TSTP Solution File: GRP270-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP270-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:18:25 EDT 2022
% Result : Unsatisfiable 239.16s 239.47s
% Output : Refutation 239.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP270-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.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 : Tue Jun 14 13:18:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 190.14/190.40 ============================== Prover9 ===============================
% 190.14/190.40 Prover9 (32) version 2009-11A, November 2009.
% 190.14/190.40 Process 22657 was started by sandbox on n008.cluster.edu,
% 190.14/190.40 Tue Jun 14 13:18:38 2022
% 190.14/190.40 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22275_n008.cluster.edu".
% 190.14/190.40 ============================== end of head ===========================
% 190.14/190.40
% 190.14/190.40 ============================== INPUT =================================
% 190.14/190.40
% 190.14/190.40 % Reading from file /tmp/Prover9_22275_n008.cluster.edu
% 190.14/190.40
% 190.14/190.40 set(prolog_style_variables).
% 190.14/190.40 set(auto2).
% 190.14/190.40 % set(auto2) -> set(auto).
% 190.14/190.40 % set(auto) -> set(auto_inference).
% 190.14/190.40 % set(auto) -> set(auto_setup).
% 190.14/190.40 % set(auto_setup) -> set(predicate_elim).
% 190.14/190.40 % set(auto_setup) -> assign(eq_defs, unfold).
% 190.14/190.40 % set(auto) -> set(auto_limits).
% 190.14/190.40 % set(auto_limits) -> assign(max_weight, "100.000").
% 190.14/190.40 % set(auto_limits) -> assign(sos_limit, 20000).
% 190.14/190.40 % set(auto) -> set(auto_denials).
% 190.14/190.40 % set(auto) -> set(auto_process).
% 190.14/190.40 % set(auto2) -> assign(new_constants, 1).
% 190.14/190.40 % set(auto2) -> assign(fold_denial_max, 3).
% 190.14/190.40 % set(auto2) -> assign(max_weight, "200.000").
% 190.14/190.40 % set(auto2) -> assign(max_hours, 1).
% 190.14/190.40 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 190.14/190.40 % set(auto2) -> assign(max_seconds, 0).
% 190.14/190.40 % set(auto2) -> assign(max_minutes, 5).
% 190.14/190.40 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 190.14/190.40 % set(auto2) -> set(sort_initial_sos).
% 190.14/190.40 % set(auto2) -> assign(sos_limit, -1).
% 190.14/190.40 % set(auto2) -> assign(lrs_ticks, 3000).
% 190.14/190.40 % set(auto2) -> assign(max_megs, 400).
% 190.14/190.40 % set(auto2) -> assign(stats, some).
% 190.14/190.40 % set(auto2) -> clear(echo_input).
% 190.14/190.40 % set(auto2) -> set(quiet).
% 190.14/190.40 % set(auto2) -> clear(print_initial_clauses).
% 190.14/190.40 % set(auto2) -> clear(print_given).
% 190.14/190.40 assign(lrs_ticks,-1).
% 190.14/190.40 assign(sos_limit,10000).
% 190.14/190.40 assign(order,kbo).
% 190.14/190.40 set(lex_order_vars).
% 190.14/190.40 clear(print_given).
% 190.14/190.40
% 190.14/190.40 % formulas(sos). % not echoed (29 formulas)
% 190.14/190.40
% 190.14/190.40 ============================== end of input ==========================
% 190.14/190.40
% 190.14/190.40 % From the command line: assign(max_seconds, 300).
% 190.14/190.40
% 190.14/190.40 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 190.14/190.40
% 190.14/190.40 % Formulas that are not ordinary clauses:
% 190.14/190.40
% 190.14/190.40 ============================== end of process non-clausal formulas ===
% 190.14/190.40
% 190.14/190.40 ============================== PROCESS INITIAL CLAUSES ===============
% 190.14/190.40
% 190.14/190.40 ============================== PREDICATE ELIMINATION =================
% 190.14/190.40
% 190.14/190.40 ============================== end predicate elimination =============
% 190.14/190.40
% 190.14/190.40 Auto_denials: (non-Horn, no changes).
% 190.14/190.40
% 190.14/190.40 Term ordering decisions:
% 190.14/190.40
% 190.14/190.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 190.14/190.40 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 190.14/190.40
% 190.14/190.40 ============================== end of process initial clauses ========
% 190.14/190.40
% 190.14/190.40 ============================== CLAUSES FOR SEARCH ====================
% 190.14/190.40
% 190.14/190.40 ============================== end of clauses for search =============
% 190.14/190.40
% 190.14/190.40 ============================== SEARCH ================================
% 190.14/190.40
% 190.14/190.40 % Starting search at 0.02 seconds.
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=41.000, iters=3531
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=37.000, iters=3352
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=36.000, iters=3358
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=35.000, iters=3334
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=34.000, iters=3335
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=33.000, iters=3359
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=32.000, iters=3413
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=31.000, iters=3384
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=30.000, iters=3346
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=29.000, iters=3340
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=28.000, iters=3394
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=27.000, iters=3345
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=25.000, iters=3335
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=23.000, iters=3389
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=21.000, iters=3429
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=19.000, iters=3670
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=17.000, iters=3377
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=16.000, iters=3432
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=15.000, iters=3334
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=14.000, iters=3352
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=13.000, iters=3333
% 190.14/190.40
% 190.14/190.40 Low Water (displace): id=4112, wt=49.000
% 190.14/190.40
% 190.14/190.40 Low Water (displace): id=1615, wt=48.000
% 190.14/190.40
% 190.14/190.40 Low Water (displace): id=15211, wt=12.000
% 190.14/190.40
% 190.14/190.40 Low Water (displace): id=15418, wt=11.000
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=12.000, iters=3343
% 190.14/190.40
% 190.14/190.40 Low Water (keep): wt=11.000, iters=3335
% 239.16/239.47
% 239.16/239.47 Low Water (displace): id=42152, wt=10.000
% 239.16/239.47
% 239.16/239.47 ============================== PROOF =================================
% 239.16/239.47 % SZS status Unsatisfiable
% 239.16/239.47 % SZS output start Refutation
% 239.16/239.47
% 239.16/239.47 % Proof 1 at 232.27 (+ 6.22) seconds.
% 239.16/239.47 % Length of proof is 272.
% 239.16/239.47 % Level of proof is 34.
% 239.16/239.47 % Maximum clause weight is 46.000.
% 239.16/239.47 % Given clauses 10143.
% 239.16/239.47
% 239.16/239.47 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 239.16/239.47 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 239.16/239.47 3 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 239.16/239.47 4 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 239.16/239.47 5 inverse(sk_c2) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 239.16/239.47 6 inverse(sk_c2) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 239.16/239.47 7 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 239.16/239.47 8 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 239.16/239.47 9 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 239.16/239.47 10 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 239.16/239.47 11 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 239.16/239.47 12 multiply(sk_c7,sk_c5) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 239.16/239.47 14 multiply(sk_c2,sk_c7) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 239.16/239.47 15 multiply(sk_c2,sk_c7) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 239.16/239.47 16 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 239.16/239.47 17 inverse(sk_c2) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 239.16/239.47 18 inverse(sk_c2) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 239.16/239.47 19 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 239.16/239.47 20 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 239.16/239.47 21 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 239.16/239.47 22 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 239.16/239.47 23 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 239.16/239.47 24 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 239.16/239.47 26 multiply(sk_c2,sk_c7) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 239.16/239.47 27 multiply(sk_c2,sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 239.16/239.47 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 239.16/239.47 29 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(D) != sk_c6 | multiply(D,sk_c5) != sk_c6 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 239.16/239.47 49 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 239.16/239.47 50 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 239.16/239.47 51 inverse(sk_c2) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 239.16/239.47 52 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 239.16/239.47 53 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 239.16/239.47 55 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(7(a,1),28(a,2,2)),rewrite([28(8)])].
% 239.16/239.47 60 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(10(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 61 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),28(a,2,2)),rewrite([28(8)])].
% 239.16/239.47 62 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(11(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 63 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(11(b,1),28(a,2,2)),rewrite([28(8)])].
% 239.16/239.47 72 inverse(sk_c2) = sk_c7 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(16(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 74 inverse(sk_c2) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(17(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 76 inverse(sk_c2) = sk_c7 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(18(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 77 inverse(sk_c2) = sk_c7 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(18(b,1),28(a,2,2)),rewrite([28(8)])].
% 239.16/239.47 86 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(23(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 116 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(inverse(sk_c6)) != sk_c7 | identity != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(2(a,1),29(h,1))].
% 239.16/239.47 215 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | inverse(inverse(sk_c6)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [factor(116,e,g)].
% 239.16/239.47 476 inverse(sk_c1) = sk_c7 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(49(b,1),28(a,1,1)),rewrite([1(6)]),flip(b)].
% 239.16/239.47 494 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),53(a,1,2))].
% 239.16/239.47 496 inverse(sk_c2) = sk_c7 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(5(b,1),53(a,1,1))].
% 239.16/239.47 497 inverse(sk_c2) = sk_c7 | multiply(sk_c6,multiply(sk_c4,A)) = A. [para(6(b,1),53(a,1,1))].
% 239.16/239.47 501 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(10(b,1),53(a,1,2))].
% 239.16/239.47 503 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c5. [para(12(a,1),53(a,1,2))].
% 239.16/239.47 507 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(16(b,1),53(a,1,2))].
% 239.16/239.47 508 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(17(b,1),53(a,1,2))].
% 239.16/239.47 509 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(18(b,1),53(a,1,2))].
% 239.16/239.47 513 multiply(sk_c7,sk_c5) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(22(b,1),53(a,1,2))].
% 239.16/239.47 517 multiply(sk_c2,sk_c7) = sk_c5 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(26(b,1),53(a,1,2))].
% 239.16/239.47 520 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),identity) = sk_c3. [para(49(b,1),53(a,1,2))].
% 239.16/239.47 521 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(53(a,1),53(a,1,2))].
% 239.16/239.47 522 multiply(A,identity) = A. [back_rewrite(494),rewrite([521(4)])].
% 239.16/239.47 523 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c3. [back_rewrite(520),rewrite([522(8)])].
% 239.16/239.47 525 inverse(identity) = identity. [para(522(a,1),2(a,1))].
% 239.16/239.47 564 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c4. [para(50(b,1),53(a,1,2)),rewrite([522(8)])].
% 239.16/239.47 570 inverse(sk_c2) = sk_c7 | inverse(sk_c7) = sk_c3. [para(51(b,1),53(a,1,2)),rewrite([522(8)])].
% 239.16/239.47 571 inverse(sk_c7) = sk_c3 | multiply(sk_c7,sk_c2) = identity. [para(570(a,1),2(a,1,1))].
% 239.16/239.47 573 inverse(sk_c2) = sk_c7 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(52(b,1),28(a,2,2)),rewrite([28(8),522(10)])].
% 239.16/239.47 574 inverse(sk_c2) = sk_c7 | inverse(sk_c6) = sk_c4. [para(52(b,1),53(a,1,2)),rewrite([522(8)])].
% 239.16/239.47 591 inverse(sk_c6) = sk_c4 | multiply(sk_c7,sk_c2) = identity. [para(574(a,1),2(a,1,1))].
% 239.16/239.47 593 multiply(A,inverse(A)) = identity. [para(521(a,1),2(a,1))].
% 239.16/239.47 638 multiply(A,multiply(inverse(A),B)) = B. [para(521(a,1),53(a,1))].
% 239.16/239.47 639 inverse(inverse(A)) = A. [para(521(a,1),522(a,1)),rewrite([522(2)]),flip(a)].
% 239.16/239.47 659 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | sk_c6 != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [back_rewrite(215),rewrite([639(21)])].
% 239.16/239.47 671 inverse(sk_c6) = sk_c4 | inverse(sk_c7) = sk_c1. [para(564(a,1),639(a,1,1))].
% 239.16/239.47 672 inverse(sk_c7) = sk_c3 | inverse(sk_c7) = sk_c2. [para(570(a,1),639(a,1,1))].
% 239.16/239.47 674 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c7) = identity. [para(3(b,1),593(a,1,2))].
% 239.16/239.47 675 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = identity. [para(4(b,1),593(a,1,2))].
% 239.16/239.47 678 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(593(a,1),28(a,1)),flip(a)].
% 239.16/239.47 679 inverse(sk_c7) = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(523(a,1),593(a,1,2))].
% 239.16/239.47 680 inverse(sk_c6) = sk_c4 | multiply(sk_c1,sk_c7) = identity. [para(564(a,1),593(a,1,2))].
% 239.16/239.47 681 inverse(sk_c7) = sk_c3 | multiply(sk_c2,sk_c7) = identity. [para(570(a,1),593(a,1,2))].
% 239.16/239.47 684 inverse(sk_c6) = sk_c4 | multiply(sk_c2,sk_c7) = identity. [para(574(a,1),593(a,1,2))].
% 239.16/239.47 699 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(4(b,1),638(a,1,2,1))].
% 239.16/239.47 701 inverse(sk_c2) = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(6(b,1),638(a,1,2,1))].
% 239.16/239.47 703 inverse(sk_c7) = sk_c3 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(523(a,1),638(a,1,2,1))].
% 239.16/239.47 704 inverse(sk_c6) = sk_c4 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(564(a,1),638(a,1,2,1))].
% 239.16/239.47 722 inverse(sk_c7) = sk_c2 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(672(a,1),53(a,1,1))].
% 239.16/239.47 829 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c4,sk_c6)) = A. [para(675(b,1),28(a,2,2)),rewrite([28(8),522(10)])].
% 239.16/239.47 895 inverse(sk_c7) = sk_c3 | identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(679(b,1),7(a,1))].
% 239.16/239.47 902 inverse(sk_c6) = sk_c4 | identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(680(b,1),8(a,1))].
% 239.16/239.47 907 inverse(sk_c7) = sk_c3 | identity = sk_c5 | inverse(sk_c3) = sk_c7. [para(681(b,1),14(a,1))].
% 239.16/239.47 911 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c7). [para(9(b,1),60(b,1,2)),merge(b)].
% 239.16/239.47 913 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = identity. [para(49(b,1),60(b,2)),merge(b)].
% 239.16/239.47 952 inverse(sk_c6) = sk_c4 | identity = sk_c5 | inverse(sk_c4) = sk_c6. [para(684(b,1),15(a,1))].
% 239.16/239.47 980 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(9(b,1),61(b,2)),merge(b)].
% 239.16/239.47 984 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c3,sk_c6)) = identity. [para(674(b,1),61(b,2)),merge(b)].
% 239.16/239.47 1219 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(b,1),501(b,1,1)),merge(b)].
% 239.16/239.47 1399 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c7),multiply(sk_c1,sk_c7)) = sk_c5. [para(503(b,1),55(b,2)),merge(b)].
% 239.16/239.47 1525 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c6),multiply(sk_c5,A)) = multiply(sk_c7,A). [para(507(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 1555 inverse(sk_c2) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(5(b,1),508(b,1,1)),merge(b)].
% 239.16/239.47 1556 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c3),multiply(sk_c7,A)) = multiply(sk_c6,A). [para(508(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 1613 inverse(sk_c2) = sk_c7 | multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(1555(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 1639 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c6) = sk_c5. [para(6(b,1),509(b,1,1)),merge(b)].
% 239.16/239.47 1667 inverse(sk_c2) = sk_c7 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(1639(b,1),28(a,1,1)),flip(b)].
% 239.16/239.47 1698 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(678(a,1),53(a,1,2)),rewrite([522(3)]),flip(a)].
% 239.16/239.47 1827 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3). [para(20(b,1),1698(a,1,2,1))].
% 239.16/239.47 1828 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(21(b,1),1698(a,1,2,1))].
% 239.16/239.47 1834 multiply(sk_c2,sk_c7) = sk_c5 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(27(b,1),1698(a,1,2,1))].
% 239.16/239.47 1838 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1698(a,1),53(a,1,2)),flip(a)].
% 239.16/239.47 2478 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c3) = sk_c6. [para(51(b,1),72(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 2481 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6). [para(1555(b,1),72(b,1,2)),flip(c),merge(b)].
% 239.16/239.47 2550 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c5),sk_c6) = sk_c3. [para(2478(b,1),53(a,1,2))].
% 239.16/239.47 2743 inverse(sk_c2) = sk_c7 | multiply(sk_c7,sk_c4) = sk_c3. [para(52(b,1),74(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 2790 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c7),sk_c3) = sk_c4. [para(2743(b,1),53(a,1,2))].
% 239.16/239.47 4697 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c7). [para(22(b,1),86(b,1,2)),merge(b)].
% 239.16/239.47 5983 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c7. [para(9(b,1),699(b,1,2)),merge(b)].
% 239.16/239.47 5993 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c5. [para(5983(b,1),53(a,1,2))].
% 239.16/239.47 6123 inverse(sk_c2) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c7. [para(16(b,1),701(b,1,2)),merge(b)].
% 239.16/239.47 6133 inverse(sk_c2) = sk_c7 | multiply(inverse(sk_c4),sk_c7) = sk_c5. [para(6123(b,1),53(a,1,2))].
% 239.16/239.47 6182 inverse(sk_c7) = sk_c3 | sk_c2 = sk_c1. [para(571(b,1),703(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 6201 sk_c2 = sk_c1 | multiply(sk_c3,sk_c7) = identity. [para(6182(a,1),2(a,1,1))].
% 239.16/239.47 6202 sk_c2 = sk_c1 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(6182(a,1),53(a,1,1))].
% 239.16/239.47 6284 sk_c2 = sk_c1 | multiply(inverse(sk_c7),inverse(sk_c3)) = identity. [para(6201(b,1),1838(a,1,1)),rewrite([525(5)]),flip(b)].
% 239.16/239.47 6563 inverse(sk_c6) = sk_c4 | sk_c2 = sk_c1. [para(591(b,1),704(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 6582 sk_c2 = sk_c1 | multiply(sk_c4,sk_c6) = identity. [para(6563(a,1),2(a,1,1))].
% 239.16/239.47 7468 inverse(sk_c7) = sk_c3 | identity = sk_c6. [para(895(c,1),639(a,1,1)),merge(c)].
% 239.16/239.47 7471 identity = sk_c6 | inverse(sk_c3) = sk_c7. [para(7468(a,1),639(a,1,1))].
% 239.16/239.47 7766 inverse(sk_c6) = sk_c4 | identity = sk_c6. [para(902(c,1),639(a,1,1)),merge(c)].
% 239.16/239.47 7773 identity = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(7766(a,1),53(a,1,1))].
% 239.16/239.47 7774 identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(7766(a,1),639(a,1,1))].
% 239.16/239.47 8025 inverse(sk_c7) = sk_c3 | identity = sk_c5. [para(907(c,1),639(a,1,1)),merge(c)].
% 239.16/239.47 8285 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c6. [para(1219(b,1),911(b,2)),merge(b)].
% 239.16/239.47 8290 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c6) = sk_c5. [para(8285(b,1),53(a,1,2))].
% 239.16/239.47 8317 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(913(b,1),53(a,1,2)),rewrite([522(8)]),flip(b)].
% 239.16/239.47 8319 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = sk_c7. [para(913(b,1),476(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 8359 inverse(sk_c6) = sk_c4 | identity = sk_c5. [para(952(c,1),639(a,1,1)),merge(c)].
% 239.16/239.47 8642 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = inverse(sk_c3). [para(984(b,1),53(a,1,2)),rewrite([522(8)]),flip(b)].
% 239.16/239.47 8649 inverse(sk_c1) = sk_c7 | multiply(sk_c6,inverse(sk_c3)) = sk_c5. [para(8642(b,1),980(b,1,2)),merge(b)].
% 239.16/239.47 8667 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = inverse(sk_c3). [para(8649(b,1),699(b,1,2)),merge(b)].
% 239.16/239.47 8668 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6. [para(8667(b,1),11(b,1)),merge(b)].
% 239.16/239.47 8675 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = identity. [para(8668(b,1),2(a,1,1))].
% 239.16/239.47 8677 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c3. [para(8668(b,1),639(a,1,1))].
% 239.16/239.47 8704 inverse(sk_c6) = sk_c3 | inverse(sk_c7) = sk_c1. [para(8677(a,1),639(a,1,1))].
% 239.16/239.47 8720 inverse(sk_c7) = sk_c1 | sk_c4 = sk_c3. [para(8704(a,1),671(a,1)),flip(b),merge(c)].
% 239.16/239.47 8818 inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(8675(b,1),8319(b,1)),merge(b)].
% 239.16/239.47 8819 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = identity. [para(8675(b,1),8317(b,1)),flip(c),merge(b)].
% 239.16/239.47 8842 identity = sk_c7 | inverse(sk_c7) = sk_c1. [para(8818(a,1),639(a,1,1))].
% 239.16/239.47 8899 inverse(sk_c1) = sk_c7 | multiply(sk_c3,A) = A. [para(8819(b,1),53(a,1,1)),rewrite([1(8)])].
% 239.16/239.47 8906 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = identity. [para(8819(b,1),8667(b,2)),merge(b)].
% 239.16/239.47 8907 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(8819(b,1),8668(b,1)),merge(b)].
% 239.16/239.47 8921 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(8907(a,1),593(a,1,2))].
% 239.16/239.47 9145 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5. [para(8921(b,1),19(a,1)),merge(b)].
% 239.16/239.47 9333 identity = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(9145(b,1),53(a,1,2))].
% 239.16/239.47 9635 inverse(sk_c1) = sk_c7 | multiply(sk_c7,A) = A. [para(8899(b,1),476(b,1,2)),merge(b)].
% 239.16/239.47 9646 inverse(sk_c1) = sk_c7 | multiply(A,sk_c6) = A. [para(8906(b,1),63(b,1,2)),rewrite([522(10)]),flip(c),merge(b)].
% 239.16/239.47 9936 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7). [para(9333(b,1),1838(a,1,1)),rewrite([639(10)]),flip(b)].
% 239.16/239.47 10312 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c7),A) = A. [para(9635(b,1),53(a,1,2))].
% 239.16/239.47 10356 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c5. [para(9646(b,1),8290(b,1)),merge(b)].
% 239.16/239.47 10428 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c3) = identity. [para(10356(b,1),2(a,1,1))].
% 239.16/239.47 11444 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = sk_c4. [para(10428(b,1),62(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 11685 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c4. [para(11444(b,1),8317(b,1)),flip(c),merge(b)].
% 239.16/239.47 11721 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c3. [para(11685(b,1),639(a,1,1))].
% 239.16/239.47 11728 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c6) = sk_c5. [para(11685(b,1),8290(b,1,1)),merge(b)].
% 239.16/239.47 11759 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c7) = sk_c5. [para(11721(b,1),5993(b,1,1)),merge(b)].
% 239.16/239.47 11868 inverse(sk_c1) = sk_c7 | multiply(A,sk_c5) = A. [para(11728(b,1),829(b,1,2)),merge(b)].
% 239.16/239.47 11900 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c5) = sk_c7. [para(11759(b,1),53(a,1,2))].
% 239.16/239.47 13213 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c5. [para(10312(b,1),11868(b,1)),flip(c),merge(b)].
% 239.16/239.47 13220 inverse(sk_c7) = sk_c5 | multiply(sk_c1,sk_c7) = identity. [para(13213(a,1),593(a,1,2))].
% 239.16/239.47 13309 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6. [para(1(a,1),659(a,1)),rewrite([525(5)]),flip(a),merge(e),merge(g)].
% 239.16/239.47 13311 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(A),inverse(B)) != sk_c6 | multiply(B,multiply(A,sk_c5)) != sk_c6. [para(28(a,1),13309(g,1)),rewrite([1838(24)])].
% 239.16/239.47 13312 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c5,inverse(A)) != sk_c6 | sk_c6 != A. [para(2(a,1),13311(g,1,2)),rewrite([639(25),522(29)]),flip(g)].
% 239.16/239.47 13364 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c5,A) != sk_c6 | inverse(A) != sk_c6. [para(639(a,1),13312(f,1,2)),flip(g)].
% 239.16/239.47 13367 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != A | multiply(inverse(A),sk_c5) != sk_c6. [para(638(a,1),13364(f,1)),rewrite([1838(28),639(28)]),flip(f)].
% 239.16/239.47 14395 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c5) = sk_c7. [para(10356(b,1),11900(b,1,1)),merge(b)].
% 239.16/239.47 28640 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c7) = sk_c5. [para(1639(b,1),2481(b,2)),merge(b)].
% 239.16/239.47 28641 inverse(sk_c2) = sk_c7 | identity = sk_c7. [para(28640(b,1),53(a,1,2)),rewrite([2(8)])].
% 239.16/239.47 28653 identity = sk_c7 | inverse(sk_c7) = sk_c2. [para(28641(a,1),639(a,1,1))].
% 239.16/239.47 28675 identity = sk_c7 | sk_c2 = sk_c1. [para(28653(b,1),8842(b,1)),merge(b)].
% 239.16/239.47 28688 sk_c2 = sk_c1 | inverse(sk_c7) = identity. [para(28675(a,1),525(a,1,1))].
% 239.16/239.47 28777 sk_c2 = sk_c1 | inverse(sk_c2) = sk_c7 | sk_c4 = sk_c3. [para(28688(b,1),2790(b,1,1)),rewrite([1(10)]),flip(c)].
% 239.16/239.47 28778 sk_c2 = sk_c1 | identity = sk_c3. [para(28688(b,1),6182(a,1)),merge(c)].
% 239.16/239.47 28814 sk_c2 = sk_c1 | inverse(sk_c7) = sk_c7. [para(28675(a,1),28688(b,2)),merge(b)].
% 239.16/239.47 28833 sk_c2 = sk_c1 | multiply(sk_c4,sk_c6) = sk_c3. [para(28778(b,1),6582(b,2)),merge(b)].
% 239.16/239.47 28912 sk_c2 = sk_c1 | sk_c3 = sk_c7. [para(28778(b,1),28675(a,1)),merge(c)].
% 239.16/239.47 28957 sk_c2 = sk_c1 | multiply(sk_c7,inverse(sk_c3)) = identity. [para(28814(b,1),6284(b,1,1)),merge(b)].
% 239.16/239.47 29189 sk_c2 = sk_c1 | multiply(inverse(sk_c4),sk_c3) = sk_c6. [para(28833(b,1),53(a,1,2))].
% 239.16/239.47 29502 sk_c2 = sk_c1 | multiply(sk_c7,inverse(sk_c3)) = sk_c3. [para(28778(b,1),28957(b,2)),merge(b)].
% 239.16/239.47 29734 sk_c2 = sk_c1 | multiply(sk_c3,sk_c3) = inverse(sk_c3). [para(29502(b,1),6202(b,1,2)),merge(b)].
% 239.16/239.47 29993 sk_c2 = sk_c1 | sk_c4 = sk_c3 | inverse(sk_c7) = sk_c2. [para(28777(b,1),639(a,1,1))].
% 239.16/239.47 31008 sk_c2 = sk_c1 | sk_c4 = sk_c3. [para(29993(c,1),8720(a,1)),merge(c),merge(d)].
% 239.16/239.47 31031 sk_c2 = sk_c1 | sk_c4 = sk_c7. [para(28912(b,1),31008(b,2)),merge(b)].
% 239.16/239.47 31038 sk_c2 = sk_c1 | identity = sk_c6. [para(31008(b,1),29189(b,1,1,1)),rewrite([2(10)]),merge(b)].
% 239.16/239.47 31067 sk_c2 = sk_c1 | multiply(sk_c7,sk_c5) = sk_c6. [para(31031(b,1),24(b,1,1)),merge(c)].
% 239.16/239.47 31117 sk_c2 = sk_c1 | multiply(A,sk_c6) = A. [para(31038(b,1),522(a,1,2))].
% 239.16/239.47 31420 sk_c2 = sk_c1 | multiply(sk_c3,sk_c6) = sk_c5. [para(31067(b,1),6202(b,1,2)),merge(b)].
% 239.16/239.47 31563 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c7. [para(13220(b,1),1399(b,1,2)),rewrite([522(12)]),merge(c)].
% 239.16/239.47 31743 sk_c2 = sk_c1 | sk_c3 = sk_c5. [para(31420(b,1),31117(b,1)),flip(c),merge(b)].
% 239.16/239.47 31827 sk_c2 = sk_c1 | multiply(sk_c5,sk_c3) = inverse(sk_c3). [para(31743(b,1),29734(b,1,1)),merge(b)].
% 239.16/239.47 32026 inverse(sk_c7) = sk_c5 | inverse(sk_c7) = sk_c3. [para(31563(b,1),639(a,1,1))].
% 239.16/239.47 32254 inverse(sk_c7) = sk_c5 | identity = sk_c7 | sk_c3 = sk_c2. [para(32026(b,1),28653(b,1))].
% 239.16/239.47 32671 sk_c2 = sk_c1 | multiply(sk_c5,sk_c5) = inverse(sk_c3). [para(31743(b,1),31827(b,1,2)),merge(b)].
% 239.16/239.47 34304 identity = sk_c7 | sk_c3 = sk_c2 | inverse(sk_c5) = sk_c7. [para(32254(a,1),639(a,1,1))].
% 239.16/239.47 34344 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c4) = sk_c6. [para(52(b,1),1667(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 34357 inverse(sk_c2) = sk_c7 | multiply(sk_c7,sk_c4) = identity. [para(34344(b,1),1525(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 239.16/239.47 34376 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c4) = inverse(sk_c3). [para(34357(b,1),1556(b,1,2)),rewrite([522(12)]),flip(c),merge(b)].
% 239.16/239.47 34377 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c4) = sk_c7. [para(34357(b,1),1613(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 34509 inverse(sk_c2) = sk_c7 | multiply(A,sk_c7) = A. [para(34377(b,1),573(b,1,2)),merge(b)].
% 239.16/239.47 34605 inverse(sk_c2) = sk_c7 | inverse(sk_c7) = identity. [para(34509(b,1),2(a,1))].
% 239.16/239.47 34617 inverse(sk_c2) = sk_c7 | inverse(sk_c4) = sk_c5. [para(34509(b,1),6133(b,1)),merge(b)].
% 239.16/239.47 34663 inverse(sk_c7) = identity | inverse(sk_c7) = sk_c2. [para(34605(a,1),639(a,1,1))].
% 239.16/239.47 34685 inverse(sk_c2) = sk_c7 | multiply(sk_c5,sk_c4) = identity. [para(34617(b,1),2(a,1,1))].
% 239.16/239.47 34688 inverse(sk_c2) = sk_c7 | multiply(sk_c4,sk_c5) = identity. [para(34617(b,1),593(a,1,2))].
% 239.16/239.47 34714 inverse(sk_c7) = sk_c2 | multiply(sk_c7,A) = A. [para(34663(a,1),53(a,1,1)),rewrite([1(8)])].
% 239.16/239.47 35188 inverse(sk_c2) = sk_c7 | multiply(sk_c6,sk_c4) = sk_c4. [para(34685(b,1),76(b,1,2)),rewrite([522(11)]),flip(c),merge(b)].
% 239.16/239.47 35194 inverse(sk_c2) = sk_c7 | multiply(A,sk_c6) = A. [para(34688(b,1),77(b,1,2)),rewrite([522(10)]),flip(c),merge(b)].
% 239.16/239.47 35198 inverse(sk_c7) = sk_c2 | multiply(sk_c3,A) = A. [para(34714(b,1),722(b,1,2)),merge(b)].
% 239.16/239.47 35449 inverse(sk_c2) = sk_c7 | multiply(A,sk_c4) = A. [para(35188(b,1),573(b,1,2)),merge(b)].
% 239.16/239.47 35505 inverse(sk_c2) = sk_c7 | inverse(sk_c5) = sk_c3. [para(35194(b,1),2550(b,1)),merge(b)].
% 239.16/239.47 35569 inverse(sk_c5) = sk_c3 | inverse(sk_c7) = sk_c2. [para(35505(a,1),639(a,1,1))].
% 239.16/239.47 35613 inverse(sk_c7) = sk_c2 | inverse(sk_c3) = sk_c5. [para(35569(a,1),639(a,1,1))].
% 239.16/239.47 35620 inverse(sk_c7) = sk_c2 | inverse(sk_c3) = identity. [para(35198(b,1),593(a,1))].
% 239.16/239.47 35626 inverse(sk_c7) = sk_c2 | identity = sk_c5. [para(35620(b,1),35613(b,1)),merge(b)].
% 239.16/239.47 35637 identity = sk_c5 | multiply(sk_c2,sk_c7) = identity. [para(35626(a,1),2(a,1,1))].
% 239.16/239.47 35642 identity = sk_c5 | sk_c3 = sk_c2. [para(35626(a,1),8025(a,1)),flip(b),merge(c)].
% 239.16/239.47 35649 sk_c3 = sk_c2 | inverse(sk_c5) = identity. [para(35642(a,1),525(a,1,1))].
% 239.16/239.47 35874 inverse(sk_c2) = sk_c7 | inverse(sk_c4) = identity. [para(35449(b,1),2(a,1))].
% 239.16/239.47 35918 inverse(sk_c2) = sk_c7 | multiply(sk_c4,A) = A. [para(35874(b,1),53(a,1,1)),rewrite([1(8)])].
% 239.16/239.47 36172 inverse(sk_c2) = sk_c7 | multiply(sk_c6,A) = A. [para(35918(b,1),497(b,1,2)),merge(b)].
% 239.16/239.47 36432 multiply(sk_c6,inverse(sk_c7)) = inverse(sk_c3) | identity = sk_c6. [para(1827(a,1),8921(b,1)),flip(c),merge(c)].
% 239.16/239.47 36452 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c6. [para(1828(a,1),8921(b,1)),flip(c),merge(c)].
% 239.16/239.47 36568 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c5. [para(1834(a,1),35637(b,1)),flip(c),merge(c)].
% 239.16/239.47 38807 identity = sk_c7 | sk_c3 = sk_c2. [para(34304(c,1),35649(b,1)),flip(d),merge(c),merge(d)].
% 239.16/239.47 38810 sk_c3 = sk_c2 | inverse(sk_c7) = identity. [para(38807(a,1),525(a,1,1))].
% 239.16/239.47 38915 sk_c3 = sk_c2 | inverse(sk_c7) = sk_c7. [para(38807(a,1),38810(b,2)),merge(b)].
% 239.16/239.47 38963 sk_c3 = sk_c2 | multiply(sk_c7,sk_c7) = identity. [para(38915(b,1),2(a,1,1))].
% 239.16/239.47 39126 sk_c3 = sk_c2 | multiply(sk_c7,sk_c7) = sk_c5. [para(35642(a,1),38963(b,2)),merge(b)].
% 239.16/239.47 39901 inverse(sk_c2) = sk_c7 | inverse(sk_c3) = sk_c4. [para(34376(b,1),36172(b,1)),merge(b)].
% 239.16/239.47 39904 inverse(sk_c2) = sk_c7 | inverse(sk_c4) = sk_c3. [para(39901(b,1),639(a,1,1))].
% 239.16/239.47 39910 inverse(sk_c2) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c5. [para(39904(b,1),509(b,1,1)),merge(b)].
% 239.16/239.47 39964 inverse(sk_c2) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6. [para(39910(b,1),496(b,1,2)),merge(b)].
% 239.16/239.47 41388 identity = sk_c6 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(7468(a,1),36432(a,1,2)),merge(c)].
% 239.16/239.47 41389 identity = sk_c6 | multiply(sk_c6,inverse(sk_c7)) = sk_c7. [para(7471(b,1),36432(a,2)),merge(c)].
% 239.16/239.47 41423 identity = sk_c6 | multiply(sk_c6,sk_c3) = sk_c7. [para(7471(b,1),41388(b,2)),merge(b)].
% 239.16/239.47 41446 identity = sk_c6 | multiply(sk_c4,sk_c7) = sk_c3. [para(41423(b,1),7773(b,1,2)),merge(b)].
% 239.16/239.47 41450 identity = sk_c6 | multiply(sk_c4,sk_c7) = inverse(sk_c7). [para(41389(b,1),7773(b,1,2)),merge(b)].
% 239.16/239.47 41637 identity = sk_c6 | multiply(sk_c5,sk_c4) = inverse(sk_c4). [para(7766(a,1),36452(a,1,2)),merge(c)].
% 239.16/239.47 41643 identity = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(7774(b,1),41637(b,2)),merge(b)].
% 239.16/239.47 41644 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = sk_c4. [para(41643(b,1),53(a,1,2))].
% 239.16/239.47 41666 identity = sk_c6 | inverse(sk_c7) = sk_c4. [para(41644(b,1),9936(b,1)),flip(c),merge(b)].
% 239.16/239.47 41706 identity = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(41666(b,1),2(a,1,1))].
% 239.16/239.47 41973 identity = sk_c6 | identity = sk_c3. [para(41706(b,1),41446(b,1)),merge(b)].
% 239.16/239.47 41976 identity = sk_c6 | inverse(sk_c7) = identity. [para(41706(b,1),41450(b,1)),flip(c),merge(b)].
% 239.16/239.47 41993 identity = sk_c6 | inverse(sk_c3) = identity. [para(41973(b,1),525(a,1,1))].
% 239.16/239.47 42090 identity = sk_c6 | inverse(sk_c3) = sk_c6. [para(41976(b,1),36432(a,1,2)),rewrite([522(6)]),flip(b),merge(c)].
% 239.16/239.47 42264 identity = sk_c6. [para(42090(b,1),41993(b,1)),flip(c),merge(b),merge(c)].
% 239.16/239.47 43286 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | sk_c5 = sk_c6. [back_rewrite(36568),rewrite([42264(8)]),flip(b)].
% 239.16/239.47 45666 sk_c6 != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | multiply(inverse(sk_c6),sk_c7) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != A | multiply(inverse(A),sk_c5) != sk_c6. [back_rewrite(13367),rewrite([42264(4)]),merge(b)].
% 239.16/239.47 46587 inverse(sk_c6) = sk_c4 | sk_c5 = sk_c6. [back_rewrite(8359),rewrite([42264(5)]),flip(b)].
% 239.16/239.47 47036 inverse(sk_c6) = sk_c6. [back_rewrite(525),rewrite([42264(1),42264(3)])].
% 239.16/239.47 47037 multiply(A,sk_c6) = A. [back_rewrite(522),rewrite([42264(1)])].
% 239.16/239.47 47038 multiply(inverse(A),A) = sk_c6. [back_rewrite(2),rewrite([42264(3)])].
% 239.16/239.47 47039 multiply(sk_c6,A) = A. [back_rewrite(1),rewrite([42264(1)])].
% 239.16/239.47 47350 sk_c6 != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | sk_c5 != sk_c7 | multiply(inverse(sk_c7),sk_c5) != sk_c6. [factor(45666,a,e),rewrite([47036(10),47039(11),47039(14)]),flip(c),flip(d),merge(d)].
% 239.16/239.47 47362 sk_c4 = sk_c6 | sk_c5 = sk_c6. [back_rewrite(46587),rewrite([47036(2)]),flip(a)].
% 239.16/239.47 47416 inverse(sk_c4) = sk_c5 | sk_c5 = sk_c6. [back_rewrite(43286),rewrite([47036(3),47037(3)]),flip(a)].
% 239.16/239.47 47523 multiply(sk_c7,sk_c5) = sk_c6 | sk_c5 = sk_c7. [back_rewrite(513),rewrite([47036(7),47039(8)])].
% 239.16/239.47 48529 sk_c5 = sk_c6. [para(47362(a,1),47416(a,1,1)),rewrite([47036(5)]),flip(b),merge(b),merge(c)].
% 239.16/239.47 48879 sk_c6 = sk_c7. [back_rewrite(47523),rewrite([48529(2),47037(3),48529(4)]),flip(a),merge(b)].
% 239.16/239.47 48976 multiply(sk_c7,sk_c7) != sk_c7. [back_rewrite(47350),rewrite([48879(1),48529(5),48879(5),48879(7),48529(9),48879(9),48529(14),48879(14),47038(15),48879(12),48879(13)]),xx(a),xx(c),xx(d)].
% 239.16/239.47 49089 inverse(sk_c2) = sk_c7. [back_rewrite(39964),rewrite([48529(6),48879(6),48879(8)]),unit_del(b,48976)].
% 239.16/239.47 49092 sk_c3 = sk_c2. [back_rewrite(39126),rewrite([48529(7),48879(7)]),unit_del(b,48976)].
% 239.16/239.47 49206 sk_c2 = sk_c1. [back_rewrite(32671),rewrite([48529(4),48879(4),48529(5),48879(5),49092(7),49089(8)]),unit_del(b,48976)].
% 239.16/239.47 49291 inverse(sk_c1) = sk_c7. [back_rewrite(14395),rewrite([48529(5),48879(5),48529(6),48879(6)]),unit_del(b,48976)].
% 239.16/239.47 49306 multiply(sk_c1,sk_c7) = multiply(sk_c7,sk_c7). [back_rewrite(4697),rewrite([48529(2),48879(2),48879(4),49092(6),49206(6),48529(7),48879(7)]),unit_del(a,48976)].
% 239.16/239.47 49315 $F. [back_rewrite(517),rewrite([49206(1),49306(3),48529(4),48879(4),49092(6),49206(6),49291(7),48879(9)]),merge(b),unit_del(a,48976)].
% 239.16/239.47
% 239.16/239.47 % SZS output end Refutation
% 239.16/239.47 ============================== end of proof ==========================
% 239.16/239.47
% 239.16/239.47 ============================== STATISTICS ============================
% 239.16/239.47
% 239.16/239.47 Given=10143. Generated=11537307. Kept=49314. proofs=1.
% 239.16/239.47 Usable=853. Sos=1205. Demods=25. Limbo=786, Disabled=46499. Hints=0.
% 239.16/239.47 Megabytes=40.91.
% 239.16/239.47 User_CPU=232.27, System_CPU=6.22, Wall_clock=238.
% 239.16/239.47
% 239.16/239.47 ============================== end of statistics =====================
% 239.16/239.47
% 239.16/239.47 ============================== end of search =========================
% 239.16/239.47
% 239.16/239.47 THEOREM PROVED
% 239.16/239.47 % SZS status Unsatisfiable
% 239.16/239.47
% 239.16/239.47 Exiting with 1 proof.
% 239.16/239.47
% 239.16/239.47 Process 22657 exit (max_proofs) Tue Jun 14 13:22:36 2022
% 239.16/239.47 Prover9 interrupted
%------------------------------------------------------------------------------