TSTP Solution File: GRP215-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP215-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 11:18:11 EDT 2022
% Result : Unsatisfiable 21.04s 21.36s
% Output : Refutation 21.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP215-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:32:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 21.04/21.36 ============================== Prover9 ===============================
% 21.04/21.36 Prover9 (32) version 2009-11A, November 2009.
% 21.04/21.36 Process 5434 was started by sandbox2 on n022.cluster.edu,
% 21.04/21.36 Mon Jun 13 10:32:04 2022
% 21.04/21.36 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5177_n022.cluster.edu".
% 21.04/21.36 ============================== end of head ===========================
% 21.04/21.36
% 21.04/21.36 ============================== INPUT =================================
% 21.04/21.36
% 21.04/21.36 % Reading from file /tmp/Prover9_5177_n022.cluster.edu
% 21.04/21.36
% 21.04/21.36 set(prolog_style_variables).
% 21.04/21.36 set(auto2).
% 21.04/21.36 % set(auto2) -> set(auto).
% 21.04/21.36 % set(auto) -> set(auto_inference).
% 21.04/21.36 % set(auto) -> set(auto_setup).
% 21.04/21.36 % set(auto_setup) -> set(predicate_elim).
% 21.04/21.36 % set(auto_setup) -> assign(eq_defs, unfold).
% 21.04/21.36 % set(auto) -> set(auto_limits).
% 21.04/21.36 % set(auto_limits) -> assign(max_weight, "100.000").
% 21.04/21.36 % set(auto_limits) -> assign(sos_limit, 20000).
% 21.04/21.36 % set(auto) -> set(auto_denials).
% 21.04/21.36 % set(auto) -> set(auto_process).
% 21.04/21.36 % set(auto2) -> assign(new_constants, 1).
% 21.04/21.36 % set(auto2) -> assign(fold_denial_max, 3).
% 21.04/21.36 % set(auto2) -> assign(max_weight, "200.000").
% 21.04/21.36 % set(auto2) -> assign(max_hours, 1).
% 21.04/21.36 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 21.04/21.36 % set(auto2) -> assign(max_seconds, 0).
% 21.04/21.36 % set(auto2) -> assign(max_minutes, 5).
% 21.04/21.36 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 21.04/21.36 % set(auto2) -> set(sort_initial_sos).
% 21.04/21.36 % set(auto2) -> assign(sos_limit, -1).
% 21.04/21.36 % set(auto2) -> assign(lrs_ticks, 3000).
% 21.04/21.36 % set(auto2) -> assign(max_megs, 400).
% 21.04/21.36 % set(auto2) -> assign(stats, some).
% 21.04/21.36 % set(auto2) -> clear(echo_input).
% 21.04/21.36 % set(auto2) -> set(quiet).
% 21.04/21.36 % set(auto2) -> clear(print_initial_clauses).
% 21.04/21.36 % set(auto2) -> clear(print_given).
% 21.04/21.36 assign(lrs_ticks,-1).
% 21.04/21.36 assign(sos_limit,10000).
% 21.04/21.36 assign(order,kbo).
% 21.04/21.36 set(lex_order_vars).
% 21.04/21.36 clear(print_given).
% 21.04/21.36
% 21.04/21.36 % formulas(sos). % not echoed (24 formulas)
% 21.04/21.36
% 21.04/21.36 ============================== end of input ==========================
% 21.04/21.36
% 21.04/21.36 % From the command line: assign(max_seconds, 300).
% 21.04/21.36
% 21.04/21.36 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 21.04/21.36
% 21.04/21.36 % Formulas that are not ordinary clauses:
% 21.04/21.36
% 21.04/21.36 ============================== end of process non-clausal formulas ===
% 21.04/21.36
% 21.04/21.36 ============================== PROCESS INITIAL CLAUSES ===============
% 21.04/21.36
% 21.04/21.36 ============================== PREDICATE ELIMINATION =================
% 21.04/21.36
% 21.04/21.36 ============================== end predicate elimination =============
% 21.04/21.36
% 21.04/21.36 Auto_denials: (non-Horn, no changes).
% 21.04/21.36
% 21.04/21.36 Term ordering decisions:
% 21.04/21.36
% 21.04/21.36 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 21.04/21.36 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 21.04/21.36
% 21.04/21.36 ============================== end of process initial clauses ========
% 21.04/21.36
% 21.04/21.36 ============================== CLAUSES FOR SEARCH ====================
% 21.04/21.36
% 21.04/21.36 ============================== end of clauses for search =============
% 21.04/21.36
% 21.04/21.36 ============================== SEARCH ================================
% 21.04/21.36
% 21.04/21.36 % Starting search at 0.02 seconds.
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=42.000, iters=3453
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=41.000, iters=3459
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=40.000, iters=3449
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=39.000, iters=3496
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=38.000, iters=3369
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=36.000, iters=3460
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=35.000, iters=3560
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=34.000, iters=3619
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=32.000, iters=3440
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=31.000, iters=3372
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=30.000, iters=3368
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=28.000, iters=3402
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=27.000, iters=3388
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=26.000, iters=3335
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=25.000, iters=3339
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=24.000, iters=3368
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=23.000, iters=3341
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=22.000, iters=3369
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=21.000, iters=3418
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=20.000, iters=3348
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=19.000, iters=3345
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=18.000, iters=3411
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=17.000, iters=3337
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=16.000, iters=3336
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=15.000, iters=3336
% 21.04/21.36
% 21.04/21.36 Low Water (keep): wt=14.000, iters=3389
% 21.04/21.36
% 21.04/21.36 ============================== PROOF =================================
% 21.04/21.36 % SZS status Unsatisfiable
% 21.04/21.36 % SZS output start Refutation
% 21.04/21.36
% 21.04/21.36 % Proof 1 at 19.76 (+ 0.60) seconds.
% 21.04/21.36 % Length of proof is 210.
% 21.04/21.36 % Level of proof is 46.
% 21.04/21.36 % Maximum clause weight is 41.000.
% 21.04/21.36 % Given clauses 3358.
% 21.04/21.36
% 21.04/21.36 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 21.04/21.36 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 21.04/21.36 3 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 21.04/21.36 4 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 21.04/21.36 5 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 21.04/21.36 6 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 21.04/21.36 7 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 21.04/21.36 8 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 21.04/21.36 9 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 21.04/21.36 10 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 21.04/21.36 11 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 21.04/21.36 12 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 21.04/21.36 13 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 21.04/21.36 15 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 21.04/21.36 16 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 21.04/21.36 17 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 21.04/21.36 18 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 21.04/21.36 19 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 21.04/21.36 21 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 21.04/21.36 22 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 21.04/21.36 23 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 21.04/21.36 24 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | multiply(sk_c7,D) != sk_c6 | multiply(E,sk_c7) != D | inverse(E) != sk_c7 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 21.04/21.36 48 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 21.04/21.36 49 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 21.04/21.36 50 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 21.04/21.36 52 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),23(a,1,1)),rewrite([1(2)]),flip(a)].
% 21.04/21.36 53 inverse(sk_c3) = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(7(a,1),23(a,1,1)),flip(b)].
% 21.04/21.36 57 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(9(b,1),23(a,1,1)),flip(b)].
% 21.04/21.36 62 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5). [para(11(b,1),23(a,2,2)),rewrite([23(8)])].
% 21.04/21.36 63 inverse(sk_c3) = sk_c7 | multiply(sk_c2,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(12(a,1),23(a,1,1)),flip(b)].
% 21.04/21.36 71 inverse(sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(16(b,1),23(a,1,1)),flip(b)].
% 21.04/21.36 72 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5). [para(16(b,1),23(a,2,2)),rewrite([23(8)])].
% 21.04/21.36 75 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(18(a,1),23(a,1,1)),flip(b)].
% 21.04/21.36 78 multiply(sk_c1,sk_c7) = sk_c6 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5). [para(19(b,1),23(a,2,2)),rewrite([23(9)])].
% 21.04/21.36 83 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(22(b,1),23(a,1,1)),flip(b)].
% 21.04/21.36 112 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | multiply(D,sk_c7) != C | inverse(D) != sk_c7. [para(1(a,1),24(a,1)),flip(a)].
% 21.04/21.36 116 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | multiply(D,sk_c7) != C | inverse(D) != sk_c7. [para(2(a,1),24(a,1))].
% 21.04/21.36 117 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | multiply(D,sk_c7) != C | inverse(D) != sk_c7. [para(2(a,1),24(c,1))].
% 21.04/21.36 258 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7. [factor(112,b,e),rewrite([1(17)]),merge(e)].
% 21.04/21.36 269 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | identity != C. [factor(116,b,i),rewrite([2(30)])].
% 21.04/21.36 274 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7. [factor(117,b,e)].
% 21.04/21.36 471 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B. [factor(258,b,g),rewrite([1(21)])].
% 21.04/21.36 482 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,B) != sk_c6 | identity != B. [factor(269,c,f)].
% 21.04/21.36 771 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c7,sk_c3)) = multiply(A,identity). [para(48(b,1),23(a,2,2)),rewrite([23(8)])].
% 21.04/21.36 795 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),52(a,1,2))].
% 21.04/21.36 808 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c4),sk_c5) = sk_c7. [para(16(b,1),52(a,1,2))].
% 21.04/21.36 813 multiply(sk_c7,sk_c5) = sk_c6 | multiply(inverse(sk_c2),sk_c7) = sk_c6. [para(21(a,1),52(a,1,2))].
% 21.04/21.36 816 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),identity) = sk_c3. [para(48(b,1),52(a,1,2))].
% 21.04/21.36 817 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(52(a,1),52(a,1,2))].
% 21.04/21.36 818 multiply(A,identity) = A. [back_rewrite(795),rewrite([817(4)])].
% 21.04/21.36 819 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c3. [back_rewrite(816),rewrite([818(8)])].
% 21.04/21.36 820 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c7,sk_c3)) = A. [back_rewrite(771),rewrite([818(10)])].
% 21.04/21.36 831 inverse(identity) = identity. [para(818(a,1),2(a,1))].
% 21.04/21.36 861 sk_c6 != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B. [back_rewrite(471),rewrite([831(5)])].
% 21.04/21.36 893 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c4. [para(49(b,1),52(a,1,2)),rewrite([818(8)])].
% 21.04/21.36 916 inverse(sk_c2) = sk_c6 | inverse(sk_c7) = sk_c3. [para(50(b,1),52(a,1,2)),rewrite([818(8)])].
% 21.04/21.36 952 sk_c6 != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | multiply(sk_c7,A) != sk_c6 | sk_c7 != A. [para(2(a,1),861(c,1)),merge(c)].
% 21.04/21.36 967 multiply(A,inverse(A)) = identity. [para(817(a,1),2(a,1))].
% 21.04/21.36 1020 multiply(A,multiply(inverse(A),B)) = B. [para(817(a,1),52(a,1))].
% 21.04/21.36 1021 inverse(inverse(A)) = A. [para(817(a,1),818(a,1)),rewrite([818(2)]),flip(a)].
% 21.04/21.36 1026 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,A) != sk_c6 | sk_c7 != A. [back_rewrite(952),rewrite([1021(9)]),xx(c)].
% 21.04/21.36 1054 identity != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,B) != sk_c6 | identity != B. [back_rewrite(482),rewrite([1021(6)]),xx(b)].
% 21.04/21.36 1062 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7. [back_rewrite(274),rewrite([1021(13)]),xx(d)].
% 21.04/21.36 1073 inverse(sk_c7) = sk_c3 | inverse(sk_c7) = sk_c1. [para(819(a,1),1021(a,1,1))].
% 21.04/21.36 1074 inverse(sk_c7) = sk_c4 | inverse(sk_c7) = sk_c1. [para(893(a,1),1021(a,1,1))].
% 21.04/21.36 1075 inverse(sk_c7) = sk_c3 | inverse(sk_c6) = sk_c2. [para(916(a,1),1021(a,1,1))].
% 21.04/21.36 1078 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(4(b,1),967(a,1,2))].
% 21.04/21.36 1080 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(6(b,1),967(a,1,2))].
% 21.04/21.36 1081 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(967(a,1),23(a,1)),flip(a)].
% 21.04/21.36 1095 inverse(sk_c3) = sk_c7 | multiply(sk_c6,inverse(sk_c7)) = sk_c1. [para(967(a,1),53(b,1,2)),rewrite([818(7)]),flip(b)].
% 21.04/21.36 1106 sk_c6 != sk_c7 | identity != sk_c7. [para(818(a,1),1026(c,1)),flip(c),flip(d),merge(c),merge(d)].
% 21.04/21.36 1117 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(3(b,1),1020(a,1,2,1))].
% 21.04/21.36 1150 inverse(sk_c7) = sk_c1 | sk_c4 = sk_c3. [para(1074(a,1),1073(a,1)),merge(c)].
% 21.04/21.36 1151 sk_c4 = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(1150(a,1),2(a,1,1))].
% 21.04/21.36 1233 sk_c4 = sk_c3 | identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(1151(b,1),7(a,1))].
% 21.04/21.36 1234 sk_c4 = sk_c3 | identity = sk_c6 | inverse(sk_c4) = sk_c7. [para(1151(b,1),8(a,1))].
% 21.04/21.36 1417 inverse(sk_c1) = sk_c7 | identity = sk_c5. [para(1078(b,1),11(b,1)),merge(b)].
% 21.04/21.36 1425 identity = sk_c5 | multiply(sk_c1,sk_c7) = identity. [para(1417(a,1),967(a,1,2))].
% 21.04/21.36 1539 identity != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(A) != sk_c7 | inverse(sk_c7) != identity. [para(967(a,1),1054(e,1)),flip(f),merge(e)].
% 21.04/21.36 1550 identity = sk_c5 | multiply(A,multiply(sk_c1,sk_c7)) = A. [para(1425(b,1),23(a,2,2)),rewrite([23(7),818(9)])].
% 21.04/21.36 1556 inverse(sk_c2) = sk_c6 | identity = sk_c5. [para(1080(b,1),16(b,1)),merge(b)].
% 21.04/21.36 1563 identity = sk_c5 | multiply(sk_c2,sk_c6) = identity. [para(1556(a,1),967(a,1,2))].
% 21.04/21.36 1581 identity != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c7 | inverse(multiply(A,B)) != sk_c6 | inverse(multiply(A,B)) != sk_c7 | inverse(sk_c7) != identity. [para(23(a,1),1539(b,1))].
% 21.04/21.36 1878 inverse(sk_c1) = sk_c7 | multiply(A,sk_c5) = A. [para(1078(b,1),62(b,1,2)),rewrite([818(10)]),flip(c),merge(b)].
% 21.04/21.36 3329 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c5) = sk_c7. [para(6(b,1),808(b,1,1)),merge(b)].
% 21.04/21.36 3508 inverse(sk_c2) = sk_c6 | sk_c6 = sk_c7. [para(3329(b,1),15(b,1)),flip(c),merge(b)].
% 21.04/21.36 3516 sk_c6 = sk_c7 | multiply(sk_c6,sk_c2) = identity. [para(3508(a,1),2(a,1,1))].
% 21.04/21.36 3526 sk_c6 = sk_c7 | multiply(A,multiply(sk_c6,sk_c2)) = A. [para(3516(b,1),23(a,2,2)),rewrite([23(7),818(9)])].
% 21.04/21.36 3809 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1081(a,1),52(a,1,2)),rewrite([818(3)]),flip(a)].
% 21.04/21.36 3872 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(3809(a,1),52(a,1,2)),flip(a)].
% 21.04/21.36 4413 identity != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c7 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(inverse(B),inverse(A)) != sk_c7 | inverse(sk_c7) != identity. [back_rewrite(1581),rewrite([3872(10),3872(15)])].
% 21.04/21.36 4565 inverse(sk_c3) = sk_c7 | multiply(sk_c2,sk_c1) = identity. [para(1095(b,1),63(b,1,2)),rewrite([967(15)]),merge(b)].
% 21.04/21.36 4617 inverse(sk_c3) = sk_c7 | inverse(sk_c2) = sk_c1. [para(4565(b,1),52(a,1,2)),rewrite([818(8)])].
% 21.04/21.36 4618 inverse(sk_c2) = sk_c1 | multiply(sk_c7,sk_c3) = identity. [para(4617(a,1),2(a,1,1))].
% 21.04/21.36 4670 inverse(sk_c2) = sk_c6 | multiply(sk_c5,sk_c3) = sk_c4. [para(50(b,1),71(b,1,2)),rewrite([818(11)]),flip(c),merge(b)].
% 21.04/21.36 4795 inverse(sk_c2) = sk_c6 | multiply(A,sk_c5) = A. [para(1080(b,1),72(b,1,2)),rewrite([818(10)]),flip(c),merge(b)].
% 21.04/21.36 5754 inverse(sk_c2) = sk_c6 | inverse(sk_c5) = identity. [para(4795(b,1),2(a,1))].
% 21.04/21.36 5766 inverse(sk_c2) = sk_c6 | multiply(sk_c5,A) = A. [para(5754(b,1),52(a,1,1)),rewrite([1(8)])].
% 21.04/21.36 5817 inverse(sk_c2) = sk_c6 | sk_c4 = sk_c3. [para(5766(b,1),4670(b,1)),flip(c),merge(b)].
% 21.04/21.36 5828 sk_c4 = sk_c3 | multiply(sk_c2,sk_c6) = identity. [para(5817(a,1),967(a,1,2))].
% 21.04/21.36 5997 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c3) = sk_c7. [para(5828(b,1),12(a,1))].
% 21.04/21.36 5998 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c4) = sk_c7. [para(5828(b,1),13(a,1))].
% 21.04/21.36 6051 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),multiply(inverse(sk_c4),sk_c5)) = identity. [para(78(b,1),2(a,1)),rewrite([3872(9),23(12)])].
% 21.04/21.36 7316 sk_c4 = sk_c3 | identity = sk_c6 | inverse(sk_c7) = sk_c3. [para(1233(c,1),1021(a,1,1))].
% 21.04/21.36 7324 sk_c4 = sk_c3 | identity = sk_c6 | inverse(sk_c7) = sk_c4. [para(1234(c,1),1021(a,1,1))].
% 21.04/21.36 7526 identity = sk_c5 | multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,multiply(sk_c7,multiply(sk_c1,sk_c7))) = sk_c5. [para(1550(b,1),83(b,2))].
% 21.04/21.36 7912 identity != sk_c6 | sk_c7 != A | multiply(sk_c6,inverse(A)) != sk_c6 | multiply(sk_c6,inverse(A)) != sk_c7 | inverse(sk_c7) != identity. [para(2(a,1),4413(b,1,2)),rewrite([818(5),1021(8),1021(13)]),flip(b)].
% 21.04/21.36 7914 identity != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,A) != sk_c7 | inverse(sk_c7) != identity. [para(1021(a,1),7912(c,1,2)),rewrite([1021(13)]),flip(b)].
% 21.04/21.36 7930 identity != sk_c6 | multiply(inverse(A),sk_c6) != sk_c7 | sk_c6 != A | sk_c7 != A | inverse(sk_c7) != identity. [para(1020(a,1),7914(c,1)),rewrite([3872(7),1021(7),1020(15)]),flip(c),flip(d)].
% 21.04/21.36 8762 sk_c6 = sk_c7 | multiply(inverse(sk_c2),inverse(sk_c6)) = identity. [para(3526(b,1),2(a,1)),rewrite([3872(7)])].
% 21.04/21.36 8900 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),inverse(sk_c4)) = inverse(sk_c5). [para(19(b,1),3872(a,1,1)),flip(b)].
% 21.04/21.36 9604 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c7) = sk_c3. [para(5997(c,1),1021(a,1,1))].
% 21.04/21.36 9613 sk_c4 = sk_c3 | identity = sk_c7 | inverse(sk_c7) = sk_c4. [para(5998(c,1),1021(a,1,1))].
% 21.04/21.36 9972 sk_c4 = sk_c3 | identity = sk_c6. [para(7324(c,1),7316(c,1)),merge(c),merge(d),merge(e)].
% 21.04/21.36 12775 sk_c4 = sk_c3 | identity = sk_c7. [para(9613(c,1),9604(c,1)),merge(c),merge(d),merge(e)].
% 21.04/21.36 12784 sk_c4 = sk_c3 | inverse(sk_c7) = identity. [para(12775(b,1),831(a,1,1))].
% 21.04/21.36 12832 sk_c4 = sk_c3 | inverse(sk_c7) = sk_c7. [para(12775(b,1),12784(b,2)),merge(b)].
% 21.04/21.36 12934 sk_c4 = sk_c3 | multiply(sk_c7,sk_c7) = identity. [para(12832(b,1),2(a,1,1))].
% 21.04/21.36 13230 sk_c4 = sk_c3 | multiply(sk_c7,sk_c7) = sk_c6. [para(9972(b,1),12934(b,2)),merge(b)].
% 21.04/21.36 13357 sk_c4 = sk_c3 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(13230(b,1),52(a,1,2))].
% 21.04/21.36 14170 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B. [para(1(a,1),1062(f,1)),rewrite([831(22)]),merge(g)].
% 21.04/21.36 14189 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7. [resolve(14170,e,1020,a),flip(e)].
% 21.04/21.36 14193 identity != sk_c6 | identity != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7. [factor(14189,d,e),rewrite([2(4),1021(6)]),xx(b)].
% 21.04/21.36 14195 identity != sk_c6 | identity != sk_c7 | sk_c4 = sk_c3. [resolve(14193,c,13357,b)].
% 21.04/21.36 14303 identity != sk_c7 | sk_c4 = sk_c3. [resolve(14195,a,9972,b),merge(c)].
% 21.04/21.36 14304 sk_c4 = sk_c3. [resolve(14303,a,12775,b),merge(b)].
% 21.04/21.36 14360 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),inverse(sk_c3)) = inverse(sk_c5). [back_rewrite(8900),rewrite([14304(8)])].
% 21.04/21.36 14421 identity = sk_c5 | multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c3,multiply(sk_c7,multiply(sk_c1,sk_c7))) = sk_c5. [back_rewrite(7526),rewrite([14304(9)])].
% 21.04/21.36 14461 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),multiply(inverse(sk_c3),sk_c5)) = identity. [back_rewrite(6051),rewrite([14304(8)])].
% 21.04/21.36 16052 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c5. [para(10(b,1),1117(b,1,2)),merge(b)].
% 21.04/21.36 16062 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c5) = sk_c6. [para(16052(b,1),52(a,1,2))].
% 21.04/21.36 16091 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6. [para(16062(b,1),1878(b,1)),flip(c),merge(b)].
% 21.04/21.36 16099 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = identity. [para(16091(b,1),2(a,1,1))].
% 21.04/21.36 16102 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = identity. [para(16091(b,1),967(a,1,2))].
% 21.04/21.36 16173 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = sk_c3. [para(16099(b,1),57(b,1,2)),rewrite([818(11)]),flip(c),merge(b)].
% 21.04/21.36 16188 inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(16102(b,1),9(b,1)),merge(b)].
% 21.04/21.36 16195 identity = sk_c7 | inverse(sk_c7) = sk_c1. [para(16188(a,1),1021(a,1,1))].
% 21.04/21.36 16197 identity = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(16188(a,1),1020(a,1,2,1))].
% 21.04/21.36 16374 inverse(sk_c1) = sk_c7 | multiply(A,sk_c3) = A. [para(16173(b,1),820(b,1,2)),merge(b)].
% 21.04/21.36 16874 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(16374(b,1),16099(b,1)),flip(c),merge(b)].
% 21.04/21.36 16877 identity = sk_c6 | inverse(sk_c7) = sk_c1. [para(16874(a,1),1021(a,1,1))].
% 21.04/21.36 16878 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(16874(a,1),967(a,1,2))].
% 21.04/21.36 16920 identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(16878(b,1),7(a,1)),merge(b)].
% 21.04/21.36 16921 identity = sk_c6 | multiply(sk_c7,sk_c5) = sk_c6. [para(16878(b,1),18(a,1)),merge(b)].
% 21.04/21.36 16932 identity = sk_c6 | inverse(sk_c7) = sk_c3. [para(16920(b,1),1021(a,1,1))].
% 21.04/21.36 16953 identity = sk_c6 | sk_c3 = sk_c1. [para(16932(b,1),16877(b,1)),merge(b)].
% 21.04/21.36 16968 sk_c3 = sk_c1 | inverse(sk_c6) = identity. [para(16953(a,1),831(a,1,1))].
% 21.04/21.36 17035 sk_c3 = sk_c1 | inverse(sk_c7) = sk_c3 | identity = sk_c2. [para(16968(b,1),1075(b,1))].
% 21.04/21.36 17090 identity = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c5. [para(16921(b,1),52(a,1,2))].
% 21.04/21.36 17766 identity = sk_c6 | multiply(inverse(sk_c6),sk_c7) = inverse(sk_c5). [para(17090(b,1),3872(a,1,1)),rewrite([1021(10)]),flip(b)].
% 21.04/21.36 17775 identity = sk_c6 | multiply(sk_c1,sk_c6) = sk_c5. [para(16877(b,1),17090(b,1,1)),merge(b)].
% 21.04/21.36 17788 identity = sk_c6 | multiply(inverse(sk_c1),sk_c5) = sk_c6. [para(17775(b,1),52(a,1,2))].
% 21.04/21.36 18051 identity = sk_c6 | multiply(inverse(sk_c5),sk_c1) = inverse(sk_c6). [para(17788(b,1),3872(a,1,1)),rewrite([1021(10)]),flip(b)].
% 21.04/21.36 18235 inverse(sk_c2) = sk_c1 | identity = sk_c7 | sk_c3 = sk_c1. [para(4618(b,1),16197(b,1,2)),rewrite([818(10)]),flip(c)].
% 21.04/21.36 18880 sk_c3 = sk_c1 | identity = sk_c2 | identity = sk_c7. [para(17035(b,1),16195(b,1)),merge(d)].
% 21.04/21.36 18888 sk_c3 = sk_c1 | identity = sk_c7 | inverse(sk_c2) = identity. [para(18880(b,1),831(a,1,1))].
% 21.04/21.36 19788 identity = sk_c6 | multiply(sk_c6,inverse(sk_c5)) = sk_c7. [para(17766(b,1),52(a,1,2)),rewrite([1021(6)])].
% 21.04/21.36 20399 sk_c3 = sk_c1 | identity = sk_c7 | identity = sk_c1. [para(18888(c,1),18235(a,1)),merge(d),merge(e)].
% 21.04/21.36 20402 sk_c3 = sk_c1 | identity = sk_c7 | inverse(sk_c1) = identity. [para(20399(c,1),831(a,1,1))].
% 21.04/21.36 21558 sk_c3 = sk_c1 | identity = sk_c7. [para(20402(c,1),16188(a,1)),merge(c),merge(d)].
% 21.04/21.36 21563 sk_c3 = sk_c1 | inverse(sk_c7) = identity. [para(21558(b,1),831(a,1,1))].
% 21.04/21.36 21656 sk_c3 = sk_c1 | inverse(sk_c7) = sk_c7. [para(21558(b,1),21563(b,2)),merge(b)].
% 21.04/21.36 21775 sk_c3 = sk_c1 | multiply(sk_c7,sk_c7) = identity. [para(21656(b,1),2(a,1,1))].
% 21.04/21.36 22097 sk_c3 = sk_c1 | multiply(sk_c7,sk_c7) = sk_c6. [para(16953(a,1),21775(b,2)),merge(b)].
% 21.04/21.36 22295 sk_c3 = sk_c1 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(22097(b,1),52(a,1,2))].
% 21.04/21.36 22761 sk_c3 = sk_c1 | identity != sk_c6 | identity != sk_c7. [resolve(22295,b,14193,c)].
% 21.04/21.36 23051 sk_c3 = sk_c1 | identity != sk_c7. [resolve(22761,b,16953,a),merge(c)].
% 21.04/21.36 23052 sk_c3 = sk_c1. [resolve(23051,b,21558,b),merge(b)].
% 21.04/21.36 23864 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),multiply(inverse(sk_c1),sk_c5)) = identity. [back_rewrite(14461),rewrite([23052(8)])].
% 21.04/21.36 23902 identity = sk_c5 | multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c1,multiply(sk_c7,multiply(sk_c1,sk_c7))) = sk_c5. [back_rewrite(14421),rewrite([23052(9)])].
% 21.04/21.36 23952 multiply(sk_c1,sk_c7) = sk_c6 | multiply(inverse(sk_c7),inverse(sk_c1)) = inverse(sk_c5). [back_rewrite(14360),rewrite([23052(8)])].
% 21.04/21.36 25288 inverse(sk_c7) = sk_c1. [back_rewrite(1073),rewrite([23052(3)]),merge(b)].
% 21.04/21.36 25472 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c1,sk_c6) = sk_c7. [back_rewrite(17),rewrite([23052(6)])].
% 21.04/21.36 25477 inverse(sk_c1) = sk_c7. [back_rewrite(3),rewrite([23052(5)]),merge(b)].
% 21.04/21.36 25643 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c1,sk_c7) = inverse(sk_c5). [back_rewrite(23952),rewrite([25288(7),25477(8)])].
% 21.04/21.36 25648 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c1,multiply(sk_c7,sk_c5)) = identity. [back_rewrite(23864),rewrite([25288(7),25477(8)])].
% 21.04/21.36 26939 identity != sk_c6 | multiply(inverse(A),sk_c6) != sk_c7 | sk_c6 != A | sk_c7 != A | identity != sk_c1. [back_rewrite(7930),rewrite([25288(14)]),flip(e)].
% 21.04/21.36 27670 multiply(sk_c1,sk_c7) = identity. [para(25288(a,1),2(a,1,1))].
% 21.04/21.36 27671 multiply(sk_c1,multiply(sk_c7,A)) = A. [para(25288(a,1),52(a,1,1))].
% 21.04/21.36 28253 identity = sk_c6 | identity = sk_c5. [back_rewrite(25648),rewrite([27670(3),27671(8)]),flip(b)].
% 21.04/21.36 28254 identity = sk_c6 | inverse(sk_c5) = identity. [back_rewrite(25643),rewrite([27670(3),27670(6)]),flip(b)].
% 21.04/21.36 28271 identity = sk_c6 | multiply(sk_c1,sk_c6) = sk_c7. [back_rewrite(25472),rewrite([27670(3)])].
% 21.04/21.36 28310 identity = sk_c5 | multiply(sk_c2,sk_c6) = sk_c7. [back_rewrite(23902),rewrite([27670(13),818(12),27670(11)]),merge(c)].
% 21.04/21.36 28367 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c6,A) = A. [back_rewrite(75),rewrite([27671(9)]),flip(b)].
% 21.04/21.36 29540 identity = sk_c6 | sk_c6 = sk_c7. [para(28254(b,1),19788(b,1,2)),rewrite([818(9)]),merge(b)].
% 21.04/21.36 29553 identity = sk_c6 | inverse(sk_c6) = sk_c1. [para(28254(b,1),18051(b,1,1)),rewrite([1(9)]),flip(c),merge(b)].
% 21.04/21.36 29579 sk_c6 = sk_c7 | inverse(sk_c6) = identity. [para(29540(a,1),831(a,1,1))].
% 21.04/21.36 29986 identity = sk_c6 | multiply(sk_c1,sk_c6) = identity. [para(29553(b,1),2(a,1,1))].
% 21.04/21.36 30247 sk_c6 = sk_c7 | inverse(sk_c2) = identity. [para(29579(b,1),8762(b,1,2)),rewrite([818(10)]),merge(b)].
% 21.04/21.36 31639 sk_c6 = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6. [para(30247(b,1),813(b,1,1)),rewrite([1(11)]),flip(c),merge(c)].
% 21.04/21.36 32689 identity = sk_c5 | identity = sk_c7. [para(28310(b,1),1563(b,1)),flip(c),merge(b)].
% 21.04/21.36 32749 identity = sk_c7 | multiply(A,sk_c5) = A. [para(32689(a,1),818(a,1,2))].
% 21.04/21.36 33049 identity != sk_c6 | multiply(sk_c7,sk_c6) != sk_c7 | sk_c1 != sk_c6 | sk_c1 != sk_c7 | identity != sk_c1. [para(25477(a,1),26939(b,1,1)),flip(c),flip(d)].
% 21.04/21.36 34004 identity = sk_c6 | identity = sk_c7. [para(29986(b,1),28271(b,1)),merge(b)].
% 21.04/21.36 34010 identity = sk_c7 | sk_c6 != sk_c7. [para(34004(a,1),1106(b,1)),merge(c)].
% 21.04/21.36 34013 identity = sk_c7 | sk_c5 = sk_c6. [para(34004(a,1),32689(a,1)),flip(b),merge(c)].
% 21.04/21.36 34020 sk_c5 = sk_c6 | sk_c6 != sk_c7. [resolve(34013,a,1106,b)].
% 21.04/21.36 34023 sk_c5 = sk_c6 | identity = sk_c1. [para(34013(a,1),831(a,1,1)),rewrite([25288(5)]),flip(b)].
% 21.04/21.36 34063 sk_c5 = sk_c6 | sk_c1 = sk_c7. [para(34023(b,1),34013(a,1)),merge(c)].
% 21.04/21.36 34097 sk_c1 = sk_c7 | identity = sk_c6. [para(34063(a,1),28253(b,2)),merge(c)].
% 21.04/21.36 34105 sk_c1 = sk_c7 | inverse(sk_c6) = identity. [para(34097(b,1),831(a,1,1))].
% 21.04/21.36 34341 sk_c1 = sk_c7 | inverse(sk_c6) = sk_c6. [para(34097(b,1),34105(b,2)),merge(b)].
% 21.04/21.36 35557 identity = sk_c7 | sk_c6 = sk_c7. [para(32749(b,1),31639(b,1)),flip(c),merge(c)].
% 21.04/21.36 35566 sk_c6 = sk_c7. [para(35557(a,1),29540(a,1)),flip(b),merge(b),merge(c)].
% 21.04/21.36 35829 sk_c1 = sk_c7. [back_rewrite(34341),rewrite([35566(4),25288(5),35566(5)]),merge(b)].
% 21.04/21.36 35854 sk_c5 = sk_c7. [back_rewrite(34020),rewrite([35566(2),35566(4)]),xx(b)].
% 21.04/21.36 35856 identity = sk_c7. [back_rewrite(34010),rewrite([35566(4)]),xx(b)].
% 21.04/21.36 35882 multiply(sk_c7,sk_c7) != sk_c7. [back_rewrite(33049),rewrite([35856(1),35566(2),35566(5),35829(9),35566(10),35829(12),35856(15),35829(16)]),xx(a),xx(c),xx(d),xx(e)].
% 21.04/21.36 36073 multiply(sk_c7,A) = A. [back_rewrite(28367),rewrite([35854(2),35566(4),35566(6)]),unit_del(a,35882)].
% 21.04/21.36 36074 $F. [resolve(36073,a,35882,a)].
% 21.04/21.36
% 21.04/21.36 % SZS output end Refutation
% 21.04/21.36 ============================== end of proof ==========================
% 21.04/21.36
% 21.04/21.36 ============================== STATISTICS ============================
% 21.04/21.36
% 21.04/21.36 Given=3358. Generated=1129502. Kept=36073. proofs=1.
% 21.04/21.36 Usable=902. Sos=3651. Demods=24. Limbo=507, Disabled=31036. Hints=0.
% 21.04/21.36 Megabytes=28.27.
% 21.04/21.36 User_CPU=19.76, System_CPU=0.60, Wall_clock=20.
% 21.04/21.36
% 21.04/21.36 ============================== end of statistics =====================
% 21.04/21.36
% 21.04/21.36 ============================== end of search =========================
% 21.04/21.36
% 21.04/21.36 THEOREM PROVED
% 21.04/21.36 % SZS status Unsatisfiable
% 21.04/21.36
% 21.04/21.36 Exiting with 1 proof.
% 21.04/21.36
% 21.04/21.36 Process 5434 exit (max_proofs) Mon Jun 13 10:32:24 2022
% 21.04/21.36 Prover9 interrupted
%------------------------------------------------------------------------------