TSTP Solution File: GRP221-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP221-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 11:18:12 EDT 2022
% Result : Unsatisfiable 119.55s 119.84s
% Output : Refutation 119.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP221-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 01:15:10 EDT 2022
% 0.14/0.36 % CPUTime :
% 2.94/3.24 ============================== Prover9 ===============================
% 2.94/3.24 Prover9 (32) version 2009-11A, November 2009.
% 2.94/3.24 Process 32598 was started by sandbox on n003.cluster.edu,
% 2.94/3.24 Tue Jun 14 01:15:10 2022
% 2.94/3.24 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32424_n003.cluster.edu".
% 2.94/3.24 ============================== end of head ===========================
% 2.94/3.24
% 2.94/3.24 ============================== INPUT =================================
% 2.94/3.24
% 2.94/3.24 % Reading from file /tmp/Prover9_32424_n003.cluster.edu
% 2.94/3.24
% 2.94/3.24 set(prolog_style_variables).
% 2.94/3.24 set(auto2).
% 2.94/3.24 % set(auto2) -> set(auto).
% 2.94/3.24 % set(auto) -> set(auto_inference).
% 2.94/3.24 % set(auto) -> set(auto_setup).
% 2.94/3.24 % set(auto_setup) -> set(predicate_elim).
% 2.94/3.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.94/3.24 % set(auto) -> set(auto_limits).
% 2.94/3.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.94/3.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.94/3.24 % set(auto) -> set(auto_denials).
% 2.94/3.24 % set(auto) -> set(auto_process).
% 2.94/3.24 % set(auto2) -> assign(new_constants, 1).
% 2.94/3.24 % set(auto2) -> assign(fold_denial_max, 3).
% 2.94/3.24 % set(auto2) -> assign(max_weight, "200.000").
% 2.94/3.24 % set(auto2) -> assign(max_hours, 1).
% 2.94/3.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.94/3.24 % set(auto2) -> assign(max_seconds, 0).
% 2.94/3.24 % set(auto2) -> assign(max_minutes, 5).
% 2.94/3.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.94/3.24 % set(auto2) -> set(sort_initial_sos).
% 2.94/3.24 % set(auto2) -> assign(sos_limit, -1).
% 2.94/3.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.94/3.24 % set(auto2) -> assign(max_megs, 400).
% 2.94/3.24 % set(auto2) -> assign(stats, some).
% 2.94/3.24 % set(auto2) -> clear(echo_input).
% 2.94/3.24 % set(auto2) -> set(quiet).
% 2.94/3.24 % set(auto2) -> clear(print_initial_clauses).
% 2.94/3.24 % set(auto2) -> clear(print_given).
% 2.94/3.24 assign(lrs_ticks,-1).
% 2.94/3.24 assign(sos_limit,10000).
% 2.94/3.24 assign(order,kbo).
% 2.94/3.24 set(lex_order_vars).
% 2.94/3.24 clear(print_given).
% 2.94/3.24
% 2.94/3.24 % formulas(sos). % not echoed (52 formulas)
% 2.94/3.24
% 2.94/3.24 ============================== end of input ==========================
% 2.94/3.24
% 2.94/3.24 % From the command line: assign(max_seconds, 300).
% 2.94/3.24
% 2.94/3.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.94/3.24
% 2.94/3.24 % Formulas that are not ordinary clauses:
% 2.94/3.24
% 2.94/3.24 ============================== end of process non-clausal formulas ===
% 2.94/3.24
% 2.94/3.24 ============================== PROCESS INITIAL CLAUSES ===============
% 2.94/3.24
% 2.94/3.24 ============================== PREDICATE ELIMINATION =================
% 2.94/3.24
% 2.94/3.24 ============================== end predicate elimination =============
% 2.94/3.24
% 2.94/3.24 Auto_denials: (non-Horn, no changes).
% 2.94/3.24
% 2.94/3.24 Term ordering decisions:
% 2.94/3.24
% 2.94/3.24 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 2.94/3.24 Function symbol KB weights: sk_c10=1. sk_c9=1. sk_c3=1. sk_c6=1. sk_c7=1. sk_c8=1. sk_c1=1. sk_c2=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 2.94/3.24
% 2.94/3.24 ============================== end of process initial clauses ========
% 2.94/3.24
% 2.94/3.24 ============================== CLAUSES FOR SEARCH ====================
% 2.94/3.24
% 2.94/3.24 ============================== end of clauses for search =============
% 2.94/3.24
% 2.94/3.24 ============================== SEARCH ================================
% 2.94/3.24
% 2.94/3.24 % Starting search at 0.06 seconds.
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=43.000, iters=3367
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=42.000, iters=3430
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=39.000, iters=3385
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=38.000, iters=3407
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=37.000, iters=3628
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=35.000, iters=3397
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=34.000, iters=3460
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=33.000, iters=3411
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=32.000, iters=3380
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=31.000, iters=3337
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=30.000, iters=3334
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=29.000, iters=3348
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=28.000, iters=3355
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=27.000, iters=3351
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=26.000, iters=3353
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=25.000, iters=3334
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=24.000, iters=3377
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=23.000, iters=3439
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=22.000, iters=3397
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=21.000, iters=3337
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=20.000, iters=3351
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=19.000, iters=3340
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=17.000, iters=3343
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=16.000, iters=3344
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=15.000, iters=3337
% 2.94/3.24
% 2.94/3.24 Low Water (keep): wt=14.000, iters=3344
% 119.55/119.84
% 119.55/119.84 Low Water (keep): wt=13.000, iters=3398
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4012, wt=49.000
% 119.55/119.84
% 119.55/119.84 Low Water (keep): wt=12.000, iters=3412
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4013, wt=47.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4018, wt=46.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4014, wt=45.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4033, wt=44.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4015, wt=43.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4019, wt=42.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4035, wt=41.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=4182, wt=40.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=16380, wt=11.000
% 119.55/119.84
% 119.55/119.84 Low Water (displace): id=27794, wt=10.000
% 119.55/119.84
% 119.55/119.84 Low Water (keep): wt=11.000, iters=3336
% 119.55/119.84
% 119.55/119.84 ============================== PROOF =================================
% 119.55/119.84 % SZS status Unsatisfiable
% 119.55/119.84 % SZS output start Refutation
% 119.55/119.84
% 119.55/119.84 % Proof 1 at 115.28 (+ 3.52) seconds.
% 119.55/119.84 % Length of proof is 215.
% 119.55/119.84 % Level of proof is 35.
% 119.55/119.84 % Maximum clause weight is 64.000.
% 119.55/119.84 % Given clauses 9307.
% 119.55/119.84
% 119.55/119.84 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 119.55/119.84 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 119.55/119.84 6 inverse(sk_c2) = sk_c3 | inverse(sk_c10) = sk_c9 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 119.55/119.84 7 inverse(sk_c2) = sk_c3 | inverse(sk_c6) = sk_c10 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 119.55/119.84 8 inverse(sk_c2) = sk_c3 | inverse(sk_c7) = sk_c10 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 119.55/119.84 9 inverse(sk_c4) = sk_c10 | inverse(sk_c10) = sk_c9 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 119.55/119.84 10 inverse(sk_c4) = sk_c10 | inverse(sk_c6) = sk_c10 # label(prove_this_44) # label(negated_conjecture). [assumption].
% 119.55/119.84 11 inverse(sk_c4) = sk_c10 | inverse(sk_c7) = sk_c10 # label(prove_this_48) # label(negated_conjecture). [assumption].
% 119.55/119.84 12 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c9) = sk_c10 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 119.55/119.84 13 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c8) = sk_c9 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 119.55/119.84 15 multiply(sk_c1,sk_c9) = sk_c10 | inverse(sk_c10) = sk_c9 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 119.55/119.84 18 multiply(sk_c2,sk_c3) = sk_c9 | inverse(sk_c10) = sk_c9 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 119.55/119.84 19 multiply(sk_c2,sk_c3) = sk_c9 | inverse(sk_c6) = sk_c10 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 119.55/119.84 20 multiply(sk_c2,sk_c3) = sk_c9 | inverse(sk_c7) = sk_c10 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 119.55/119.84 22 inverse(sk_c2) = sk_c3 | multiply(sk_c10,sk_c8) = sk_c9 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 119.55/119.84 23 inverse(sk_c2) = sk_c3 | multiply(sk_c7,sk_c10) = sk_c8 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 119.55/119.84 27 multiply(sk_c10,sk_c5) = sk_c9 | inverse(sk_c10) = sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 119.55/119.84 30 multiply(sk_c4,sk_c10) = sk_c5 | inverse(sk_c10) = sk_c9 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 119.55/119.84 31 multiply(sk_c4,sk_c10) = sk_c5 | inverse(sk_c6) = sk_c10 # label(prove_this_38) # label(negated_conjecture). [assumption].
% 119.55/119.84 32 multiply(sk_c4,sk_c10) = sk_c5 | inverse(sk_c7) = sk_c10 # label(prove_this_42) # label(negated_conjecture). [assumption].
% 119.55/119.84 35 inverse(sk_c4) = sk_c10 | multiply(sk_c7,sk_c10) = sk_c8 # label(prove_this_47) # label(negated_conjecture). [assumption].
% 119.55/119.84 36 multiply(sk_c1,sk_c9) = sk_c10 | multiply(sk_c6,sk_c9) = sk_c10 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 119.55/119.84 40 multiply(sk_c2,sk_c3) = sk_c9 | multiply(sk_c10,sk_c8) = sk_c9 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 119.55/119.84 41 multiply(sk_c2,sk_c3) = sk_c9 | multiply(sk_c7,sk_c10) = sk_c8 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 119.55/119.84 47 multiply(sk_c10,sk_c5) = sk_c9 | multiply(sk_c7,sk_c10) = sk_c8 # label(prove_this_35) # label(negated_conjecture). [assumption].
% 119.55/119.84 50 multiply(sk_c4,sk_c10) = sk_c5 | multiply(sk_c7,sk_c10) = sk_c8 # label(prove_this_41) # label(negated_conjecture). [assumption].
% 119.55/119.84 51 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 119.55/119.84 52 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(sk_c10,D) != sk_c9 | multiply(E,sk_c10) != D | inverse(E) != sk_c10 | inverse(sk_c10) != sk_c9 | inverse(F) != sk_c10 | multiply(F,sk_c9) != sk_c10 | multiply(sk_c10,V6) != sk_c9 | multiply(V7,sk_c10) != V6 | inverse(V7) != sk_c10 # label(prove_this_49) # label(negated_conjecture). [assumption].
% 119.55/119.84 55 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(sk_c10,D) != sk_c9 | multiply(E,sk_c10) != D | inverse(E) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(sk_c10,F) != sk_c9 | multiply(V6,sk_c10) != F | inverse(V6) != sk_c10. [factor(52,a,j),merge(j)].
% 119.55/119.84 70 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(sk_c10,D) != sk_c9 | multiply(E,sk_c10) != D | inverse(E) != sk_c10 | inverse(sk_c10) != sk_c9. [factor(55,g,k),merge(j),merge(k)].
% 119.55/119.84 132 inverse(sk_c10) = sk_c9 | multiply(sk_c3,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 119.55/119.84 135 inverse(sk_c10) = sk_c9 | multiply(sk_c10,sk_c4) = identity. [para(9(a,1),2(a,1,1))].
% 119.55/119.84 138 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),51(a,1,1)),rewrite([1(2)]),flip(a)].
% 119.55/119.84 139 inverse(sk_c1) = sk_c10 | multiply(sk_c6,multiply(sk_c9,A)) = multiply(sk_c10,A). [para(12(b,1),51(a,1,1)),flip(b)].
% 119.55/119.84 142 inverse(sk_c1) = sk_c10 | multiply(A,multiply(sk_c10,sk_c8)) = multiply(A,sk_c9). [para(13(b,1),51(a,2,2)),rewrite([51(8)])].
% 119.55/119.84 145 inverse(sk_c10) = sk_c9 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c10,A). [para(15(a,1),51(a,1,1)),flip(b)].
% 119.55/119.84 146 inverse(sk_c10) = sk_c9 | multiply(A,multiply(sk_c1,sk_c9)) = multiply(A,sk_c10). [para(15(a,1),51(a,2,2)),rewrite([51(8)])].
% 119.55/119.84 152 inverse(sk_c10) = sk_c9 | multiply(A,multiply(sk_c2,sk_c3)) = multiply(A,sk_c9). [para(18(a,1),51(a,2,2)),rewrite([51(8)])].
% 119.55/119.84 162 inverse(sk_c2) = sk_c3 | multiply(A,multiply(sk_c7,sk_c10)) = multiply(A,sk_c8). [para(23(b,1),51(a,2,2)),rewrite([51(8)])].
% 119.55/119.84 176 inverse(sk_c10) = sk_c9 | multiply(A,multiply(sk_c4,sk_c10)) = multiply(A,sk_c5). [para(30(a,1),51(a,2,2)),rewrite([51(8)])].
% 119.55/119.84 195 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c2,multiply(sk_c3,A)) = multiply(sk_c9,A). [para(40(a,1),51(a,1,1)),flip(b)].
% 119.55/119.84 251 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(sk_c10,multiply(D,multiply(E,sk_c10))) != sk_c9 | inverse(multiply(D,E)) != sk_c10 | inverse(sk_c10) != sk_c9. [resolve(70,g,51,a)].
% 119.55/119.84 265 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(sk_c10,identity) != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9. [resolve(70,g,2,a)].
% 119.55/119.84 274 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,inverse(sk_c10)) != sk_c9 | inverse(sk_c10) != inverse(B) | identity != sk_c9 | multiply(sk_c10,C) != sk_c9 | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | inverse(sk_c10) != sk_c9. [para(2(a,1),70(e,1)),flip(d)].
% 119.55/119.84 600 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(sk_c10,inverse(sk_c10)) != sk_c9 | identity != sk_c9 | multiply(B,sk_c10) != inverse(sk_c10) | inverse(B) != sk_c10 | inverse(sk_c10) != sk_c9. [factor(274,c,f),xx(d)].
% 119.55/119.84 1506 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),138(a,1,2))].
% 119.55/119.84 1530 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c10),sk_c9) = sk_c5. [para(27(a,1),138(a,1,2))].
% 119.55/119.84 1560 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(138(a,1),138(a,1,2))].
% 119.55/119.84 1567 multiply(A,identity) = A. [back_rewrite(1506),rewrite([1560(4)])].
% 119.55/119.84 1587 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | sk_c9 != sk_c10 | inverse(inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9. [back_rewrite(265),rewrite([1567(19)]),flip(f)].
% 119.55/119.84 1595 inverse(identity) = identity. [para(1567(a,1),2(a,1))].
% 119.55/119.84 1684 inverse(sk_c10) = sk_c9 | inverse(sk_c3) = sk_c2. [para(132(b,1),138(a,1,2)),rewrite([1567(8)])].
% 119.55/119.84 1691 inverse(sk_c10) = sk_c9 | multiply(sk_c2,sk_c3) = identity. [para(1684(b,1),2(a,1,1))].
% 119.55/119.84 1704 inverse(sk_c10) = sk_c9 | inverse(sk_c10) = sk_c4. [para(135(b,1),138(a,1,2)),rewrite([1567(8)])].
% 119.55/119.84 1727 inverse(sk_c10) = sk_c9 | multiply(sk_c4,sk_c10) = identity. [para(1704(b,1),2(a,1,1))].
% 119.55/119.84 1918 multiply(A,inverse(A)) = identity. [para(1560(a,1),2(a,1))].
% 119.55/119.84 1981 multiply(A,multiply(inverse(A),B)) = B. [para(1560(a,1),138(a,1))].
% 119.55/119.84 1982 inverse(inverse(A)) = A. [para(1560(a,1),1567(a,1)),rewrite([1567(2)]),flip(a)].
% 119.55/119.84 1996 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | identity != sk_c9 | multiply(B,sk_c10) != inverse(sk_c10) | inverse(B) != sk_c10 | inverse(sk_c10) != sk_c9. [back_rewrite(600),rewrite([1918(11)]),merge(d)].
% 119.55/119.84 2011 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | sk_c9 != sk_c10 | inverse(sk_c10) != sk_c9. [back_rewrite(1587),rewrite([1982(22)]),xx(g)].
% 119.55/119.84 2084 inverse(sk_c6) = sk_c10 | multiply(sk_c2,sk_c3) = identity. [para(7(a,1),1918(a,1,2))].
% 119.55/119.84 2085 inverse(sk_c7) = sk_c10 | multiply(sk_c2,sk_c3) = identity. [para(8(a,1),1918(a,1,2))].
% 119.55/119.84 2086 inverse(sk_c6) = sk_c10 | multiply(sk_c4,sk_c10) = identity. [para(10(a,1),1918(a,1,2))].
% 119.55/119.84 2087 inverse(sk_c7) = sk_c10 | multiply(sk_c4,sk_c10) = identity. [para(11(a,1),1918(a,1,2))].
% 119.55/119.84 2088 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1918(a,1),51(a,1)),flip(a)].
% 119.55/119.84 2328 inverse(sk_c1) = sk_c10 | multiply(sk_c6,multiply(sk_c9,multiply(sk_c10,sk_c8))) = multiply(sk_c10,sk_c9). [para(142(b,1),139(b,2)),merge(b)].
% 119.55/119.84 2549 inverse(sk_c10) = sk_c9 | multiply(sk_c10,inverse(sk_c9)) = sk_c1. [para(1918(a,1),145(b,1,2)),rewrite([1567(7)]),flip(b)].
% 119.55/119.84 2576 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(2(a,1),1996(d,1)),rewrite([1982(17)]),flip(d),xx(e)].
% 119.55/119.84 2631 inverse(sk_c6) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9 | inverse(sk_c1) = sk_c10. [resolve(2576,b,12,b)].
% 119.55/119.84 2632 inverse(multiply(A,B)) != sk_c10 | multiply(A,multiply(B,sk_c9)) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(51(a,1),2576(b,1))].
% 119.55/119.84 2698 inverse(multiply(A,multiply(B,C))) != sk_c10 | multiply(A,multiply(B,multiply(C,sk_c9))) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(51(a,1),2632(b,1,2))].
% 119.55/119.84 2734 inverse(sk_c10) = sk_c9 | identity = sk_c9. [para(1691(b,1),18(a,1)),merge(c)].
% 119.55/119.84 2973 inverse(sk_c10) = sk_c9 | identity = sk_c5. [para(1727(b,1),30(a,1)),merge(c)].
% 119.55/119.84 3300 inverse(sk_c6) = sk_c10 | identity = sk_c9. [para(2084(b,1),19(a,1)),merge(c)].
% 119.55/119.84 3304 identity = sk_c9 | inverse(sk_c10) = sk_c6. [para(3300(a,1),1982(a,1,1))].
% 119.55/119.84 3468 identity = sk_c9 | sk_c6 = sk_c9. [para(3304(b,1),2734(a,1)),merge(c)].
% 119.55/119.84 3478 sk_c6 = sk_c9 | inverse(sk_c9) = identity. [para(3468(a,1),1595(a,1,1))].
% 119.55/119.84 3510 sk_c6 = sk_c9 | inverse(sk_c9) = sk_c9. [para(3468(a,1),3478(b,2)),merge(b)].
% 119.55/119.84 3511 sk_c6 = sk_c9 | multiply(sk_c9,sk_c9) = identity. [para(3510(b,1),2(a,1,1))].
% 119.55/119.84 3524 inverse(sk_c10) = sk_c9 | multiply(A,sk_c9) = A. [para(1691(b,1),152(b,1,2)),rewrite([1567(10)]),flip(c),merge(b)].
% 119.55/119.84 3985 inverse(sk_c7) = sk_c10 | identity = sk_c9. [para(2085(b,1),20(a,1)),merge(c)].
% 119.55/119.84 3989 identity = sk_c9 | inverse(sk_c10) = sk_c7. [para(3985(a,1),1982(a,1,1))].
% 119.55/119.84 4003 identity = sk_c9 | sk_c7 = sk_c6. [para(3989(b,1),3304(b,1)),merge(b)].
% 119.55/119.84 4135 sk_c7 = sk_c6 | inverse(sk_c9) = identity. [para(4003(a,1),1595(a,1,1))].
% 119.55/119.84 4175 sk_c7 = sk_c6 | inverse(sk_c9) = sk_c9. [para(4003(a,1),4135(b,2)),merge(b)].
% 119.55/119.84 4306 sk_c7 = sk_c6 | multiply(sk_c9,sk_c9) = identity. [para(4175(b,1),2(a,1,1))].
% 119.55/119.84 5098 inverse(sk_c6) = sk_c10 | identity = sk_c5. [para(2086(b,1),31(a,1)),merge(c)].
% 119.55/119.84 5113 identity = sk_c5 | inverse(sk_c10) = sk_c6. [para(5098(a,1),1982(a,1,1))].
% 119.55/119.84 5327 identity = sk_c5 | sk_c6 = sk_c9. [para(5113(b,1),2973(a,1)),merge(c)].
% 119.55/119.84 5371 sk_c6 = sk_c9 | sk_c5 = sk_c9. [para(5327(a,1),3468(a,1)),merge(c)].
% 119.55/119.84 5804 inverse(multiply(A,multiply(inverse(multiply(B,sk_c9)),B))) != sk_c10 | sk_c10 != A | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(2(a,1),2698(b,1,2)),rewrite([1567(10)]),flip(b)].
% 119.55/119.84 5852 inverse(multiply(A,multiply(B,multiply(inverse(multiply(C,sk_c9)),C)))) != sk_c10 | multiply(A,B) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(51(a,1),5804(a,1,1)),flip(b)].
% 119.55/119.84 5924 inverse(sk_c2) = sk_c3 | multiply(sk_c10,multiply(sk_c7,sk_c10)) = sk_c9. [para(22(b,1),162(b,2)),merge(b)].
% 119.55/119.84 6004 inverse(sk_c7) = sk_c10 | identity = sk_c5. [para(2087(b,1),32(a,1)),merge(c)].
% 119.55/119.84 6020 identity = sk_c5 | inverse(sk_c10) = sk_c7. [para(6004(a,1),1982(a,1,1))].
% 119.55/119.84 6054 identity = sk_c5 | sk_c7 = sk_c6. [para(6020(b,1),5113(b,1)),merge(b)].
% 119.55/119.84 6217 sk_c7 = sk_c6 | sk_c5 = sk_c9. [para(6054(a,1),4003(a,1)),merge(c)].
% 119.55/119.84 7376 inverse(multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(D,sk_c9)),D))))) != sk_c10 | multiply(A,multiply(B,C)) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(51(a,1),5852(a,1,1,2))].
% 119.55/119.84 7611 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = identity. [para(3524(b,1),2(a,1))].
% 119.55/119.84 7757 inverse(sk_c10) = sk_c9 | multiply(sk_c9,A) = A. [para(7611(b,1),138(a,1,1)),rewrite([1(8)])].
% 119.55/119.84 7834 inverse(sk_c10) = sk_c9 | multiply(A,sk_c5) = A. [para(1727(b,1),176(b,1,2)),rewrite([1567(10)]),flip(c),merge(b)].
% 119.55/119.84 7876 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | sk_c9 != B | multiply(C,B) != C | multiply(C,multiply(B,sk_c10)) != sk_c9 | sk_c9 != sk_c10 | inverse(sk_c10) != sk_c9. [para(138(a,1),2011(c,1)),rewrite([1982(11),51(14)]),flip(c),flip(d)].
% 119.55/119.84 9319 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c9),A) = A. [para(7757(b,1),138(a,1,2))].
% 119.55/119.84 9633 inverse(sk_c10) = sk_c9 | inverse(sk_c5) = identity. [para(7834(b,1),2(a,1))].
% 119.55/119.84 9793 inverse(sk_c10) = sk_c9 | multiply(sk_c5,A) = A. [para(9633(b,1),138(a,1,1)),rewrite([1(8)])].
% 119.55/119.84 10363 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c5),A) = A. [para(9793(b,1),138(a,1,2))].
% 119.55/119.84 11462 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(B,inverse(sk_c10)) != B | sk_c9 != B | sk_c9 != sk_c10. [para(2(a,1),7876(e,1,2)),rewrite([1567(17)]),flip(c),flip(e),merge(g)].
% 119.55/119.84 11467 inverse(multiply(A,B)) != sk_c10 | multiply(A,multiply(B,sk_c9)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(C,inverse(sk_c10)) != C | sk_c9 != C | sk_c9 != sk_c10. [para(51(a,1),11462(b,1))].
% 119.55/119.84 11469 inverse(multiply(A,inverse(sk_c9))) != sk_c10 | sk_c10 != A | inverse(sk_c10) != sk_c9 | multiply(B,inverse(sk_c10)) != B | sk_c9 != B | sk_c9 != sk_c10. [para(2(a,1),11467(b,1,2)),rewrite([1567(8)]),flip(b)].
% 119.55/119.84 11472 inverse(multiply(A,multiply(B,inverse(sk_c9)))) != sk_c10 | multiply(A,B) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(C,inverse(sk_c10)) != C | sk_c9 != C | sk_c9 != sk_c10. [para(51(a,1),11469(a,1,1)),flip(b)].
% 119.55/119.84 11509 inverse(multiply(A,multiply(B,multiply(C,inverse(sk_c9))))) != sk_c10 | multiply(A,multiply(B,C)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(D,inverse(sk_c10)) != D | sk_c9 != D | sk_c9 != sk_c10. [para(51(a,1),11472(a,1,1,2))].
% 119.55/119.84 11677 inverse(sk_c10) = sk_c9 | inverse(sk_c10) = sk_c5. [para(1530(b,1),3524(b,1)),flip(c),merge(b)].
% 119.55/119.84 11683 inverse(sk_c10) = sk_c9 | inverse(sk_c5) = sk_c10. [para(11677(b,1),1982(a,1,1))].
% 119.55/119.84 11685 sk_c6 = sk_c9 | inverse(sk_c10) = sk_c9. [para(5371(b,1),11677(b,2)),merge(c)].
% 119.55/119.84 11687 sk_c7 = sk_c6 | inverse(sk_c10) = sk_c9. [para(6217(b,1),11677(b,2)),merge(c)].
% 119.55/119.84 11737 sk_c6 = sk_c9 | inverse(sk_c9) = sk_c10. [para(11685(b,1),1982(a,1,1))].
% 119.55/119.84 11769 sk_c7 = sk_c6 | inverse(sk_c9) = sk_c10. [para(11687(b,1),1982(a,1,1))].
% 119.55/119.84 11842 sk_c6 = sk_c9 | identity = sk_c10. [para(11737(b,1),3478(b,1)),flip(c),merge(b)].
% 119.55/119.84 11863 sk_c6 = sk_c9 | multiply(sk_c9,sk_c9) = sk_c10. [para(11842(b,1),3511(b,2)),merge(b)].
% 119.55/119.84 12065 sk_c7 = sk_c6 | identity = sk_c10. [para(11769(b,1),4135(b,1)),flip(c),merge(b)].
% 119.55/119.84 12087 sk_c7 = sk_c6 | multiply(sk_c9,sk_c9) = sk_c10. [para(12065(b,1),4306(b,2)),merge(b)].
% 119.55/119.84 12819 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | multiply(D,sk_c10) != sk_c9 | inverse(multiply(inverse(sk_c10),D)) != sk_c10 | inverse(sk_c10) != sk_c9. [para(1981(a,1),251(f,1))].
% 119.55/119.84 12852 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c10) != sk_c9 | inverse(multiply(inverse(sk_c10),C)) != sk_c10 | inverse(sk_c10) != sk_c9. [factor(12819,e,f)].
% 119.55/119.84 15128 inverse(A) != sk_c10 | multiply(A,multiply(inverse(multiply(B,multiply(inverse(multiply(C,sk_c9)),C))),B)) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(2(a,1),7376(a,1,1,2)),rewrite([1567(2)])].
% 119.55/119.84 15130 inverse(multiply(sk_c10,multiply(inverse(multiply(A,sk_c9)),A))) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [resolve(15128,b,1981,a)].
% 119.55/119.84 15134 inverse(multiply(sk_c10,multiply(inverse(multiply(A,multiply(B,sk_c9))),multiply(A,B)))) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(51(a,1),15130(a,1,1,2,1,1))].
% 119.55/119.84 18496 inverse(A) != sk_c10 | multiply(A,multiply(inverse(multiply(B,inverse(sk_c9))),B)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(C,inverse(sk_c10)) != C | sk_c9 != C | sk_c9 != sk_c10. [para(2(a,1),11509(a,1,1,2)),rewrite([1567(2)])].
% 119.55/119.84 18499 inverse(multiply(sk_c10,inverse(sk_c9))) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(A,inverse(sk_c10)) != A | sk_c9 != A | sk_c9 != sk_c10. [resolve(18496,b,1981,a)].
% 119.55/119.84 18511 inverse(multiply(sk_c10,inverse(sk_c9))) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(A,multiply(B,inverse(sk_c10))) != multiply(A,B) | multiply(A,B) != sk_c9 | sk_c9 != sk_c10. [para(51(a,1),18499(c,1)),flip(d)].
% 119.55/119.84 18732 inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | sk_c9 != B | identity != B | multiply(B,sk_c10) != sk_c9 | inverse(multiply(inverse(sk_c10),B)) != sk_c10 | inverse(sk_c10) != sk_c9. [para(1(a,1),12852(c,1)),rewrite([1595(11)]),flip(c)].
% 119.55/119.84 18736 inverse(multiply(A,B)) != sk_c10 | multiply(A,multiply(B,sk_c9)) != sk_c10 | sk_c9 != C | identity != C | multiply(C,sk_c10) != sk_c9 | inverse(multiply(inverse(sk_c10),C)) != sk_c10 | inverse(sk_c10) != sk_c9. [para(51(a,1),18732(b,1))].
% 119.55/119.84 20196 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(2088(a,1),138(a,1,2)),rewrite([1567(3)]),flip(a)].
% 119.55/119.84 21264 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(20196(a,1),138(a,1,2)),flip(a)].
% 119.55/119.84 21610 multiply(sk_c9,inverse(sk_c10)) != sk_c10 | identity != sk_c9 | inverse(sk_c10) != identity | inverse(sk_c10) != sk_c9. [para(20196(a,1),15134(a,1,1,2,2)),rewrite([21264(3),51(6),1981(7),21264(5),1982(5),51(6),1918(5),1567(5),21264(5),1982(3)])].
% 119.55/119.84 21955 multiply(sk_c9,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(inverse(A),inverse(sk_c10)) != inverse(A) | inverse(A) != sk_c9 | sk_c9 != sk_c10. [para(20196(a,1),18511(c,2)),rewrite([21264(5),1982(3),21264(12),51(16),1981(17),21264(18),1981(20)])].
% 119.55/119.84 22716 multiply(inverse(A),inverse(B)) != sk_c10 | multiply(B,multiply(A,sk_c9)) != sk_c10 | sk_c9 != C | identity != C | multiply(C,sk_c10) != sk_c9 | multiply(inverse(C),sk_c10) != sk_c10 | inverse(sk_c10) != sk_c9. [back_rewrite(18736),rewrite([21264(2),21264(22),1982(22)])].
% 119.55/119.84 23698 multiply(sk_c9,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c9 | multiply(inverse(sk_c10),inverse(sk_c10)) != inverse(sk_c10) | sk_c9 != sk_c10. [factor(21955,b,d)].
% 119.55/119.84 30672 multiply(sk_c9,inverse(A)) != sk_c10 | sk_c10 != A | sk_c9 != B | identity != B | multiply(B,sk_c10) != sk_c9 | multiply(inverse(B),sk_c10) != sk_c10 | inverse(sk_c10) != sk_c9. [para(2(a,1),22716(b,1,2)),rewrite([1982(3),1567(7)]),flip(b)].
% 119.55/119.84 30674 multiply(sk_c9,A) != sk_c10 | inverse(A) != sk_c10 | sk_c9 != B | identity != B | multiply(B,sk_c10) != sk_c9 | multiply(inverse(B),sk_c10) != sk_c10 | inverse(sk_c10) != sk_c9. [para(1982(a,1),30672(a,1,2)),flip(b)].
% 119.55/119.84 30676 multiply(inverse(sk_c10),sk_c9) != sk_c10 | sk_c9 != A | identity != A | multiply(A,sk_c10) != sk_c9 | multiply(inverse(A),sk_c10) != sk_c10 | inverse(sk_c10) != sk_c9. [resolve(30674,a,1981,a),rewrite([21264(5),1982(5)])].
% 119.55/119.84 30957 inverse(sk_c10) = sk_c9 | multiply(sk_c10,A) = A. [para(11683(b,1),10363(b,1,1)),merge(b)].
% 119.55/119.84 30972 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = sk_c1. [para(30957(b,1),2549(b,1)),merge(b)].
% 119.55/119.84 30992 inverse(sk_c10) = sk_c9 | multiply(sk_c1,sk_c9) = identity. [para(30972(b,1),2(a,1,1))].
% 119.55/119.84 31024 inverse(sk_c10) = sk_c9 | multiply(A,sk_c10) = A. [para(30992(b,1),146(b,1,2)),rewrite([1567(10)]),flip(c),merge(b)].
% 119.55/119.84 31067 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = sk_c10. [para(31024(b,1),9319(b,1)),merge(b)].
% 119.55/119.84 31084 inverse(sk_c10) = sk_c9. [para(31067(b,1),1982(a,1,1)),merge(b)].
% 119.55/119.84 31243 multiply(sk_c9,sk_c9) != sk_c10 | sk_c9 != A | identity != A | multiply(A,sk_c10) != sk_c9 | multiply(inverse(A),sk_c10) != sk_c10. [back_rewrite(30676),rewrite([31084(2),31084(20)]),xx(f)].
% 119.55/119.84 33135 multiply(sk_c9,sk_c9) != sk_c10 | multiply(sk_c9,sk_c9) != sk_c9 | sk_c9 != sk_c10. [back_rewrite(23698),rewrite([31084(3),31084(7),31084(10),31084(11),31084(13)]),xx(b)].
% 119.55/119.84 33964 multiply(sk_c9,sk_c9) != sk_c10 | identity != sk_c9. [back_rewrite(21610),rewrite([31084(3),31084(10),31084(13)]),flip(c),xx(d),merge(c)].
% 119.55/119.84 34471 inverse(sk_c6) != sk_c10 | identity != sk_c9 | inverse(sk_c1) = sk_c10. [back_rewrite(2631),rewrite([31084(9),31084(12)]),flip(c),xx(d),merge(c)].
% 119.55/119.84 34667 multiply(sk_c9,sk_c10) = identity. [para(31084(a,1),2(a,1,1))].
% 119.55/119.84 34668 multiply(sk_c9,multiply(sk_c10,A)) = A. [para(31084(a,1),138(a,1,1))].
% 119.55/119.84 34669 inverse(sk_c9) = sk_c10. [para(31084(a,1),1982(a,1,1))].
% 119.55/119.84 34670 multiply(sk_c10,sk_c9) = identity. [para(31084(a,1),1918(a,1,2))].
% 119.55/119.84 34721 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c8) = identity. [back_rewrite(2328),rewrite([34668(10),34670(10)])].
% 119.55/119.84 34933 identity != sk_c9 | sk_c7 = sk_c6. [resolve(33964,a,12087,b)].
% 119.55/119.84 34935 identity != sk_c9 | sk_c6 = sk_c9. [resolve(33964,a,11863,b)].
% 119.55/119.84 35280 sk_c7 = sk_c6. [resolve(34933,a,4003,a),merge(b)].
% 119.55/119.84 35407 inverse(sk_c2) = sk_c3 | multiply(sk_c10,multiply(sk_c6,sk_c10)) = sk_c9. [back_rewrite(5924),rewrite([35280(6)])].
% 119.55/119.84 35468 multiply(sk_c4,sk_c10) = sk_c5 | multiply(sk_c6,sk_c10) = sk_c8. [back_rewrite(50),rewrite([35280(6)])].
% 119.55/119.84 35469 multiply(sk_c10,sk_c5) = sk_c9 | multiply(sk_c6,sk_c10) = sk_c8. [back_rewrite(47),rewrite([35280(6)])].
% 119.55/119.84 35471 multiply(sk_c2,sk_c3) = sk_c9 | multiply(sk_c6,sk_c10) = sk_c8. [back_rewrite(41),rewrite([35280(6)])].
% 119.55/119.84 35473 inverse(sk_c4) = sk_c10 | multiply(sk_c6,sk_c10) = sk_c8. [back_rewrite(35),rewrite([35280(5)])].
% 119.55/119.84 35474 inverse(sk_c2) = sk_c3 | multiply(sk_c6,sk_c10) = sk_c8. [back_rewrite(23),rewrite([35280(5)])].
% 119.55/119.84 35476 sk_c6 = sk_c9. [resolve(34935,a,3468,a),merge(b)].
% 119.55/119.84 35478 inverse(sk_c2) = sk_c3 | identity = sk_c8. [back_rewrite(35474),rewrite([35476(5),34667(7)])].
% 119.55/119.84 35479 inverse(sk_c4) = sk_c10 | identity = sk_c8. [back_rewrite(35473),rewrite([35476(5),34667(7)])].
% 119.55/119.84 35481 multiply(sk_c2,sk_c3) = sk_c9 | identity = sk_c8. [back_rewrite(35471),rewrite([35476(6),34667(8)])].
% 119.55/119.84 35483 multiply(sk_c10,sk_c5) = sk_c9 | identity = sk_c8. [back_rewrite(35469),rewrite([35476(6),34667(8)])].
% 119.55/119.84 35484 multiply(sk_c4,sk_c10) = sk_c5 | identity = sk_c8. [back_rewrite(35468),rewrite([35476(6),34667(8)])].
% 119.55/119.84 35529 inverse(sk_c2) = sk_c3 | sk_c9 = sk_c10. [back_rewrite(35407),rewrite([35476(6),34667(8),1567(7)]),flip(b)].
% 119.55/119.84 35593 inverse(sk_c1) = sk_c10 | multiply(sk_c9,sk_c8) = identity. [back_rewrite(34721),rewrite([35476(5)])].
% 119.55/119.84 35599 identity != sk_c9 | inverse(sk_c1) = sk_c10. [back_rewrite(34471),rewrite([35476(1),34669(2)]),xx(a)].
% 119.55/119.84 35682 multiply(sk_c1,sk_c9) = sk_c10 | multiply(sk_c9,sk_c9) = sk_c10. [back_rewrite(36),rewrite([35476(6)])].
% 119.55/119.84 35726 identity = sk_c8 | multiply(sk_c2,sk_c3) = identity. [para(35478(a,1),1918(a,1,2))].
% 119.55/119.84 35736 identity = sk_c8 | multiply(sk_c4,sk_c10) = identity. [para(35479(a,1),1918(a,1,2))].
% 119.55/119.84 35796 sk_c9 = sk_c10 | multiply(sk_c2,sk_c3) = identity. [para(35529(a,1),1918(a,1,2))].
% 119.55/119.84 36524 identity = sk_c8 | identity = sk_c9. [para(35726(b,1),35481(a,1)),merge(c)].
% 119.55/119.84 36526 identity = sk_c9 | multiply(sk_c8,A) = A. [para(36524(a,1),1(a,1,1))].
% 119.55/119.84 36527 identity = sk_c9 | multiply(A,sk_c8) = A. [para(36524(a,1),1567(a,1,2))].
% 119.55/119.84 36528 identity = sk_c9 | inverse(sk_c8) = identity. [para(36524(a,1),1595(a,1,1))].
% 119.55/119.84 36544 identity = sk_c9 | inverse(sk_c8) = sk_c8. [para(36524(a,1),36528(b,2)),merge(b)].
% 119.55/119.84 36545 identity = sk_c9 | multiply(sk_c8,sk_c8) = identity. [para(36544(b,1),2(a,1,1))].
% 119.55/119.84 36546 identity = sk_c9 | multiply(sk_c8,multiply(sk_c8,A)) = A. [para(36544(b,1),138(a,1,1))].
% 119.55/119.84 36644 identity = sk_c8 | identity = sk_c5. [para(35736(b,1),35484(a,1)),merge(c)].
% 119.55/119.84 36648 identity = sk_c8 | multiply(A,sk_c5) = A. [para(36644(b,1),1567(a,1,2))].
% 119.55/119.84 37603 identity = sk_c9 | multiply(A,multiply(sk_c8,B)) = multiply(A,B). [para(36526(b,1),51(a,2,2)),rewrite([51(6)])].
% 119.55/119.84 37657 identity = sk_c9 | multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c2,multiply(sk_c3,sk_c8)) = sk_c9. [para(36527(b,1),195(b,2))].
% 119.55/119.84 37687 identity = sk_c9 | multiply(A,multiply(sk_c8,sk_c8)) = A. [para(36545(b,1),51(a,2,2)),rewrite([51(7),1567(9)])].
% 119.55/119.84 37866 identity = sk_c8 | sk_c9 = sk_c10. [para(36648(b,1),35483(a,1)),flip(b),merge(c)].
% 119.55/119.84 37876 sk_c9 = sk_c10 | inverse(sk_c8) = identity. [para(37866(a,1),1595(a,1,1))].
% 119.55/119.84 37888 sk_c9 = sk_c10 | multiply(sk_c2,sk_c3) = sk_c8. [para(37866(a,1),35796(b,2)),merge(b)].
% 119.55/119.84 37902 sk_c9 = sk_c10 | inverse(sk_c8) = sk_c8. [para(37866(a,1),37876(b,2)),merge(b)].
% 119.55/119.84 37903 sk_c9 = sk_c10 | multiply(sk_c8,sk_c8) = identity. [para(37902(b,1),2(a,1,1))].
% 119.55/119.84 38506 sk_c9 = sk_c10 | multiply(A,multiply(sk_c8,sk_c8)) = A. [para(37903(b,1),51(a,2,2)),rewrite([51(7),1567(9)])].
% 119.55/119.84 39185 identity = sk_c9 | multiply(sk_c9,sk_c9) != sk_c10 | sk_c8 != sk_c9 | identity != sk_c8 | multiply(sk_c8,sk_c10) != sk_c9. [para(36528(b,1),31243(e,1,1)),rewrite([1(22)]),flip(c),xx(f)].
% 119.55/119.84 40537 inverse(sk_c1) = sk_c10 | identity = sk_c9. [para(35593(b,1),36527(b,1)),merge(c)].
% 119.55/119.84 40543 identity = sk_c9 | sk_c1 = sk_c9. [para(40537(a,1),1982(a,1,1)),rewrite([31084(5)]),flip(b)].
% 119.55/119.84 40618 sk_c1 = sk_c9 | inverse(sk_c1) = sk_c10. [resolve(40543,a,35599,a)].
% 119.55/119.84 40727 sk_c1 = sk_c9. [para(40618(b,1),1982(a,1,1)),rewrite([31084(5)]),flip(b),merge(b)].
% 119.55/119.84 40918 multiply(sk_c9,sk_c9) = sk_c10. [back_rewrite(35682),rewrite([40727(1)]),merge(b)].
% 119.55/119.84 41167 identity = sk_c9 | sk_c8 != sk_c9 | identity != sk_c8 | multiply(sk_c8,sk_c10) != sk_c9. [back_rewrite(39185),rewrite([40918(6)]),xx(b)].
% 119.55/119.84 41879 identity != sk_c9. [back_rewrite(33964),rewrite([40918(3)]),xx(a)].
% 119.55/119.84 42001 sk_c9 != sk_c10. [back_rewrite(33135),rewrite([40918(3),40918(6)]),flip(b),xx(a),merge(b)].
% 119.55/119.84 42075 sk_c8 != sk_c9 | identity != sk_c8 | multiply(sk_c8,sk_c10) != sk_c9. [back_unit_del(41167),unit_del(a,41879)].
% 119.55/119.84 42083 multiply(A,multiply(sk_c8,sk_c8)) = A. [back_unit_del(37687),unit_del(a,41879)].
% 119.55/119.84 42090 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c2,multiply(sk_c3,sk_c8)) = sk_c9. [back_unit_del(37657),unit_del(a,41879)].
% 119.55/119.84 42102 multiply(A,multiply(sk_c8,B)) = multiply(A,B). [back_unit_del(37603),unit_del(a,41879)].
% 119.55/119.84 42108 multiply(sk_c8,A) = A. [back_unit_del(36546),rewrite([42102(7)]),unit_del(a,41879)].
% 119.55/119.84 42109 identity = sk_c8. [back_unit_del(36545),rewrite([42108(6)]),flip(b),unit_del(a,41879)].
% 119.55/119.84 42144 multiply(A,sk_c8) = A. [back_unit_del(38506),rewrite([42108(6)]),unit_del(a,42001)].
% 119.55/119.84 42154 multiply(sk_c2,sk_c3) = sk_c8. [back_unit_del(37888),unit_del(a,42001)].
% 119.55/119.84 42161 sk_c8 = sk_c9. [back_rewrite(42090),rewrite([42144(3),42144(7),42154(6)]),flip(a),unit_del(a,42001)].
% 119.55/119.84 42162 multiply(A,sk_c10) = A. [back_rewrite(42083),rewrite([42161(1),42161(2),40918(3)])].
% 119.55/119.84 42166 $F. [back_rewrite(42075),rewrite([42161(1),42109(4),42161(4),42161(5),42161(7),42162(9)]),xx(a),xx(b),xx(c)].
% 119.55/119.84
% 119.55/119.84 % SZS output end Refutation
% 119.55/119.84 ============================== end of proof ==========================
% 119.55/119.84
% 119.55/119.84 ============================== STATISTICS ============================
% 119.55/119.84
% 119.55/119.84 Given=9307. Generated=6595434. Kept=42165. proofs=1.
% 119.55/119.84 Usable=110. Sos=790. Demods=42. Limbo=58, Disabled=41259. Hints=0.
% 119.55/119.84 Megabytes=32.76.
% 119.55/119.84 User_CPU=115.28, System_CPU=3.52, Wall_clock=119.
% 119.55/119.85
% 119.55/119.85 ============================== end of statistics =====================
% 119.55/119.85
% 119.55/119.85 ============================== end of search =========================
% 119.55/119.85
% 119.55/119.85 THEOREM PROVED
% 119.55/119.85 % SZS status Unsatisfiable
% 119.55/119.85
% 119.55/119.85 Exiting with 1 proof.
% 119.55/119.85
% 119.55/119.85 Process 32598 exit (max_proofs) Tue Jun 14 01:17:09 2022
% 119.55/119.85 Prover9 interrupted
%------------------------------------------------------------------------------