,B) != sk_c9 | sk_c8 != sk_c9 | inverse(multiply(A,B)) != identity. [para(33(a,1),7272(a,1,1)),flip(b)].
% 38.54/38.83 7504 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(multiply(A,sk_c8)) != identity. [para(2(a,1),7361(a,1,1,2)),rewrite([945(2),1181(6),1181(13)])].
% 38.54/38.83 7542 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c7),A) = A. [para(4899(b,1),70(a,1,2))].
% 38.54/38.83 7920 inverse(sk_c2) = sk_c9 | inverse(sk_c7) = identity. [para(6171(b,1),2(a,1))].
% 38.54/38.83 8042 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | sk_c9 != B | identity != sk_c9. [para(1(a,1),1214(d,1)),rewrite([972(15)]),merge(f)].
% 38.54/38.83 8061 inverse(sk_c2) = sk_c9 | multiply(sk_c7,A) = A. [para(7920(b,1),70(a,1,1)),rewrite([1(8)])].
% 38.54/38.83 8153 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | identity != sk_c9. [resolve(8042,c,1180,a),flip(c)].
% 38.54/38.83 8185 multiply(inverse(sk_c9),sk_c8) != sk_c9 | identity != sk_c9. [factor(8153,b,c),rewrite([1181(3)]),xx(a)].
% 38.54/38.83 8604 inverse(sk_c2) = sk_c9 | multiply(inverse(sk_c7),A) = A. [para(8061(b,1),70(a,1,2))].
% 38.54/38.83 8662 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c9,multiply(sk_c6,sk_c9)) = sk_c8. [para(27(b,1),114(b,2)),merge(b)].
% 38.54/38.83 10051 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1233(a,1),70(a,1,2)),rewrite([945(3)]),flip(a)].
% 38.54/38.83 10077 inverse(sk_c6) = sk_c9 | multiply(sk_c3,inverse(multiply(sk_c2,sk_c9))) = identity. [para(1233(a,1),89(b,1)),flip(b)].
% 38.54/38.83 10109 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c7,inverse(multiply(sk_c6,sk_c9))) = identity. [para(1233(a,1),105(b,1)),flip(b)].
% 38.54/38.83 10144 multiply(sk_c9,sk_c7) = sk_c8 | multiply(sk_c3,inverse(multiply(sk_c2,sk_c9))) = identity. [para(1233(a,1),119(b,1)),flip(b)].
% 38.54/38.83 10215 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(10051(a,1),70(a,1,2)),flip(a)].
% 38.54/38.83 10323 multiply(sk_c9,sk_c7) = sk_c8 | multiply(sk_c3,multiply(inverse(sk_c9),inverse(sk_c2))) = identity. [back_rewrite(10144),rewrite([10215(10)])].
% 38.54/38.83 10340 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c7,multiply(inverse(sk_c9),inverse(sk_c6))) = identity. [back_rewrite(10109),rewrite([10215(10)])].
% 38.54/38.83 10358 inverse(sk_c6) = sk_c9 | multiply(sk_c3,multiply(inverse(sk_c9),inverse(sk_c2))) = identity. [back_rewrite(10077),rewrite([10215(9)])].
% 38.54/38.83 10479 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | multiply(inverse(sk_c8),inverse(A)) != identity. [back_rewrite(7504),rewrite([10215(13)])].
% 38.54/38.83 11849 inverse(sk_c6) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = multiply(sk_c9,sk_c2). [para(4055(b,1),85(b,1,2)),flip(c),merge(b)].
% 38.54/38.83 12043 sk_c7 = sk_c6 | identity = sk_c3 | inverse(sk_c9) = sk_c6. [para(6650(c,1),1181(a,1,1))].
% 38.54/38.83 12111 inverse(sk_c1) = sk_c9 | inverse(sk_c7) = sk_c9. [para(7542(b,1),1699(b,1)),flip(c),merge(b)].
% 38.54/38.83 12113 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c7) = identity. [para(12111(b,1),2(a,1,1))].
% 38.54/38.83 12119 inverse(sk_c1) = sk_c9 | multiply(sk_c9,A) = A. [para(12111(b,1),7542(b,1,1)),merge(b)].
% 38.54/38.83 12146 inverse(sk_c1) = sk_c9 | identity = sk_c8. [para(12113(b,1),9(b,1)),merge(b)].
% 38.54/38.83 12150 inverse(sk_c1) = sk_c9 | multiply(A,sk_c8) = A. [para(12113(b,1),76(b,1,2)),rewrite([945(10)]),flip(c),merge(b)].
% 38.54/38.83 12156 identity = sk_c8 | inverse(sk_c9) = sk_c1. [para(12146(a,1),1181(a,1,1))].
% 38.54/38.83 12245 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c9),A) = A. [para(12119(b,1),70(a,1,2))].
% 38.54/38.83 12404 inverse(sk_c1) = sk_c9 | inverse(sk_c7) = sk_c8. [para(12150(b,1),7542(b,1)),merge(b)].
% 38.54/38.83 12489 inverse(sk_c1) = sk_c9 | multiply(sk_c8,A) = A. [para(12404(b,1),7542(b,1,1)),merge(b)].
% 38.54/38.83 13223 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c8),A) = A. [para(12489(b,1),70(a,1,2))].
% 38.54/38.83 14178 inverse(sk_c2) = sk_c9 | inverse(sk_c7) = sk_c9. [para(8604(b,1),4677(b,1)),flip(c),merge(b)].
% 38.54/38.83 14181 inverse(sk_c2) = sk_c9 | multiply(sk_c9,sk_c7) = identity. [para(14178(b,1),2(a,1,1))].
% 38.54/38.83 14226 inverse(sk_c2) = sk_c9 | identity = sk_c8. [para(14181(b,1),19(b,1)),merge(b)].
% 38.54/38.83 14235 identity = sk_c8 | inverse(sk_c9) = sk_c2. [para(14226(a,1),1181(a,1,1))].
% 38.54/38.83 14274 identity = sk_c8 | sk_c2 = sk_c1. [para(14235(b,1),12156(b,1)),merge(b)].
% 38.54/38.83 14287 sk_c2 = sk_c1 | sk_c7 = sk_c8. [para(14274(a,1),2602(a,1)),flip(b),merge(c)].
% 38.54/38.83 14353 sk_c2 = sk_c1 | multiply(inverse(sk_c9),sk_c8) = sk_c9. [para(14287(b,1),3286(b,1,2)),merge(b)].
% 38.54/38.83 14891 multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | sk_c9 != B | identity != B | multiply(B,sk_c8) != sk_c9. [para(1(a,1),1220(d,1)),rewrite([972(16)]),flip(d)].
% 38.54/38.83 14897 multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | sk_c9 != A | multiply(A,sk_c8) != sk_c9. [factor(14891,c,e)].
% 38.54/38.83 14904 multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != identity | multiply(inverse(sk_c9),multiply(sk_c8,sk_c8)) != sk_c9. [resolve(14897,b,1180,a),rewrite([33(24)]),flip(b),flip(c),merge(c)].
% 38.54/38.83 16005 sk_c2 = sk_c1 | identity != sk_c9. [resolve(14353,b,8185,a)].
% 38.54/38.83 16009 sk_c2 = sk_c1. [resolve(16005,b,2019,a),merge(b)].
% 38.54/38.83 16063 inverse(sk_c6) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = multiply(sk_c9,sk_c1). [back_rewrite(11849),rewrite([16009(10)])].
% 38.54/38.83 16105 inverse(sk_c6) = sk_c9 | multiply(sk_c3,multiply(inverse(sk_c9),inverse(sk_c1))) = identity. [back_rewrite(10358),rewrite([16009(8)])].
% 38.54/38.83 16111 multiply(sk_c9,sk_c7) = sk_c8 | multiply(sk_c3,multiply(inverse(sk_c9),inverse(sk_c1))) = identity. [back_rewrite(10323),rewrite([16009(9)])].
% 38.54/38.83 16448 multiply(sk_c1,sk_c9) = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7. [back_rewrite(32),rewrite([16009(1)])].
% 38.54/38.83 16451 multiply(sk_c1,sk_c9) = sk_c3 | multiply(sk_c4,sk_c5) = sk_c9. [back_rewrite(29),rewrite([16009(1)])].
% 38.54/38.83 18109 sk_c7 = sk_c6 | identity = sk_c3 | sk_c6 = sk_c1. [para(12043(c,1),4032(b,1)),merge(c)].
% 38.54/38.83 21793 inverse(sk_c1) = sk_c9 | multiply(sk_c6,A) = A. [para(906(b,1),12119(b,1)),flip(c),merge(b)].
% 38.54/38.83 21802 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c6),A) = A. [para(21793(b,1),70(a,1,2))].
% 38.54/38.83 21843 inverse(sk_c1) = sk_c9 | inverse(sk_c6) = sk_c8. [para(21802(b,1),12150(b,1)),flip(c),merge(b)].
% 38.54/38.83 21863 inverse(sk_c1) = sk_c9 | multiply(sk_c8,sk_c6) = identity. [para(21843(b,1),2(a,1,1))].
% 38.54/38.83 21895 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c6) = sk_c5. [para(21863(b,1),73(b,1,2)),rewrite([945(11)]),flip(c),merge(b)].
% 38.54/38.83 22160 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c4) = inverse(sk_c7). [para(947(b,1),7542(b,1)),flip(c),merge(b)].
% 38.54/38.83 22162 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c4) = inverse(sk_c9). [para(947(b,1),12245(b,1)),flip(c),merge(b)].
% 38.54/38.83 22163 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c4) = inverse(sk_c8). [para(947(b,1),13223(b,1)),flip(c),merge(b)].
% 38.54/38.83 22190 inverse(sk_c1) = sk_c9 | multiply(A,inverse(sk_c7)) = A. [para(22160(b,1),947(b,1,2)),merge(b)].
% 38.54/38.83 22209 inverse(sk_c1) = sk_c9 | multiply(A,inverse(sk_c9)) = A. [para(22162(b,1),947(b,1,2)),merge(b)].
% 38.54/38.83 22225 inverse(sk_c1) = sk_c9 | inverse(sk_c8) = inverse(sk_c9). [para(22163(b,1),22162(b,1)),merge(b)].
% 38.54/38.83 22246 inverse(sk_c8) = inverse(sk_c9) | inverse(sk_c9) = sk_c1. [para(22225(a,1),1181(a,1,1))].
% 38.54/38.83 22253 inverse(sk_c9) = sk_c1 | multiply(inverse(sk_c9),sk_c8) = identity. [para(22246(a,1),2(a,1,1))].
% 38.54/38.83 22348 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c6) = inverse(sk_c7). [para(22190(b,1),906(b,1,2)),merge(b)].
% 38.54/38.83 22551 inverse(sk_c9) = sk_c1 | identity != sk_c9. [para(22253(b,1),8185(a,1)),merge(c)].
% 38.54/38.83 22628 inverse(sk_c1) = sk_c9 | inverse(sk_c7) = sk_c5. [para(22348(b,1),21895(b,1)),merge(b)].
% 38.54/38.83 22635 inverse(sk_c1) = sk_c9 | multiply(sk_c5,A) = A. [para(22628(b,1),7542(b,1,1)),merge(b)].
% 38.54/38.83 22797 inverse(sk_c1) = sk_c9 | multiply(sk_c4,A) = A. [para(22635(b,1),889(b,1)),merge(b)].
% 38.54/38.83 23065 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c4),A) = A. [para(22797(b,1),70(a,1,2))].
% 38.54/38.83 23740 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = inverse(sk_c9). [para(23065(b,1),22209(b,1)),flip(c),merge(b)].
% 38.54/38.83 24743 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c9) = sk_c8. [para(12119(b,1),1099(b,2)),merge(b)].
% 38.54/38.83 24746 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c4),sk_c8) = sk_c9. [para(24743(b,1),70(a,1,2))].
% 38.54/38.83 24771 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c9),sk_c8) = sk_c9. [para(23740(b,1),24746(b,1,1)),merge(b)].
% 38.54/38.83 25351 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(B,multiply(C,sk_c9)) != multiply(inverse(sk_c9),sk_c8) | multiply(inverse(C),inverse(B)) != sk_c9 | multiply(D,A) != sk_c9 | inverse(D) != A. [para(33(a,1),1311(c,2)),rewrite([10215(17)]),flip(c)].
% 38.54/38.83 25356 sk_c9 != A | multiply(inverse(A),sk_c8) != sk_c9 | multiply(A,multiply(B,sk_c9)) != multiply(inverse(sk_c9),sk_c8) | multiply(inverse(B),inverse(A)) != sk_c9 | inverse(A) != B. [factor(25351,d,e),rewrite([1181(2),1181(22)]),flip(a),flip(e)].
% 38.54/38.83 26303 inverse(sk_c6) = sk_c9 | identity = sk_c9 | sk_c3 = sk_c9. [para(3496(b,1),1704(b,1)),flip(c)].
% 38.54/38.83 26304 inverse(sk_c6) = sk_c9 | identity = sk_c7 | sk_c3 = sk_c9. [para(3496(b,1),1901(b,1)),flip(c)].
% 38.54/38.83 26334 identity = sk_c9 | sk_c3 = sk_c9 | inverse(sk_c9) = sk_c6. [para(26303(a,1),1181(a,1,1))].
% 38.54/38.83 26337 identity = sk_c7 | sk_c3 = sk_c9 | inverse(sk_c9) = sk_c6. [para(26304(a,1),1181(a,1,1))].
% 38.54/38.83 26486 identity = sk_c9 | sk_c3 = sk_c9 | sk_c6 = sk_c1. [para(26334(c,1),1702(b,1)),merge(c)].
% 38.54/38.83 26490 sk_c3 = sk_c9 | sk_c6 = sk_c1 | inverse(sk_c9) = sk_c1. [resolve(26486,a,22551,b)].
% 38.54/38.83 26494 sk_c3 = sk_c9 | sk_c6 = sk_c1 | inverse(sk_c9) = identity. [para(26486(a,1),972(a,1,1))].
% 38.54/38.83 26495 sk_c3 = sk_c9 | sk_c6 = sk_c1 | sk_c7 = sk_c6. [para(26486(a,1),18109(b,1)),flip(d),merge(d),merge(e)].
% 38.54/38.83 26590 identity = sk_c7 | sk_c3 = sk_c9 | sk_c6 = sk_c1. [para(26337(c,1),1899(b,1)),merge(c)].
% 38.54/38.83 26596 sk_c3 = sk_c9 | sk_c6 = sk_c1 | identity = sk_c6. [para(26495(c,1),26590(a,2)),merge(d),merge(e)].
% 38.54/38.83 26772 sk_c3 = sk_c9 | sk_c6 = sk_c1 | identity = sk_c1. [para(26494(c,1),26490(c,1)),merge(c),merge(d)].
% 38.54/38.83 26782 sk_c3 = sk_c9 | sk_c6 = sk_c1. [para(26772(c,1),26596(c,1)),flip(e),merge(c),merge(d),merge(e)].
% 38.54/38.83 26783 sk_c3 = sk_c9 | inverse(sk_c1) = sk_c9. [para(26782(b,1),4(b,1,1)),merge(c)].
% 38.54/38.83 26788 sk_c3 = sk_c9 | multiply(sk_c1,multiply(sk_c9,A)) = A. [para(26783(b,1),1180(a,1,2,1))].
% 38.54/38.83 26908 sk_c3 = sk_c9 | inverse(sk_c4) = sk_c5. [para(26788(b,1),3001(b,1)),merge(c)].
% 38.54/38.83 26920 sk_c3 = sk_c9 | multiply(sk_c4,sk_c5) = identity. [para(26908(b,1),1145(a,1,2))].
% 38.54/38.83 26957 sk_c3 = sk_c9 | multiply(sk_c1,sk_c8) = sk_c9 | identity = sk_c9. [para(26920(b,1),21(b,1))].
% 38.54/38.83 27179 inverse(sk_c5) = sk_c4 | identity = sk_c3. [para(3572(c,1),1181(a,1,1)),merge(c)].
% 38.54/38.83 27190 identity = sk_c3 | multiply(sk_c4,sk_c5) = identity. [para(27179(a,1),2(a,1,1))].
% 38.54/38.83 27197 identity = sk_c3 | multiply(A,multiply(sk_c4,sk_c5)) = A. [para(27190(b,1),33(a,2,2)),rewrite([33(7),945(9)])].
% 38.54/38.83 27210 sk_c9 != A | multiply(inverse(A),sk_c8) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != A | multiply(sk_c9,inverse(A)) != sk_c9 | inverse(sk_c9) != inverse(A). [para(2(a,1),25356(c,1,2)),rewrite([945(9),1181(15)]),flip(c),flip(e)].
% 38.54/38.83 27235 multiply(inverse(sk_c9),sk_c8) != sk_c9 | inverse(sk_c1) = sk_c9. [resolve(27210,d,22209,b),xx(a),xx(d),merge(b)].
% 38.54/38.83 27236 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(A) != multiply(inverse(sk_c9),sk_c8) | multiply(sk_c9,A) != sk_c9 | inverse(sk_c9) != A. [para(1181(a,1),27210(b,1,1)),rewrite([1181(16),1181(21)]),flip(a),flip(c)].
% 38.54/38.83 27270 inverse(sk_c1) = sk_c9. [resolve(27235,a,24771,b),merge(b)].
% 38.54/38.83 27310 multiply(sk_c9,sk_c7) = sk_c8 | identity = sk_c3. [back_rewrite(16111),rewrite([27270(10),2(10),945(8)]),flip(b)].
% 38.54/38.83 27312 inverse(sk_c6) = sk_c9 | identity = sk_c3. [back_rewrite(16105),rewrite([27270(9),2(9),945(7)]),flip(b)].
% 38.54/38.83 27412 multiply(sk_c9,sk_c1) = identity. [para(27270(a,1),2(a,1,1))].
% 38.54/38.83 27414 inverse(sk_c9) = sk_c1. [para(27270(a,1),1181(a,1,1))].
% 38.54/38.83 27415 multiply(sk_c1,sk_c9) = identity. [para(27270(a,1),1145(a,1,2))].
% 38.54/38.83 27416 multiply(sk_c1,multiply(sk_c9,A)) = A. [para(27270(a,1),1180(a,1,2,1))].
% 38.54/38.83 28917 multiply(sk_c1,sk_c8) != sk_c9 | identity != sk_c9. [para(27270(a,1),27236(c,1)),rewrite([27270(2),27414(11),27412(16),27414(18)]),flip(c),xx(a),xx(e),merge(b)].
% 38.54/38.83 28919 inverse(sk_c6) = sk_c9 | multiply(sk_c8,sk_c1) = identity. [back_rewrite(16063),rewrite([27414(7),27412(10)])].
% 38.54/38.83 30512 multiply(sk_c1,sk_c8) != sk_c9 | multiply(sk_c1,sk_c8) != identity | multiply(sk_c1,multiply(sk_c8,sk_c8)) != sk_c9. [back_rewrite(14904),rewrite([27414(2),27414(7),27414(12)])].
% 38.54/38.83 30777 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c7,multiply(sk_c1,inverse(sk_c6))) = identity. [back_rewrite(10340),rewrite([27414(8)])].
% 38.54/38.83 31237 identity = sk_c3 | multiply(sk_c4,sk_c5) = sk_c9. [back_rewrite(16451),rewrite([27415(3)])].
% 38.54/38.83 31238 identity = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7. [back_rewrite(16448),rewrite([27415(3)])].
% 38.54/38.83 31886 identity != sk_c9 | inverse(sk_c6) = sk_c9. [resolve(28917,a,12,a)].
% 38.54/38.83 32199 identity = sk_c3 | multiply(sk_c6,sk_c9) = identity. [para(27312(a,1),1145(a,1,2))].
% 38.54/38.83 37575 identity = sk_c3 | multiply(A,sk_c9) = A. [para(31237(b,1),27197(b,1,2)),merge(b)].
% 38.54/38.83 38022 identity = sk_c3 | identity = sk_c7. [para(32199(b,1),31238(b,1)),merge(b)].
% 38.54/38.83 38040 identity = sk_c3 | multiply(A,sk_c7) = A. [para(38022(b,1),945(a,1,2))].
% 38.54/38.83 39122 identity = sk_c3 | identity = sk_c6. [para(37575(b,1),32199(b,1)),flip(c),merge(b)].
% 38.54/38.83 39334 identity = sk_c3 | multiply(sk_c6,A) = A. [para(39122(b,1),1(a,1,1))].
% 38.54/38.83 40525 identity = sk_c3 | sk_c8 = sk_c9. [para(38040(b,1),27310(a,1)),flip(b),merge(c)].
% 38.54/38.83 40529 sk_c8 = sk_c9 | multiply(A,sk_c3) = A. [para(40525(a,1),945(a,1,2))].
% 38.54/38.83 40978 identity = sk_c3 | inverse(sk_c6) != sk_c9 | sk_c8 != sk_c9 | multiply(inverse(sk_c8),inverse(sk_c6)) != identity. [para(39334(b,1),10479(b,1)),merge(d)].
% 38.54/38.83 42311 inverse(sk_c6) = sk_c9 | identity = sk_c1. [para(28919(b,1),81(b,1,2)),rewrite([945(11),27412(12)]),flip(c),merge(b)].
% 38.54/38.83 42332 identity = sk_c1 | sk_c6 = sk_c1. [para(42311(a,1),1181(a,1,1)),rewrite([27414(5)]),flip(b)].
% 38.54/38.83 42375 sk_c6 = sk_c1 | identity = sk_c9. [para(42332(a,1),972(a,1,1)),rewrite([27270(5)]),flip(b)].
% 38.54/38.83 42501 sk_c6 = sk_c1 | inverse(sk_c6) = sk_c9. [resolve(42375,b,31886,a)].
% 38.54/38.83 42679 sk_c6 = sk_c1. [para(42501(b,1),1181(a,1,1)),rewrite([27414(5)]),flip(b),merge(b)].
% 38.54/38.83 42861 identity = sk_c3 | sk_c8 != sk_c9 | multiply(inverse(sk_c8),sk_c9) != identity. [back_rewrite(40978),rewrite([42679(4),27270(5),42679(12),27270(13)]),xx(b)].
% 38.54/38.83 43305 multiply(sk_c1,sk_c8) = sk_c9 | identity = sk_c7. [back_rewrite(30777),rewrite([42679(8),27270(9),27415(9),945(8)]),flip(b)].
% 38.54/38.83 43329 multiply(sk_c9,sk_c3) = sk_c8 | sk_c8 = sk_c9. [back_rewrite(8662),rewrite([42679(7),27415(9),945(8)]),flip(b)].
% 38.54/38.83 44810 identity = sk_c7 | sk_c8 != sk_c9 | multiply(inverse(sk_c8),sk_c9) != identity. [resolve(43305,a,10479,b),rewrite([27270(5),27270(13)]),xx(b)].
% 38.54/38.83 44914 sk_c8 = sk_c9. [para(43329(a,1),40529(b,1)),merge(b),merge(c)].
% 38.54/38.83 44962 identity = sk_c7. [back_rewrite(44810),rewrite([44914(4),44914(7),27414(8),27415(9)]),xx(b),xx(c)].
% 38.54/38.83 45648 sk_c7 = sk_c3. [back_rewrite(42861),rewrite([44962(1),44914(4),44914(7),27414(8),27415(9),44962(7),44962(8)]),xx(b),xx(c)].
% 38.54/38.83 47224 sk_c3 != sk_c9. [back_rewrite(30512),rewrite([44914(2),27415(3),44962(1),45648(1),44914(5),27415(6),44962(4),45648(4),44962(5),45648(5),44914(8),44914(9),27416(11)]),xx(b),xx(c)].
% 38.54/38.83 47462 $F. [back_rewrite(26957),rewrite([44914(5),27415(6),44962(4),45648(4),44962(7),45648(7)]),merge(b),merge(c),unit_del(a,47224)].
% 38.54/38.83
% 38.54/38.83 % SZS output end Refutation
% 38.54/38.83 ============================== end of proof ==========================
% 38.54/38.83
% 38.54/38.83 ============================== STATISTICS ============================
% 38.54/38.83
% 38.54/38.83 Given=4712. Generated=2297352. Kept=47461. proofs=1.
% 38.54/38.83 Usable=1074. Sos=387. Demods=27. Limbo=2548, Disabled=43486. Hints=0.
% 38.54/38.83 Megabytes=34.74.
% 38.54/38.83 User_CPU=36.61, System_CPU=1.20, Wall_clock=38.
% 38.54/38.83
% 38.54/38.83 ============================== end of statistics =====================
% 38.54/38.83
% 38.54/38.83 ============================== end of search =========================
% 38.54/38.83
% 38.54/38.83 THEOREM PROVED
% 38.54/38.83 % SZS status Unsatisfiable
% 38.54/38.83
% 38.54/38.83 Exiting with 1 proof.
% 38.54/38.83
% 38.54/38.83 Process 18212 exit (max_proofs) Tue Jun 14 07:28:22 2022
% 38.54/38.83 Prover9 interrupted
%------------------------------------------------------------------------------