TSTP Solution File: GRP376-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP376-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 11:18:49 EDT 2022
% Result : Unsatisfiable 51.05s 51.34s
% Output : Refutation 51.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP376-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:50:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 51.05/51.34 ============================== Prover9 ===============================
% 51.05/51.34 Prover9 (32) version 2009-11A, November 2009.
% 51.05/51.34 Process 3805 was started by sandbox2 on n023.cluster.edu,
% 51.05/51.34 Mon Jun 13 13:50:51 2022
% 51.05/51.34 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3652_n023.cluster.edu".
% 51.05/51.34 ============================== end of head ===========================
% 51.05/51.34
% 51.05/51.34 ============================== INPUT =================================
% 51.05/51.34
% 51.05/51.34 % Reading from file /tmp/Prover9_3652_n023.cluster.edu
% 51.05/51.34
% 51.05/51.34 set(prolog_style_variables).
% 51.05/51.34 set(auto2).
% 51.05/51.34 % set(auto2) -> set(auto).
% 51.05/51.34 % set(auto) -> set(auto_inference).
% 51.05/51.34 % set(auto) -> set(auto_setup).
% 51.05/51.34 % set(auto_setup) -> set(predicate_elim).
% 51.05/51.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 51.05/51.34 % set(auto) -> set(auto_limits).
% 51.05/51.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 51.05/51.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 51.05/51.34 % set(auto) -> set(auto_denials).
% 51.05/51.34 % set(auto) -> set(auto_process).
% 51.05/51.34 % set(auto2) -> assign(new_constants, 1).
% 51.05/51.34 % set(auto2) -> assign(fold_denial_max, 3).
% 51.05/51.34 % set(auto2) -> assign(max_weight, "200.000").
% 51.05/51.34 % set(auto2) -> assign(max_hours, 1).
% 51.05/51.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 51.05/51.34 % set(auto2) -> assign(max_seconds, 0).
% 51.05/51.34 % set(auto2) -> assign(max_minutes, 5).
% 51.05/51.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 51.05/51.34 % set(auto2) -> set(sort_initial_sos).
% 51.05/51.34 % set(auto2) -> assign(sos_limit, -1).
% 51.05/51.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 51.05/51.34 % set(auto2) -> assign(max_megs, 400).
% 51.05/51.34 % set(auto2) -> assign(stats, some).
% 51.05/51.34 % set(auto2) -> clear(echo_input).
% 51.05/51.34 % set(auto2) -> set(quiet).
% 51.05/51.34 % set(auto2) -> clear(print_initial_clauses).
% 51.05/51.34 % set(auto2) -> clear(print_given).
% 51.05/51.34 assign(lrs_ticks,-1).
% 51.05/51.34 assign(sos_limit,10000).
% 51.05/51.34 assign(order,kbo).
% 51.05/51.34 set(lex_order_vars).
% 51.05/51.34 clear(print_given).
% 51.05/51.34
% 51.05/51.34 % formulas(sos). % not echoed (34 formulas)
% 51.05/51.34
% 51.05/51.34 ============================== end of input ==========================
% 51.05/51.34
% 51.05/51.34 % From the command line: assign(max_seconds, 300).
% 51.05/51.34
% 51.05/51.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 51.05/51.34
% 51.05/51.34 % Formulas that are not ordinary clauses:
% 51.05/51.34
% 51.05/51.34 ============================== end of process non-clausal formulas ===
% 51.05/51.34
% 51.05/51.34 ============================== PROCESS INITIAL CLAUSES ===============
% 51.05/51.34
% 51.05/51.34 ============================== PREDICATE ELIMINATION =================
% 51.05/51.34
% 51.05/51.34 ============================== end predicate elimination =============
% 51.05/51.34
% 51.05/51.34 Auto_denials: (non-Horn, no changes).
% 51.05/51.34
% 51.05/51.34 Term ordering decisions:
% 51.05/51.34
% 51.05/51.34 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 51.05/51.34 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c5=1. sk_c3=1. sk_c4=1. sk_c1=1. sk_c2=1. identity=1. multiply=1. inverse=0.
% 51.05/51.34
% 51.05/51.34 ============================== end of process initial clauses ========
% 51.05/51.34
% 51.05/51.34 ============================== CLAUSES FOR SEARCH ====================
% 51.05/51.34
% 51.05/51.34 ============================== end of clauses for search =============
% 51.05/51.34
% 51.05/51.34 ============================== SEARCH ================================
% 51.05/51.34
% 51.05/51.34 % Starting search at 0.02 seconds.
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=46.000, iters=3575
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=43.000, iters=3398
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=42.000, iters=3334
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=41.000, iters=3341
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=40.000, iters=3376
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=39.000, iters=3339
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=38.000, iters=3354
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=37.000, iters=3576
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=36.000, iters=3340
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=35.000, iters=3449
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=34.000, iters=3355
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=33.000, iters=3345
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=31.000, iters=3503
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=28.000, iters=3405
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=17.000, iters=3344
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=16.000, iters=3546
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=15.000, iters=3336
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=14.000, iters=3333
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=13.000, iters=3339
% 51.05/51.34
% 51.05/51.34 Low Water (displace): id=18565, wt=12.000
% 51.05/51.34
% 51.05/51.34 Low Water (displace): id=18596, wt=11.000
% 51.05/51.34
% 51.05/51.34 Low Water (keep): wt=12.000, iters=3335
% 51.05/51.34
% 51.05/51.34 ============================== PROOF =================================
% 51.05/51.34 % SZS status Unsatisfiable
% 51.05/51.34 % SZS output start Refutation
% 51.05/51.34
% 51.05/51.34 % Proof 1 at 49.09 (+ 1.27) seconds.
% 51.05/51.34 % Length of proof is 265.
% 51.05/51.34 % Level of proof is 35.
% 51.05/51.34 % Maximum clause weight is 50.000.
% 51.05/51.34 % Given clauses 5132.
% 51.05/51.34
% 51.05/51.34 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 51.05/51.34 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 51.05/51.34 3 inverse(sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 51.05/51.34 4 inverse(sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 51.05/51.34 5 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 51.05/51.34 6 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 51.05/51.34 7 inverse(sk_c2) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 51.05/51.34 8 inverse(sk_c2) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 51.05/51.34 9 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 51.05/51.34 10 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 51.05/51.34 11 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 51.05/51.34 12 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 51.05/51.34 13 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 51.05/51.34 14 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 51.05/51.34 15 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 51.05/51.34 16 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 51.05/51.34 17 multiply(sk_c5,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 51.05/51.34 18 multiply(sk_c5,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 51.05/51.34 19 multiply(sk_c2,sk_c5) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 51.05/51.34 20 multiply(sk_c2,sk_c5) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 51.05/51.34 21 inverse(sk_c2) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 51.05/51.34 22 inverse(sk_c2) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 51.05/51.34 23 inverse(sk_c2) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 51.05/51.34 24 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 51.05/51.34 25 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 51.05/51.34 27 multiply(sk_c5,sk_c6) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 51.05/51.34 29 multiply(sk_c5,sk_c6) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 51.05/51.34 32 multiply(sk_c2,sk_c5) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 51.05/51.34 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 51.05/51.34 34 inverse(sk_c7) != sk_c6 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(B,sk_c5) != sk_c7 | inverse(B) != sk_c5 | 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_31) # label(negated_conjecture). [assumption].
% 51.05/51.34 42 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 51.05/51.34 43 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 51.05/51.34 44 inverse(sk_c3) = sk_c7 | multiply(sk_c7,sk_c1) = identity. [para(5(a,1),2(a,1,1))].
% 51.05/51.34 48 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 51.05/51.34 49 inverse(sk_c7) = sk_c6 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(9(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 50 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 51 inverse(sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(10(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 52 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 53 inverse(sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(11(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 54 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(11(b,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 55 inverse(sk_c3) = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(12(a,1),33(a,1,1)),flip(b)].
% 51.05/51.34 56 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(12(a,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 58 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(13(a,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 62 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(15(b,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 63 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(16(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 65 inverse(sk_c3) = sk_c7 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(17(a,1),33(a,1,1)),flip(b)].
% 51.05/51.34 69 inverse(sk_c3) = sk_c7 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(19(a,1),33(a,1,1)),flip(b)].
% 51.05/51.34 70 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c2,sk_c5)) = multiply(A,sk_c7). [para(19(a,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 72 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c2,sk_c5)) = multiply(A,sk_c7). [para(20(a,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 74 inverse(sk_c2) = sk_c5 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(21(b,1),33(a,2,2)),rewrite([33(8)])].
% 51.05/51.34 75 inverse(sk_c2) = sk_c5 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(22(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 79 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(24(a,1),33(a,1,1)),flip(b)].
% 51.05/51.34 82 multiply(sk_c3,sk_c6) = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(25(a,1),33(a,2,2)),rewrite([33(9)])].
% 51.05/51.34 85 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(27(a,1),33(a,1,1)),flip(b)].
% 51.05/51.34 111 inverse(sk_c7) != sk_c6 | sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(1(a,1),34(b,1)),flip(b)].
% 51.05/51.34 168 inverse(sk_c7) != sk_c6 | sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [factor(111,c,h),rewrite([1(31)]),merge(h)].
% 51.05/51.34 308 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),48(a,1,2))].
% 51.05/51.34 309 inverse(sk_c7) = sk_c6 | multiply(sk_c6,multiply(sk_c4,A)) = A. [para(4(b,1),48(a,1,1))].
% 51.05/51.34 312 inverse(sk_c3) = sk_c7 | multiply(sk_c5,multiply(sk_c2,A)) = A. [para(7(a,1),48(a,1,1))].
% 51.05/51.34 314 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(9(b,1),48(a,1,2))].
% 51.05/51.34 315 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(10(b,1),48(a,1,2))].
% 51.05/51.34 322 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(17(a,1),48(a,1,2))].
% 51.05/51.34 323 inverse(sk_c4) = sk_c6 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(18(a,1),48(a,1,2))].
% 51.05/51.34 337 multiply(sk_c4,sk_c5) = sk_c6 | multiply(inverse(sk_c2),sk_c7) = sk_c5. [para(32(a,1),48(a,1,2))].
% 51.05/51.34 339 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c7),identity) = sk_c3. [para(42(b,1),48(a,1,2))].
% 51.05/51.34 340 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(48(a,1),48(a,1,2))].
% 51.05/51.34 341 multiply(A,identity) = A. [back_rewrite(308),rewrite([340(4)])].
% 51.05/51.34 342 inverse(sk_c7) = sk_c6 | inverse(sk_c7) = sk_c3. [back_rewrite(339),rewrite([341(8)])].
% 51.05/51.34 344 inverse(identity) = identity. [para(341(a,1),2(a,1))].
% 51.05/51.34 373 inverse(sk_c7) != sk_c6 | sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(A,sk_c5) != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [back_rewrite(168),rewrite([344(9)])].
% 51.05/51.34 377 inverse(sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(342(b,1),48(a,1,1))].
% 51.05/51.34 378 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(43(b,1),33(a,2,2)),rewrite([33(8),341(10)])].
% 51.05/51.34 379 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c4. [para(43(b,1),48(a,1,2)),rewrite([341(8)])].
% 51.05/51.34 380 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c6) = identity. [para(379(b,1),2(a,1,1))].
% 51.05/51.34 381 inverse(sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(379(b,1),48(a,1,1))].
% 51.05/51.34 382 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c7,sk_c1)) = A. [para(44(b,1),33(a,2,2)),rewrite([33(8),341(10)])].
% 51.05/51.34 424 inverse(sk_c7) = sk_c6 | multiply(sk_c5,sk_c3) = sk_c6. [para(42(b,1),49(b,1,2)),rewrite([341(11)]),flip(c),merge(b)].
% 51.05/51.34 425 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c5,A)) = multiply(sk_c7,A). [para(49(b,1),48(a,1,2))].
% 51.05/51.34 441 multiply(A,inverse(A)) = identity. [para(340(a,1),2(a,1))].
% 51.05/51.34 468 multiply(A,multiply(inverse(A),B)) = B. [para(340(a,1),48(a,1))].
% 51.05/51.34 469 inverse(inverse(A)) = A. [para(340(a,1),341(a,1)),rewrite([341(2)]),flip(a)].
% 51.05/51.34 500 inverse(sk_c3) = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(5(a,1),441(a,1,2))].
% 51.05/51.34 501 inverse(sk_c4) = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(6(a,1),441(a,1,2))].
% 51.05/51.34 502 inverse(sk_c3) = sk_c7 | multiply(sk_c2,sk_c5) = identity. [para(7(a,1),441(a,1,2))].
% 51.05/51.34 503 inverse(sk_c4) = sk_c6 | multiply(sk_c2,sk_c5) = identity. [para(8(a,1),441(a,1,2))].
% 51.05/51.34 504 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(441(a,1),33(a,1)),flip(a)].
% 51.05/51.34 524 inverse(sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [para(11(b,1),50(b,2)),merge(b)].
% 51.05/51.34 558 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c4) = sk_c3. [para(43(b,1),51(b,1,2)),rewrite([341(11)]),flip(c),merge(b)].
% 51.05/51.34 560 inverse(sk_c7) = sk_c6 | multiply(sk_c7,inverse(sk_c6)) = sk_c3. [para(441(a,1),51(b,1,2)),rewrite([341(7)]),flip(b)].
% 51.05/51.34 593 inverse(sk_c7) = sk_c6 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(9(b,1),52(b,2)),merge(b)].
% 51.05/51.34 617 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c4,sk_c6)) = A. [para(380(b,1),33(a,2,2)),rewrite([33(8),341(10)])].
% 51.05/51.34 621 inverse(sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c5,sk_c7)) = sk_c5. [para(9(b,1),53(b,2)),merge(b)].
% 51.05/51.34 624 inverse(sk_c7) = sk_c6 | multiply(sk_c4,multiply(sk_c5,sk_c4)) = identity. [para(43(b,1),53(b,2)),merge(b)].
% 51.05/51.34 662 inverse(sk_c7) != sk_c6 | sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6. [para(2(a,1),373(e,1)),rewrite([469(21)]),xx(f),merge(e)].
% 51.05/51.34 672 inverse(sk_c7) != sk_c6 | sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c6 | sk_c5 != sk_c6. [para(1(a,1),662(g,1)),rewrite([344(22)])].
% 51.05/51.34 682 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c3). [para(424(b,1),53(b,1,2)),merge(b)].
% 51.05/51.34 683 inverse(sk_c3) = sk_c7 | identity = sk_c6. [para(500(b,1),12(a,1)),merge(c)].
% 51.05/51.34 685 identity = sk_c6 | multiply(sk_c7,sk_c3) = identity. [para(683(a,1),2(a,1,1))].
% 51.05/51.34 687 identity = sk_c6 | inverse(sk_c7) = sk_c3. [para(683(a,1),469(a,1,1))].
% 51.05/51.34 688 identity = sk_c6 | multiply(sk_c3,sk_c7) = identity. [para(683(a,1),441(a,1,2))].
% 51.05/51.34 692 inverse(sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c4,sk_c5)) = sk_c7. [para(10(b,1),54(b,2)),merge(b)].
% 51.05/51.34 722 identity = sk_c6 | multiply(A,multiply(sk_c7,sk_c3)) = A. [para(685(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 51.05/51.34 723 identity = sk_c6 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(688(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 51.05/51.34 724 inverse(sk_c4) = sk_c6 | identity = sk_c6. [para(501(b,1),13(a,1)),merge(c)].
% 51.05/51.34 729 inverse(sk_c3) = sk_c7 | multiply(sk_c6,inverse(sk_c7)) = sk_c1. [para(441(a,1),55(b,1,2)),rewrite([341(7)]),flip(b)].
% 51.05/51.34 785 identity = sk_c6 | multiply(sk_c6,multiply(sk_c4,A)) = A. [para(724(a,1),48(a,1,1))].
% 51.05/51.34 786 identity = sk_c6 | inverse(sk_c6) = sk_c4. [para(724(a,1),469(a,1,1))].
% 51.05/51.34 788 identity = sk_c6 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(724(a,1),468(a,1,2,1))].
% 51.05/51.34 800 inverse(sk_c3) = sk_c7 | multiply(A,sk_c6) = A. [para(500(b,1),56(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 51.05/51.34 860 inverse(sk_c3) = sk_c7 | identity = sk_c7. [para(502(b,1),19(a,1)),merge(c)].
% 51.05/51.34 874 identity = sk_c7 | inverse(sk_c7) = sk_c3. [para(860(a,1),469(a,1,1))].
% 51.05/51.34 958 inverse(sk_c4) = sk_c6 | identity = sk_c7. [para(503(b,1),20(a,1)),merge(c)].
% 51.05/51.34 973 identity = sk_c7 | inverse(sk_c6) = sk_c4. [para(958(a,1),469(a,1,1))].
% 51.05/51.34 980 inverse(sk_c4) = sk_c6 | multiply(A,sk_c6) = A. [para(501(b,1),58(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 51.05/51.34 1462 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c7),sk_c3) = sk_c4. [para(558(b,1),48(a,1,2))].
% 51.05/51.34 1480 inverse(sk_c3) = sk_c7 | inverse(sk_c6) = identity. [para(800(b,1),2(a,1))].
% 51.05/51.34 1519 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(14(b,1),62(b,2)),merge(b)].
% 51.05/51.34 1629 inverse(sk_c6) = identity | inverse(sk_c7) = sk_c3. [para(1480(a,1),469(a,1,1))].
% 51.05/51.34 1757 inverse(sk_c4) = sk_c6 | inverse(sk_c6) = identity. [para(980(b,1),2(a,1))].
% 51.05/51.34 1850 inverse(sk_c6) = identity | inverse(sk_c6) = sk_c4. [para(1757(a,1),469(a,1,1))].
% 51.05/51.34 1962 inverse(sk_c6) = sk_c4 | multiply(sk_c6,A) = A. [para(1850(a,1),48(a,1,1)),rewrite([1(8)])].
% 51.05/51.34 2293 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c7. [para(379(b,1),314(b,1,1)),merge(b)].
% 51.05/51.34 2530 inverse(sk_c7) = sk_c6 | sk_c6 = sk_c7. [para(2293(b,1),11(b,1)),flip(c),merge(b)].
% 51.05/51.34 2533 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c4),sk_c7) = sk_c5. [para(2293(b,1),48(a,1,2))].
% 51.05/51.34 2537 sk_c6 = sk_c7 | inverse(sk_c6) = sk_c7. [para(2530(a,1),469(a,1,1))].
% 51.05/51.34 2550 sk_c6 = sk_c7 | identity = sk_c6 | sk_c4 = sk_c7. [para(2537(b,1),786(b,1)),flip(c)].
% 51.05/51.34 2551 sk_c6 = sk_c7 | identity = sk_c7 | sk_c4 = sk_c7. [para(2537(b,1),973(b,1)),flip(c)].
% 51.05/51.34 3123 sk_c6 = sk_c7 | sk_c4 = sk_c7. [para(2551(b,1),2550(b,1)),flip(d),merge(c),merge(d),merge(e)].
% 51.05/51.34 3126 sk_c6 = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6. [para(3123(b,1),29(b,1,1))].
% 51.05/51.34 3156 inverse(sk_c3) = sk_c7 | multiply(A,sk_c7) = A. [para(502(b,1),70(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 51.05/51.34 3368 inverse(sk_c3) = sk_c7 | identity = sk_c1. [para(3156(b,1),500(b,1)),flip(c),merge(b)].
% 51.05/51.34 3429 identity = sk_c1 | inverse(sk_c7) = sk_c3. [para(3368(a,1),469(a,1,1))].
% 51.05/51.34 3609 inverse(sk_c4) = sk_c6 | multiply(A,sk_c7) = A. [para(503(b,1),72(b,1,2)),rewrite([341(10)]),flip(c),merge(b)].
% 51.05/51.34 4178 inverse(sk_c2) = sk_c5 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [para(23(b,1),74(b,2)),merge(b)].
% 51.05/51.34 4899 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(b,1),315(b,1,1)),merge(b)].
% 51.05/51.34 4903 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(4899(b,1),48(a,1,2))].
% 51.05/51.34 5131 inverse(sk_c3) = sk_c7 | inverse(sk_c5) = sk_c6. [para(322(b,1),3156(b,1)),flip(c),merge(b)].
% 51.05/51.34 5134 inverse(sk_c5) = sk_c6 | inverse(sk_c7) = sk_c3. [para(5131(a,1),469(a,1,1))].
% 51.05/51.34 5140 inverse(sk_c7) = sk_c3 | inverse(sk_c6) = sk_c5. [para(5134(a,1),469(a,1,1))].
% 51.05/51.34 5232 inverse(sk_c7) = sk_c3 | identity = sk_c5. [para(5140(b,1),1629(a,1)),flip(b),merge(c)].
% 51.05/51.34 5233 identity = sk_c5 | multiply(sk_c3,sk_c7) = identity. [para(5232(a,1),2(a,1,1))].
% 51.05/51.34 5236 identity = sk_c5 | multiply(sk_c7,sk_c3) = identity. [para(5232(a,1),441(a,1,2))].
% 51.05/51.34 5377 identity = sk_c5 | multiply(A,multiply(sk_c3,sk_c7)) = A. [para(5233(b,1),33(a,2,2)),rewrite([33(7),341(9)])].
% 51.05/51.34 5401 multiply(sk_c3,sk_c6) = sk_c7 | multiply(inverse(multiply(sk_c1,sk_c7)),sk_c6) = identity. [para(82(b,1),2(a,1))].
% 51.05/51.34 5504 identity = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = sk_c1. [para(5236(b,1),79(b,1,2)),rewrite([341(11)]),flip(c)].
% 51.05/51.34 5709 inverse(sk_c4) = sk_c6 | inverse(sk_c5) = sk_c6. [para(323(b,1),3609(b,1)),flip(c),merge(b)].
% 51.05/51.34 5712 inverse(sk_c5) = sk_c6 | inverse(sk_c6) = sk_c4. [para(5709(a,1),469(a,1,1))].
% 51.05/51.34 5716 inverse(sk_c6) = sk_c4 | multiply(sk_c6,sk_c5) = identity. [para(5712(a,1),2(a,1,1))].
% 51.05/51.34 6010 inverse(sk_c6) = sk_c4 | identity = sk_c5. [para(5716(b,1),1962(b,1)),merge(b)].
% 51.05/51.34 6022 identity = sk_c5 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(6010(a,1),48(a,1,1))].
% 51.05/51.34 6023 identity = sk_c5 | inverse(sk_c4) = sk_c6. [para(6010(a,1),469(a,1,1))].
% 51.05/51.34 6024 identity = sk_c5 | multiply(sk_c6,sk_c4) = identity. [para(6010(a,1),441(a,1,2))].
% 51.05/51.34 6125 identity = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c7,sk_c4) = sk_c5. [para(6024(b,1),85(b,1,2)),rewrite([341(11)]),flip(c)].
% 51.05/51.34 6357 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(504(a,1),48(a,1,2)),rewrite([341(3)]),flip(a)].
% 51.05/51.34 6463 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(6357(a,1),48(a,1,2)),flip(a)].
% 51.05/51.34 6663 multiply(sk_c3,sk_c6) = sk_c7 | multiply(inverse(sk_c7),multiply(inverse(sk_c1),sk_c6)) = identity. [back_rewrite(5401),rewrite([6463(9),33(12)])].
% 51.05/51.34 7957 identity = sk_c6 | multiply(inverse(sk_c7),inverse(sk_c3)) = identity. [para(723(b,1),2(a,1)),rewrite([6463(7)])].
% 51.05/51.34 7977 inverse(sk_c3) = sk_c7 | multiply(sk_c5,sk_c1) = identity. [para(729(b,1),65(b,1,2)),rewrite([441(15)]),merge(b)].
% 51.05/51.34 8107 inverse(sk_c3) = sk_c7 | multiply(sk_c7,sk_c1) = sk_c2. [para(7977(b,1),69(b,1,2)),rewrite([341(11)]),flip(c),merge(b)].
% 51.05/51.34 8313 inverse(sk_c3) = sk_c7 | identity = sk_c2. [para(8107(b,1),44(b,1)),flip(c),merge(b)].
% 51.05/51.34 8318 identity = sk_c2 | inverse(sk_c7) = sk_c3. [para(8313(a,1),469(a,1,1))].
% 51.05/51.34 8572 identity = sk_c6 | multiply(sk_c6,sk_c4) = multiply(sk_c7,sk_c3). [para(722(b,1),785(b,1,2)),merge(b)].
% 51.05/51.34 10440 identity = sk_c5 | multiply(inverse(sk_c7),inverse(sk_c3)) = identity. [para(5377(b,1),2(a,1)),rewrite([6463(7)])].
% 51.05/51.34 11049 identity = sk_c6 | multiply(A,multiply(sk_c6,sk_c4)) = multiply(A,multiply(sk_c7,sk_c3)). [para(8572(b,1),33(a,2,2)),rewrite([33(7)])].
% 51.05/51.34 13418 inverse(sk_c3) = sk_c7 | multiply(sk_c5,sk_c2) = sk_c6. [para(800(b,1),312(b,1,2)),merge(b)].
% 51.05/51.34 13559 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c3) = inverse(sk_c6). [para(560(b,1),377(b,1,2)),merge(b)].
% 51.05/51.34 13603 inverse(sk_c3) = sk_c7 | multiply(A,sk_c2) = A. [para(8107(b,1),382(b,1,2)),merge(b)].
% 51.05/51.34 13630 inverse(sk_c3) = sk_c7 | sk_c5 = sk_c6. [para(13603(b,1),13418(b,1)),merge(b)].
% 51.05/51.34 13631 sk_c5 = sk_c6 | multiply(sk_c7,sk_c3) = identity. [para(13630(a,1),2(a,1,1))].
% 51.05/51.34 13671 sk_c5 = sk_c6 | inverse(sk_c2) = sk_c5 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = identity. [para(13631(b,1),75(b,2))].
% 51.05/51.34 17723 inverse(sk_c7) = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(624(b,1),309(b,1,2)),rewrite([341(11)]),flip(c),merge(b)].
% 51.05/51.34 17739 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c4) = identity. [para(17723(b,1),425(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 51.05/51.34 17747 inverse(sk_c7) = sk_c6 | inverse(sk_c7) = sk_c4. [para(17739(b,1),48(a,1,2)),rewrite([341(8)])].
% 51.05/51.34 18010 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c3) = sk_c4. [para(17747(b,1),1462(b,1,1)),merge(b)].
% 51.05/51.34 18011 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c6) = sk_c7. [para(17747(b,1),4903(b,1,1)),merge(b)].
% 51.05/51.34 18419 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c4) = sk_c3. [para(18010(b,1),309(b,1,2)),merge(b)].
% 51.05/51.34 18423 inverse(sk_c7) = sk_c6 | identity = sk_c7. [para(18011(b,1),380(b,1)),flip(c),merge(b)].
% 51.05/51.34 18475 inverse(sk_c7) = sk_c6 | multiply(A,sk_c7) = A. [para(18011(b,1),617(b,1,2)),merge(b)].
% 51.05/51.34 18489 identity = sk_c7 | sk_c3 = sk_c6. [para(18423(a,1),874(b,1)),flip(c),merge(b)].
% 51.05/51.34 18499 sk_c3 = sk_c6 | inverse(sk_c7) = identity. [para(18489(a,1),344(a,1,1))].
% 51.05/51.34 19596 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c3) = identity. [para(682(b,1),380(b,1)),merge(b)].
% 51.05/51.34 20718 inverse(sk_c7) = sk_c6 | multiply(A,sk_c3) = A. [para(18419(b,1),378(b,1,2)),merge(b)].
% 51.05/51.34 20735 inverse(sk_c7) = sk_c6 | inverse(sk_c4) = sk_c5. [para(18475(b,1),2533(b,1)),merge(b)].
% 51.05/51.34 20762 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c6) = sk_c6. [para(18475(b,1),524(b,1,2)),merge(b)].
% 51.05/51.34 20770 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c5. [para(18475(b,1),621(b,1,2)),merge(b)].
% 51.05/51.34 20896 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = identity. [para(20735(b,1),441(a,1,2))].
% 51.05/51.34 21596 inverse(sk_c7) = sk_c6 | identity = sk_c6. [para(20718(b,1),19596(b,1)),flip(c),merge(b)].
% 51.05/51.34 21602 identity = sk_c6 | sk_c3 = sk_c6. [para(21596(a,1),687(b,1)),flip(c),merge(b)].
% 51.05/51.34 21604 identity = sk_c6 | multiply(sk_c6,inverse(sk_c3)) = identity. [para(21596(a,1),7957(b,1,1)),merge(b)].
% 51.05/51.34 21656 sk_c3 = sk_c6 | inverse(sk_c7) = sk_c6. [para(21602(a,1),18499(b,2)),merge(b)].
% 51.05/51.34 21813 sk_c3 = sk_c6 | identity = sk_c1. [para(21656(b,1),3429(b,1)),flip(c),merge(c)].
% 51.05/51.34 21814 sk_c3 = sk_c6 | identity = sk_c2. [para(21656(b,1),8318(b,1)),flip(c),merge(c)].
% 51.05/51.34 21817 sk_c3 = sk_c6 | inverse(sk_c1) = identity. [para(21813(b,1),344(a,1,1))].
% 51.05/51.34 21971 sk_c3 = sk_c6 | inverse(sk_c1) = sk_c2. [para(21814(b,1),21817(b,2)),merge(b)].
% 51.05/51.34 22070 sk_c3 = sk_c6 | multiply(sk_c2,sk_c1) = identity. [para(21971(b,1),2(a,1,1))].
% 51.05/51.34 22320 sk_c3 = sk_c6 | multiply(inverse(sk_c1),inverse(sk_c2)) = identity. [para(22070(b,1),6463(a,1,1)),rewrite([344(5)]),flip(b)].
% 51.05/51.34 22781 inverse(sk_c7) = sk_c6 | multiply(A,sk_c6) = A. [para(20762(b,1),617(b,1,2)),merge(b)].
% 51.05/51.34 22834 inverse(sk_c7) = sk_c6 | identity = sk_c5. [para(20896(b,1),20770(b,1)),merge(b)].
% 51.05/51.34 22835 identity = sk_c5 | multiply(sk_c6,sk_c7) = identity. [para(22834(a,1),2(a,1,1))].
% 51.05/51.34 22840 identity = sk_c5 | multiply(sk_c6,inverse(sk_c3)) = identity. [para(22834(a,1),10440(b,1,1)),merge(b)].
% 51.05/51.34 22865 identity = sk_c5 | inverse(sk_c1) = sk_c7. [para(22835(b,1),14(b,1)),merge(c)].
% 51.05/51.34 22869 identity = sk_c5 | multiply(sk_c7,sk_c1) = identity. [para(22865(b,1),2(a,1,1))].
% 51.05/51.34 22872 identity = sk_c5 | multiply(sk_c1,sk_c7) = identity. [para(22865(b,1),441(a,1,2))].
% 51.05/51.34 23069 identity = sk_c5 | identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5. [para(22872(b,1),24(a,1))].
% 51.05/51.34 23304 identity = sk_c6 | inverse(sk_c3) = sk_c4. [para(21604(b,1),788(b,1,2)),rewrite([341(9)]),flip(c),merge(b)].
% 51.05/51.34 23313 identity = sk_c6 | multiply(sk_c4,sk_c3) = identity. [para(23304(b,1),2(a,1,1))].
% 51.05/51.34 23323 identity = sk_c6 | multiply(inverse(sk_c3),inverse(sk_c4)) = identity. [para(23313(b,1),6463(a,1,1)),rewrite([344(5)]),flip(b)].
% 51.05/51.34 23705 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c3) = sk_c5. [para(22781(b,1),593(b,1,2)),merge(b)].
% 51.05/51.34 23744 identity = sk_c5 | inverse(sk_c3) = sk_c4. [para(22840(b,1),6022(b,1,2)),rewrite([341(9)]),flip(c),merge(b)].
% 51.05/51.34 24241 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c3. [para(23705(b,1),381(b,1,2)),merge(b)].
% 51.05/51.34 24632 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c3) = sk_c7. [para(24241(b,1),692(b,1,2)),merge(b)].
% 51.05/51.34 24896 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c7. [para(24632(b,1),13559(b,1)),flip(c),merge(b)].
% 51.05/51.34 24903 inverse(sk_c7) = sk_c6. [para(24896(b,1),469(a,1,1)),merge(b)].
% 51.05/51.34 28019 multiply(sk_c3,sk_c6) = sk_c7 | multiply(sk_c6,multiply(inverse(sk_c1),sk_c6)) = identity. [back_rewrite(6663),rewrite([24903(7)])].
% 51.05/51.34 29045 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c6 | sk_c5 != sk_c6. [back_rewrite(672),rewrite([24903(2)]),xx(a)].
% 51.05/51.34 29256 multiply(sk_c6,sk_c7) = identity. [para(24903(a,1),2(a,1,1))].
% 51.05/51.34 29258 inverse(sk_c6) = sk_c7. [para(24903(a,1),469(a,1,1))].
% 51.05/51.34 29299 sk_c6 != sk_c7 | identity != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | identity != sk_c5 | identity != sk_c6 | sk_c5 != sk_c6. [back_rewrite(29045),rewrite([29256(14)])].
% 51.05/51.34 31799 identity = sk_c5 | identity = sk_c6. [back_rewrite(23069),rewrite([29256(9)]),merge(c)].
% 51.05/51.34 32062 identity = sk_c5 | multiply(sk_c7,sk_c4) = sk_c5. [back_rewrite(6125),rewrite([29256(6)]),merge(b)].
% 51.05/51.34 32083 identity = sk_c5 | multiply(sk_c6,sk_c3) = sk_c1. [back_rewrite(5504),rewrite([29256(6)]),merge(b)].
% 51.05/51.34 32103 inverse(sk_c2) = sk_c5 | sk_c4 = sk_c6. [back_rewrite(4178),rewrite([29256(8),341(7)])].
% 51.05/51.34 32698 identity = sk_c6 | multiply(sk_c3,sk_c7) = sk_c5. [para(31799(a,1),688(b,2)),merge(b)].
% 51.05/51.34 32727 identity = sk_c6 | multiply(sk_c4,sk_c3) = sk_c5. [para(31799(a,1),23313(b,2)),merge(b)].
% 51.05/51.34 32740 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c5,multiply(sk_c3,sk_c6))) = sk_c5. [para(1519(b,1),63(b,2)),merge(b)].
% 51.05/51.34 32750 sk_c4 = sk_c6 | inverse(sk_c5) = sk_c2. [para(32103(a,1),469(a,1,1))].
% 51.05/51.34 32946 identity = sk_c5 | multiply(sk_c6,sk_c5) = sk_c4. [para(32062(b,1),48(a,1,2)),rewrite([24903(5)])].
% 51.05/51.34 32958 identity = sk_c5 | multiply(sk_c7,sk_c1) = sk_c3. [para(32083(b,1),48(a,1,2)),rewrite([29258(5)])].
% 51.05/51.34 33022 identity = sk_c6 | multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(32698(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 33034 identity = sk_c6 | multiply(sk_c4,multiply(sk_c3,A)) = multiply(sk_c5,A). [para(32727(b,1),33(a,1,1)),flip(b)].
% 51.05/51.34 33282 identity = sk_c5 | multiply(sk_c4,sk_c4) = sk_c5. [para(32946(b,1),6022(b,1,2)),merge(b)].
% 51.05/51.34 33365 identity = sk_c5 | identity = sk_c3. [para(32958(b,1),22869(b,1)),flip(c),merge(b)].
% 51.05/51.34 33368 identity = sk_c5 | inverse(sk_c3) = identity. [para(33365(b,1),344(a,1,1))].
% 51.05/51.34 33484 identity = sk_c5 | identity = sk_c4. [para(33368(b,1),23744(b,1)),merge(b)].
% 51.05/51.34 33490 identity = sk_c5 | inverse(sk_c4) = identity. [para(33484(b,1),344(a,1,1))].
% 51.05/51.34 33852 identity = sk_c5 | inverse(sk_c4) = sk_c4. [para(33484(b,1),33490(b,2)),merge(b)].
% 51.05/51.34 33938 identity = sk_c5 | multiply(sk_c4,sk_c4) = identity. [para(33852(b,1),2(a,1,1))].
% 51.05/51.34 33943 identity = sk_c5 | sk_c4 = sk_c6. [para(33852(b,1),6023(b,1)),merge(b)].
% 51.05/51.34 33953 sk_c4 = sk_c6 | inverse(sk_c5) = identity. [para(33943(a,1),344(a,1,1))].
% 51.05/51.34 34013 sk_c4 = sk_c6 | identity = sk_c2. [para(33953(b,1),32750(b,1)),merge(b)].
% 51.05/51.34 34017 sk_c4 = sk_c6 | inverse(sk_c2) = identity. [para(34013(b,1),344(a,1,1))].
% 51.05/51.34 34096 sk_c4 = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 | sk_c5 = sk_c7. [para(34017(b,1),337(b,1,1)),rewrite([1(11)]),flip(c)].
% 51.05/51.34 34443 identity = sk_c5. [para(33938(b,1),33282(b,1)),merge(b),merge(c)].
% 51.05/51.34 34533 sk_c5 = sk_c6 | multiply(sk_c4,multiply(sk_c3,A)) = multiply(sk_c5,A). [back_rewrite(33034),rewrite([34443(1)])].
% 51.05/51.34 34545 sk_c5 = sk_c6 | multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c5,A). [back_rewrite(33022),rewrite([34443(1)])].
% 51.05/51.34 36685 sk_c6 != sk_c7 | sk_c5 != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | sk_c5 != sk_c6. [back_rewrite(29299),rewrite([34443(4),34443(12),34443(15)]),xx(d),merge(e)].
% 51.05/51.34 36733 multiply(sk_c3,sk_c6) = sk_c7 | multiply(sk_c6,multiply(inverse(sk_c1),sk_c6)) = sk_c5. [back_rewrite(28019),rewrite([34443(12)])].
% 51.05/51.34 36780 sk_c5 = sk_c6 | multiply(inverse(sk_c3),inverse(sk_c4)) = sk_c5. [back_rewrite(23323),rewrite([34443(1),34443(9)])].
% 51.05/51.34 36791 sk_c3 = sk_c6 | multiply(inverse(sk_c1),inverse(sk_c2)) = sk_c5. [back_rewrite(22320),rewrite([34443(9)])].
% 51.05/51.34 36880 sk_c5 = sk_c6 | inverse(sk_c2) = sk_c5 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = sk_c5. [back_rewrite(13671),rewrite([34443(13)])].
% 51.05/51.34 36964 sk_c5 = sk_c6 | multiply(A,multiply(sk_c6,sk_c4)) = multiply(A,multiply(sk_c7,sk_c3)). [back_rewrite(11049),rewrite([34443(1)])].
% 51.05/51.34 37352 multiply(A,sk_c5) = A. [back_rewrite(341),rewrite([34443(1)])].
% 51.05/51.34 37354 multiply(sk_c5,A) = A. [back_rewrite(1),rewrite([34443(1)])].
% 51.05/51.34 37596 sk_c4 = sk_c6 | sk_c5 = sk_c7. [back_rewrite(34096),rewrite([37352(6)]),merge(b)].
% 51.05/51.34 37721 sk_c6 = sk_c7. [back_rewrite(3126),rewrite([37354(6),37352(9)]),flip(c),merge(b),merge(c)].
% 51.05/51.34 37775 sk_c5 != sk_c7. [back_rewrite(36685),rewrite([37721(1),37721(8),37354(9),37721(11)]),xx(a),xx(c),merge(b)].
% 51.05/51.34 37779 multiply(sk_c3,multiply(sk_c7,A)) = A. [back_rewrite(34545),rewrite([37721(2),37354(9)]),unit_del(a,37775)].
% 51.05/51.34 37782 multiply(sk_c4,multiply(sk_c3,A)) = A. [back_rewrite(34533),rewrite([37721(2),37354(9)]),unit_del(a,37775)].
% 51.05/51.34 37797 inverse(sk_c1) = sk_c7. [back_rewrite(32740),rewrite([37721(8),37354(10),37782(9)]),flip(b),unit_del(b,37775)].
% 51.05/51.34 37933 sk_c4 = sk_c7. [back_rewrite(37596),rewrite([37721(2)]),unit_del(b,37775)].
% 51.05/51.34 37959 multiply(A,multiply(sk_c7,sk_c3)) = multiply(A,multiply(sk_c7,sk_c7)). [back_rewrite(36964),rewrite([37721(2),37721(4),37933(5)]),flip(b),unit_del(a,37775)].
% 51.05/51.34 37963 inverse(sk_c2) = sk_c5. [back_rewrite(36880),rewrite([37721(2),37721(9),37959(12),37779(12)]),flip(c),merge(c),unit_del(a,37775)].
% 51.05/51.34 37967 sk_c3 = sk_c7. [back_rewrite(36791),rewrite([37721(2),37797(5),37963(6),37352(6)]),flip(b),unit_del(b,37775)].
% 51.05/51.34 37968 multiply(sk_c7,sk_c7) = sk_c5. [back_rewrite(36780),rewrite([37721(2),37967(4),24903(5),37721(4),37933(5),24903(6),37721(5)]),unit_del(a,37775)].
% 51.05/51.34 37969 $F. [back_rewrite(36733),rewrite([37967(1),37721(2),37968(3),37721(4),37797(6),37721(6),37968(7),37352(6)]),flip(b),merge(b),unit_del(a,37775)].
% 51.05/51.34
% 51.05/51.34 % SZS output end Refutation
% 51.05/51.34 ============================== end of proof ==========================
% 51.05/51.34
% 51.05/51.34 ============================== STATISTICS ============================
% 51.05/51.34
% 51.05/51.34 Given=5132. Generated=2413912. Kept=37968. proofs=1.
% 51.05/51.34 Usable=555. Sos=1307. Demods=35. Limbo=248, Disabled=35892. Hints=0.
% 51.05/51.34 Megabytes=33.28.
% 51.05/51.34 User_CPU=49.09, System_CPU=1.27, Wall_clock=51.
% 51.05/51.34
% 51.05/51.34 ============================== end of statistics =====================
% 51.05/51.34
% 51.05/51.34 ============================== end of search =========================
% 51.05/51.34
% 51.05/51.34 THEOREM PROVED
% 51.05/51.34 % SZS status Unsatisfiable
% 51.05/51.34
% 51.05/51.34 Exiting with 1 proof.
% 51.05/51.34
% 51.05/51.34 Process 3805 exit (max_proofs) Mon Jun 13 13:51:42 2022
% 51.05/51.34 Prover9 interrupted
%------------------------------------------------------------------------------