TSTP Solution File: GRP360-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP360-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:18:46 EDT 2022
% Result : Unsatisfiable 21.99s 22.25s
% Output : Refutation 21.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP360-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 09:01:19 EDT 2022
% 0.13/0.33 % CPUTime :
% 21.99/22.25 ============================== Prover9 ===============================
% 21.99/22.25 Prover9 (32) version 2009-11A, November 2009.
% 21.99/22.25 Process 26617 was started by sandbox2 on n011.cluster.edu,
% 21.99/22.25 Tue Jun 14 09:01:20 2022
% 21.99/22.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26464_n011.cluster.edu".
% 21.99/22.25 ============================== end of head ===========================
% 21.99/22.25
% 21.99/22.25 ============================== INPUT =================================
% 21.99/22.25
% 21.99/22.25 % Reading from file /tmp/Prover9_26464_n011.cluster.edu
% 21.99/22.25
% 21.99/22.25 set(prolog_style_variables).
% 21.99/22.25 set(auto2).
% 21.99/22.25 % set(auto2) -> set(auto).
% 21.99/22.25 % set(auto) -> set(auto_inference).
% 21.99/22.25 % set(auto) -> set(auto_setup).
% 21.99/22.25 % set(auto_setup) -> set(predicate_elim).
% 21.99/22.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 21.99/22.25 % set(auto) -> set(auto_limits).
% 21.99/22.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 21.99/22.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 21.99/22.25 % set(auto) -> set(auto_denials).
% 21.99/22.25 % set(auto) -> set(auto_process).
% 21.99/22.25 % set(auto2) -> assign(new_constants, 1).
% 21.99/22.25 % set(auto2) -> assign(fold_denial_max, 3).
% 21.99/22.25 % set(auto2) -> assign(max_weight, "200.000").
% 21.99/22.25 % set(auto2) -> assign(max_hours, 1).
% 21.99/22.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 21.99/22.25 % set(auto2) -> assign(max_seconds, 0).
% 21.99/22.25 % set(auto2) -> assign(max_minutes, 5).
% 21.99/22.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 21.99/22.25 % set(auto2) -> set(sort_initial_sos).
% 21.99/22.25 % set(auto2) -> assign(sos_limit, -1).
% 21.99/22.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 21.99/22.25 % set(auto2) -> assign(max_megs, 400).
% 21.99/22.25 % set(auto2) -> assign(stats, some).
% 21.99/22.25 % set(auto2) -> clear(echo_input).
% 21.99/22.25 % set(auto2) -> set(quiet).
% 21.99/22.25 % set(auto2) -> clear(print_initial_clauses).
% 21.99/22.25 % set(auto2) -> clear(print_given).
% 21.99/22.25 assign(lrs_ticks,-1).
% 21.99/22.25 assign(sos_limit,10000).
% 21.99/22.25 assign(order,kbo).
% 21.99/22.25 set(lex_order_vars).
% 21.99/22.25 clear(print_given).
% 21.99/22.25
% 21.99/22.25 % formulas(sos). % not echoed (29 formulas)
% 21.99/22.25
% 21.99/22.25 ============================== end of input ==========================
% 21.99/22.25
% 21.99/22.25 % From the command line: assign(max_seconds, 300).
% 21.99/22.25
% 21.99/22.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 21.99/22.25
% 21.99/22.25 % Formulas that are not ordinary clauses:
% 21.99/22.25
% 21.99/22.25 ============================== end of process non-clausal formulas ===
% 21.99/22.25
% 21.99/22.25 ============================== PROCESS INITIAL CLAUSES ===============
% 21.99/22.25
% 21.99/22.25 ============================== PREDICATE ELIMINATION =================
% 21.99/22.25
% 21.99/22.25 ============================== end predicate elimination =============
% 21.99/22.25
% 21.99/22.25 Auto_denials: (non-Horn, no changes).
% 21.99/22.25
% 21.99/22.25 Term ordering decisions:
% 21.99/22.25
% 21.99/22.25 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 21.99/22.25 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.
% 21.99/22.25
% 21.99/22.25 ============================== end of process initial clauses ========
% 21.99/22.25
% 21.99/22.25 ============================== CLAUSES FOR SEARCH ====================
% 21.99/22.25
% 21.99/22.25 ============================== end of clauses for search =============
% 21.99/22.25
% 21.99/22.25 ============================== SEARCH ================================
% 21.99/22.25
% 21.99/22.25 % Starting search at 0.01 seconds.
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=44.000, iters=3343
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=43.000, iters=3375
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=42.000, iters=3345
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=41.000, iters=3346
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=40.000, iters=3334
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=39.000, iters=3333
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=38.000, iters=3389
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=37.000, iters=3334
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=36.000, iters=3343
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=35.000, iters=3349
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=34.000, iters=3337
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=33.000, iters=3438
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=32.000, iters=3344
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=31.000, iters=3350
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=29.000, iters=3346
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=28.000, iters=3333
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=26.000, iters=3570
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=18.000, iters=3915
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=17.000, iters=3632
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=16.000, iters=3349
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=15.000, iters=3354
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=14.000, iters=3334
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=13.000, iters=3349
% 21.99/22.25
% 21.99/22.25 Low Water (keep): wt=12.000, iters=3333
% 21.99/22.25
% 21.99/22.25 ============================== PROOF =================================
% 21.99/22.25 % SZS status Unsatisfiable
% 21.99/22.25 % SZS output start Refutation
% 21.99/22.25
% 21.99/22.25 % Proof 1 at 20.68 (+ 0.59) seconds.
% 21.99/22.25 % Length of proof is 234.
% 21.99/22.25 % Level of proof is 41.
% 21.99/22.25 % Maximum clause weight is 46.000.
% 21.99/22.25 % Given clauses 4311.
% 21.99/22.25
% 21.99/22.25 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 21.99/22.25 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 21.99/22.25 3 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 21.99/22.25 4 inverse(sk_c7) = sk_c5 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 21.99/22.25 5 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 21.99/22.25 6 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 21.99/22.25 7 multiply(sk_c6,sk_c5) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 21.99/22.25 9 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 21.99/22.25 10 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 21.99/22.25 11 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 21.99/22.25 12 multiply(sk_c7,sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 21.99/22.25 13 multiply(sk_c7,sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 21.99/22.25 14 multiply(sk_c1,sk_c7) = sk_c2 | inverse(sk_c3) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 21.99/22.25 15 multiply(sk_c1,sk_c7) = sk_c2 | inverse(sk_c4) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 21.99/22.25 16 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 21.99/22.25 17 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 21.99/22.25 18 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 21.99/22.25 19 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 21.99/22.25 20 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 21.99/22.25 22 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 21.99/22.25 24 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 21.99/22.25 25 multiply(sk_c1,sk_c7) = sk_c2 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 21.99/22.25 27 multiply(sk_c1,sk_c7) = sk_c2 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 21.99/22.25 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 21.99/22.25 29 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(sk_c7,A) != sk_c6 | multiply(B,sk_c7) != A | 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].
% 21.99/22.25 37 inverse(sk_c7) = sk_c5 | multiply(sk_c7,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 21.99/22.25 38 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 21.99/22.25 39 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 21.99/22.25 41 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 21.99/22.25 42 inverse(sk_c3) = sk_c7 | multiply(sk_c6,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(7(a,1),28(a,1,1)),flip(b)].
% 21.99/22.25 46 inverse(sk_c7) = sk_c5 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(9(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 48 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(10(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 49 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),28(a,2,2)),rewrite([28(8)])].
% 21.99/22.25 50 inverse(sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(11(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 51 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6). [para(11(b,1),28(a,2,2)),rewrite([28(8)])].
% 21.99/22.25 52 inverse(sk_c3) = sk_c7 | multiply(sk_c7,multiply(sk_c2,A)) = multiply(sk_c6,A). [para(12(a,1),28(a,1,1)),flip(b)].
% 21.99/22.25 56 inverse(sk_c3) = sk_c7 | multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c2,A). [para(14(a,1),28(a,1,1)),flip(b)].
% 21.99/22.25 59 inverse(sk_c4) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c2). [para(15(a,1),28(a,2,2)),rewrite([28(8)])].
% 21.99/22.25 60 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c5,A). [para(16(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 66 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c6,multiply(sk_c5,A)) = multiply(sk_c7,A). [para(19(a,1),28(a,1,1)),flip(b)].
% 21.99/22.25 68 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(20(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 73 multiply(sk_c7,sk_c2) = sk_c6 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(22(b,1),28(a,2,2)),rewrite([28(9)])].
% 21.99/22.25 76 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(24(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 102 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(sk_c7,A) != sk_c6 | multiply(B,sk_c7) != A | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(identity) != sk_c6 | sk_c5 != sk_c6. [para(1(a,1),29(j,1))].
% 21.99/22.25 103 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(sk_c7,A) != sk_c6 | identity != A | inverse(inverse(sk_c7)) != sk_c7 | 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(2(a,1),29(d,1))].
% 21.99/22.25 206 inverse(sk_c7) = sk_c5 | multiply(sk_c7,multiply(sk_c3,A)) = A. [para(37(b,1),28(a,1,1)),rewrite([1(6)]),flip(b)].
% 21.99/22.25 225 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),41(a,1,2))].
% 21.99/22.25 231 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(9(b,1),41(a,1,2))].
% 21.99/22.25 232 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(10(b,1),41(a,1,2))].
% 21.99/22.25 238 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(16(b,1),41(a,1,2))].
% 21.99/22.25 239 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(17(b,1),41(a,1,2))].
% 21.99/22.25 240 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(18(b,1),41(a,1,2))].
% 21.99/22.25 251 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c7),identity) = sk_c3. [para(37(b,1),41(a,1,2))].
% 21.99/22.25 252 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(41(a,1),41(a,1,2))].
% 21.99/22.25 253 multiply(A,identity) = A. [back_rewrite(225),rewrite([252(4)])].
% 21.99/22.25 254 inverse(sk_c7) = sk_c5 | inverse(sk_c7) = sk_c3. [back_rewrite(251),rewrite([253(8)])].
% 21.99/22.25 258 inverse(identity) = identity. [para(253(a,1),2(a,1))].
% 21.99/22.25 287 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(sk_c7,A) != sk_c6 | multiply(B,sk_c7) != A | inverse(B) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6. [back_rewrite(102),rewrite([258(33)])].
% 21.99/22.25 291 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c7) = identity. [para(254(b,1),2(a,1,1))].
% 21.99/22.25 294 inverse(sk_c7) = sk_c5 | inverse(sk_c6) = sk_c4. [para(38(b,1),41(a,1,2)),rewrite([253(8)])].
% 21.99/22.25 297 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c6) = identity. [para(294(b,1),2(a,1,1))].
% 21.99/22.25 298 inverse(sk_c7) = sk_c5 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(294(b,1),41(a,1,1))].
% 21.99/22.25 302 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c3. [para(39(b,1),41(a,1,2)),rewrite([253(8)])].
% 21.99/22.25 309 inverse(sk_c3) = sk_c7 | multiply(sk_c6,multiply(sk_c5,sk_c2)) = sk_c6. [para(12(a,1),42(b,2)),merge(b)].
% 21.99/22.25 322 multiply(A,inverse(A)) = identity. [para(252(a,1),2(a,1))].
% 21.99/22.25 339 multiply(A,multiply(inverse(A),B)) = B. [para(252(a,1),41(a,1))].
% 21.99/22.25 340 inverse(inverse(A)) = A. [para(252(a,1),253(a,1)),rewrite([253(2)]),flip(a)].
% 21.99/22.25 343 inverse(sk_c7) = sk_c3 | multiply(inverse(sk_c7),A) = multiply(sk_c1,A). [para(302(a,1),252(a,1,1,1))].
% 21.99/22.25 352 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(sk_c7,A) != sk_c6 | identity != A | 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. [back_rewrite(103),rewrite([340(18)]),xx(e)].
% 21.99/22.25 353 inverse(sk_c7) = sk_c3 | inverse(sk_c7) = sk_c1. [para(302(a,1),340(a,1,1))].
% 21.99/22.25 357 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(322(a,1),28(a,1)),flip(a)].
% 21.99/22.25 360 inverse(sk_c7) = sk_c3 | multiply(sk_c1,sk_c7) = identity. [para(302(a,1),322(a,1,2))].
% 21.99/22.25 457 inverse(sk_c7) = sk_c5 | multiply(A,multiply(sk_c4,sk_c6)) = A. [para(297(b,1),28(a,2,2)),rewrite([28(8),253(10)])].
% 21.99/22.25 501 inverse(sk_c7) = sk_c3 | identity = sk_c2 | inverse(sk_c3) = sk_c7. [para(360(b,1),14(a,1))].
% 21.99/22.25 508 inverse(sk_c7) = sk_c5 | multiply(sk_c5,sk_c3) = sk_c6. [para(37(b,1),46(b,1,2)),rewrite([253(11)]),flip(c),merge(b)].
% 21.99/22.25 586 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c5),sk_c6) = sk_c3. [para(508(b,1),41(a,1,2))].
% 21.99/22.25 589 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c5) = multiply(sk_c7,sk_c7). [para(9(b,1),48(b,1,2)),merge(b)].
% 21.99/22.25 591 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c6,sk_c3)) = identity. [para(37(b,1),48(b,2)),merge(b)].
% 21.99/22.25 699 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c7. [para(294(b,1),231(b,1,1)),merge(b)].
% 21.99/22.25 700 inverse(sk_c7) = sk_c5 | sk_c6 = sk_c7. [para(699(b,1),11(b,1)),flip(c),merge(b)].
% 21.99/22.25 714 inverse(sk_c7) = sk_c5 | multiply(sk_c6,multiply(sk_c3,sk_c6)) = sk_c5. [para(9(b,1),49(b,2)),merge(b)].
% 21.99/22.25 716 inverse(sk_c7) = sk_c5 | multiply(sk_c3,multiply(sk_c3,sk_c6)) = identity. [para(291(b,1),49(b,2)),merge(b)].
% 21.99/22.25 758 inverse(sk_c7) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6. [para(3(b,1),232(b,1,1)),merge(b)].
% 21.99/22.25 764 inverse(sk_c7) = sk_c5 | multiply(sk_c6,inverse(sk_c5)) = sk_c4. [para(322(a,1),50(b,1,2)),rewrite([253(7)]),flip(b)].
% 21.99/22.25 955 inverse(sk_c3) = sk_c7 | multiply(sk_c7,multiply(sk_c2,sk_c5)) = sk_c7. [para(7(a,1),52(b,2)),merge(b)].
% 21.99/22.25 1012 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(5(b,1),239(b,1,1)),merge(b)].
% 21.99/22.25 1025 inverse(sk_c1) = sk_c7 | multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(1012(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 1032 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c6) = sk_c5. [para(6(b,1),240(b,1,1)),merge(b)].
% 21.99/22.25 1048 inverse(sk_c1) = sk_c7 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(1032(b,1),28(a,1,1)),flip(b)].
% 21.99/22.25 1055 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c6. [para(1032(b,1),41(a,1,2))].
% 21.99/22.25 1126 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(357(a,1),41(a,1,2)),rewrite([253(3)]),flip(a)].
% 21.99/22.25 1184 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(1126(a,1),41(a,1,2)),flip(a)].
% 21.99/22.25 1538 inverse(sk_c3) = sk_c7 | multiply(A,multiply(sk_c1,multiply(sk_c7,B))) = multiply(A,multiply(sk_c2,B)). [para(56(b,1),28(a,2,2)),rewrite([28(9)])].
% 21.99/22.25 1760 inverse(sk_c1) = sk_c7 | sk_c6 = sk_c7. [para(1055(b,1),238(b,1)),merge(b)].
% 21.99/22.25 1763 sk_c6 = sk_c7 | inverse(sk_c7) = sk_c1. [para(1760(a,1),340(a,1,1))].
% 21.99/22.25 1764 sk_c6 = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(1760(a,1),322(a,1,2))].
% 21.99/22.25 1770 sk_c6 = sk_c7 | sk_c1 = sk_c5. [para(1763(b,1),700(a,1)),merge(c)].
% 21.99/22.25 1785 inverse(sk_c4) = sk_c6 | multiply(sk_c7,multiply(sk_c1,sk_c7)) = sk_c6. [para(13(a,1),59(b,2)),merge(b)].
% 21.99/22.25 1893 sk_c6 = sk_c7 | multiply(A,multiply(sk_c1,sk_c7)) = A. [para(1764(b,1),28(a,2,2)),rewrite([28(7),253(9)])].
% 21.99/22.25 2018 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6). [para(1012(b,1),60(b,1,2)),flip(c),merge(b)].
% 21.99/22.25 2624 multiply(sk_c6,sk_c7) = sk_c5 | sk_c6 = sk_c7 | multiply(A,sk_c2) = A. [para(25(a,1),1893(b,1,2))].
% 21.99/22.25 2639 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c7,inverse(sk_c5)) = sk_c6. [para(322(a,1),66(b,1,2)),rewrite([253(8)]),flip(b)].
% 21.99/22.25 2990 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c7,inverse(sk_c6)) = sk_c3. [para(322(a,1),68(b,1,2)),rewrite([253(8)]),flip(b)].
% 21.99/22.25 3622 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [resolve(352,c,339,a),flip(c)].
% 21.99/22.25 3748 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6. [para(24(b,1),73(b,2)),merge(b)].
% 21.99/22.25 3800 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(B),inverse(C)) != sk_c6 | multiply(C,multiply(B,sk_c5)) != sk_c6. [para(28(a,1),3622(h,1)),rewrite([1184(29)])].
% 21.99/22.25 4162 multiply(sk_c7,sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c5,sk_c7)) = sk_c5. [para(22(b,1),76(b,2)),merge(b)].
% 21.99/22.25 4648 inverse(sk_c3) = sk_c7 | multiply(sk_c5,sk_c2) = identity. [para(309(b,1),41(a,1,2)),rewrite([2(8)]),flip(b)].
% 21.99/22.25 4657 inverse(sk_c3) = sk_c7 | inverse(sk_c5) = sk_c2. [para(4648(b,1),41(a,1,2)),rewrite([253(8)])].
% 21.99/22.25 4670 inverse(sk_c5) = sk_c2 | inverse(sk_c7) = sk_c3. [para(4657(a,1),340(a,1,1))].
% 21.99/22.25 4727 inverse(sk_c7) = sk_c3 | inverse(sk_c2) = sk_c5. [para(4670(a,1),340(a,1,1))].
% 21.99/22.25 4728 inverse(sk_c7) = sk_c3 | multiply(sk_c5,sk_c2) = identity. [para(4670(a,1),322(a,1,2))].
% 21.99/22.25 6028 inverse(sk_c7) = sk_c3 | identity = sk_c2. [para(501(c,1),340(a,1,1)),merge(c)].
% 21.99/22.25 6030 identity = sk_c2 | multiply(sk_c3,multiply(sk_c7,A)) = A. [para(6028(a,1),41(a,1,1))].
% 21.99/22.25 6176 identity = sk_c2 | multiply(inverse(sk_c7),A) = multiply(sk_c3,A). [para(339(a,1),6030(b,1,2)),flip(b)].
% 21.99/22.25 6955 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c5) = sk_c6. [para(758(b,1),589(b,2)),merge(b)].
% 21.99/22.25 6960 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c3),sk_c6) = sk_c5. [para(6955(b,1),41(a,1,2))].
% 21.99/22.25 7000 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = inverse(sk_c3). [para(591(b,1),41(a,1,2)),rewrite([253(8)]),flip(b)].
% 21.99/22.25 7117 inverse(sk_c7) = sk_c5 | multiply(sk_c3,sk_c6) = inverse(sk_c3). [para(716(b,1),41(a,1,2)),rewrite([253(8)]),flip(b)].
% 21.99/22.25 7150 inverse(sk_c7) = sk_c5 | multiply(sk_c6,inverse(sk_c3)) = sk_c5. [para(7117(b,1),714(b,1,2)),merge(b)].
% 21.99/22.25 7160 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = inverse(sk_c3). [para(7150(b,1),298(b,1,2)),merge(b)].
% 21.99/22.25 7161 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c6. [para(7160(b,1),11(b,1)),merge(b)].
% 21.99/22.25 7189 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = identity. [para(7161(b,1),2(a,1,1))].
% 21.99/22.25 7342 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = identity. [para(7189(b,1),7000(b,1)),flip(c),merge(b)].
% 21.99/22.25 7455 inverse(sk_c7) = sk_c5 | multiply(sk_c3,A) = A. [para(7342(b,1),41(a,1,1)),rewrite([1(8)])].
% 21.99/22.25 7460 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c5) = identity. [para(7342(b,1),7160(b,2)),merge(b)].
% 21.99/22.25 7881 inverse(sk_c7) = sk_c5 | multiply(sk_c7,A) = A. [para(7455(b,1),206(b,1,2)),merge(b)].
% 21.99/22.25 7985 inverse(sk_c7) = sk_c5 | multiply(A,sk_c6) = A. [para(7460(b,1),51(b,1,2)),rewrite([253(10)]),flip(c),merge(b)].
% 21.99/22.25 8298 inverse(sk_c7) = sk_c5 | multiply(inverse(sk_c7),A) = A. [para(7881(b,1),41(a,1,2))].
% 21.99/22.25 8333 inverse(sk_c7) = sk_c5 | inverse(sk_c5) = sk_c3. [para(7985(b,1),586(b,1)),merge(b)].
% 21.99/22.25 8338 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c5. [para(7985(b,1),6960(b,1)),merge(b)].
% 21.99/22.25 8341 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c3. [para(7985(b,1),7117(b,1)),flip(c),merge(b)].
% 21.99/22.25 8390 inverse(sk_c7) = sk_c5 | multiply(sk_c6,sk_c3) = sk_c4. [para(8333(b,1),764(b,1,2)),merge(b)].
% 21.99/22.25 8487 inverse(sk_c7) = sk_c5 | sk_c3 = sk_c5. [para(8341(b,1),8338(b,1)),merge(b)].
% 21.99/22.25 8493 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c1. [para(8487(a,1),353(a,1)),flip(b),merge(b)].
% 21.99/22.25 8508 sk_c3 = sk_c5 | identity = sk_c2. [para(8487(a,1),6028(a,1)),flip(b),merge(b)].
% 21.99/22.25 8511 sk_c3 = sk_c5 | inverse(sk_c2) = identity. [para(8508(b,1),258(a,1,1))].
% 21.99/22.25 8556 sk_c3 = sk_c5 | multiply(sk_c7,sk_c1) = identity. [para(8493(b,1),322(a,1,2))].
% 21.99/22.25 8641 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c3 | identity = sk_c5. [para(8511(b,1),4727(b,1))].
% 21.99/22.25 8898 sk_c3 = sk_c5 | multiply(inverse(sk_c1),inverse(sk_c7)) = identity. [para(8556(b,1),1184(a,1,1)),rewrite([258(5)]),flip(b)].
% 21.99/22.25 8903 sk_c3 = sk_c5 | multiply(sk_c7,sk_c1) = sk_c2. [para(8508(b,1),8556(b,2)),merge(b)].
% 21.99/22.25 9030 sk_c3 = sk_c5 | multiply(inverse(sk_c7),sk_c2) = sk_c1. [para(8903(b,1),41(a,1,2))].
% 21.99/22.25 9297 inverse(sk_c7) = sk_c5 | inverse(sk_c3) = sk_c4. [para(8390(b,1),7000(b,1)),flip(c),merge(b)].
% 21.99/22.25 9341 inverse(sk_c7) = sk_c5 | multiply(sk_c4,sk_c6) = sk_c5. [para(9297(b,1),6960(b,1,1)),merge(b)].
% 21.99/22.25 9448 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | identity != sk_c6 | multiply(A,sk_c7) != inverse(sk_c7) | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | sk_c5 != sk_c6. [para(322(a,1),287(c,1)),merge(i)].
% 21.99/22.25 9565 sk_c3 = sk_c5 | multiply(sk_c5,sk_c2) = sk_c1. [para(8487(a,1),9030(b,1,1)),merge(b)].
% 21.99/22.25 9580 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c3 | identity = sk_c1. [para(9565(b,1),4728(b,1)),flip(c)].
% 21.99/22.25 9634 inverse(sk_c7) = sk_c5 | multiply(A,sk_c5) = A. [para(9341(b,1),457(b,1,2)),merge(b)].
% 21.99/22.25 9718 multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c7) != sk_c5 | identity != sk_c6 | multiply(A,sk_c7) != inverse(sk_c7) | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(B),inverse(C)) != sk_c7 | multiply(C,multiply(B,sk_c6)) != sk_c7 | sk_c5 != sk_c6. [para(28(a,1),9448(h,1)),rewrite([1184(27)])].
% 21.99/22.25 10337 sk_c3 = sk_c5 | inverse(sk_c7) = sk_c3 | multiply(sk_c1,A) = multiply(sk_c5,A). [para(8487(a,1),343(b,1,1)),flip(c)].
% 21.99/22.25 11131 inverse(sk_c7) = sk_c5. [para(8298(b,1),9634(b,1)),flip(c),merge(b),merge(c)].
% 21.99/22.25 11325 sk_c3 = sk_c5 | multiply(sk_c1,A) = multiply(sk_c5,A). [back_rewrite(10337),rewrite([11131(5)]),flip(b),merge(b)].
% 21.99/22.25 11445 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(A,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(B),inverse(C)) != sk_c7 | multiply(C,multiply(B,sk_c6)) != sk_c7 | sk_c5 != sk_c6. [back_rewrite(9718),rewrite([11131(7),11131(15)]),xx(b)].
% 21.99/22.25 11470 sk_c3 = sk_c5 | identity = sk_c1. [back_rewrite(9580),rewrite([11131(5)]),flip(b),merge(b)].
% 21.99/22.25 11603 sk_c3 = sk_c5 | multiply(inverse(sk_c1),sk_c5) = identity. [back_rewrite(8898),rewrite([11131(7)])].
% 21.99/22.25 11648 sk_c3 = sk_c5 | identity = sk_c5. [back_rewrite(8641),rewrite([11131(5)]),flip(b),merge(b)].
% 21.99/22.25 12029 identity = sk_c2 | multiply(sk_c3,A) = multiply(sk_c5,A). [back_rewrite(6176),rewrite([11131(5)]),flip(b)].
% 21.99/22.25 12423 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(B),inverse(C)) != sk_c6 | multiply(C,multiply(B,sk_c5)) != sk_c6. [back_rewrite(3800),rewrite([11131(7),11131(10)]),xx(b)].
% 21.99/22.25 13599 multiply(sk_c5,sk_c7) = identity. [para(11131(a,1),2(a,1,1))].
% 21.99/22.25 13600 multiply(sk_c5,multiply(sk_c7,A)) = A. [para(11131(a,1),41(a,1,1))].
% 21.99/22.25 13601 inverse(sk_c5) = sk_c7. [para(11131(a,1),340(a,1,1))].
% 21.99/22.25 13602 multiply(sk_c7,sk_c5) = identity. [para(11131(a,1),322(a,1,2))].
% 21.99/22.25 13623 multiply(sk_c7,sk_c2) = sk_c6 | sk_c4 = sk_c5. [back_rewrite(4162),rewrite([13599(9),253(8)])].
% 21.99/22.25 13636 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c6) = identity. [back_rewrite(2018),rewrite([13599(7)]),flip(b)].
% 21.99/22.25 13859 multiply(sk_c6,sk_c7) = sk_c5 | multiply(sk_c7,sk_c7) = sk_c6. [back_rewrite(2639),rewrite([13601(8)])].
% 21.99/22.25 14044 sk_c3 = sk_c5 | inverse(sk_c1) = identity. [para(11470(b,1),258(a,1,1))].
% 21.99/22.25 14070 sk_c3 = sk_c5 | identity = sk_c7. [para(11648(b,1),258(a,1,1)),rewrite([13601(5)]),flip(b)].
% 21.99/22.25 14139 sk_c3 = sk_c5 | sk_c5 = sk_c7. [para(14070(b,1),11648(b,1)),flip(c),merge(b)].
% 21.99/22.25 14158 sk_c5 = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7. [para(14139(a,1),20(b,1,1))].
% 21.99/22.25 14338 sk_c3 = sk_c5 | inverse(sk_c1) = sk_c5. [para(11648(b,1),14044(b,2)),merge(b)].
% 21.99/22.25 14706 sk_c4 = sk_c5 | multiply(inverse(sk_c2),sk_c5) = inverse(sk_c6). [para(13623(a,1),1184(a,1,1)),rewrite([11131(9)]),flip(b)].
% 21.99/22.25 15891 inverse(sk_c3) = sk_c7 | multiply(sk_c2,sk_c5) = identity. [para(955(b,1),41(a,1,2)),rewrite([11131(6),13599(7)]),flip(b)].
% 21.99/22.25 16283 sk_c3 = sk_c5 | multiply(sk_c5,sk_c5) = identity. [para(14338(b,1),11603(b,1,1)),merge(b)].
% 21.99/22.25 16287 sk_c3 = sk_c5 | multiply(A,multiply(sk_c5,sk_c5)) = A. [para(16283(b,1),28(a,2,2)),rewrite([28(7),253(9)])].
% 21.99/22.25 16528 inverse(sk_c1) = sk_c7 | identity = sk_c5. [para(13636(b,1),1032(b,1)),merge(b)].
% 21.99/22.25 16535 identity = sk_c5 | multiply(sk_c1,sk_c7) = identity. [para(16528(a,1),322(a,1,2))].
% 21.99/22.25 16536 identity = sk_c5 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(16528(a,1),339(a,1,2,1))].
% 21.99/22.25 16692 identity = sk_c5 | multiply(sk_c5,inverse(sk_c1)) = identity. [para(16535(b,1),1184(a,1,1)),rewrite([258(5),11131(6)]),flip(b)].
% 21.99/22.25 17114 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c5) = identity. [para(16(b,1),1048(b,1,2)),rewrite([13599(14)]),merge(b)].
% 21.99/22.25 18687 inverse(sk_c3) = sk_c7 | multiply(A,sk_c1) = A. [para(15891(b,1),1538(b,2,2)),rewrite([13602(12),253(11),253(12)]),merge(b)].
% 21.99/22.25 18931 inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(17114(b,1),1025(b,2)),rewrite([13602(12),253(11)]),flip(c),merge(b)].
% 21.99/22.25 18954 identity = sk_c7 | multiply(sk_c7,sk_c1) = identity. [para(18931(a,1),2(a,1,1))].
% 21.99/22.25 19741 sk_c6 = sk_c7 | inverse(sk_c4) = sk_c6. [para(1770(b,1),1785(b,1,2,1)),rewrite([13599(11),253(10)]),flip(c),merge(c)].
% 21.99/22.25 19754 sk_c6 = sk_c7 | multiply(sk_c4,multiply(sk_c6,A)) = A. [para(19741(b,1),339(a,1,2,1))].
% 21.99/22.25 20193 inverse(sk_c3) = sk_c7 | identity = sk_c7. [para(18687(b,1),18954(b,1)),flip(c),merge(c)].
% 21.99/22.25 20194 identity = sk_c7 | multiply(sk_c7,sk_c3) = identity. [para(20193(a,1),2(a,1,1))].
% 21.99/22.25 20196 identity = sk_c7 | multiply(sk_c3,sk_c7) = identity. [para(20193(a,1),322(a,1,2))].
% 21.99/22.25 20221 identity = sk_c7 | multiply(sk_c5,inverse(sk_c3)) = identity. [para(20196(b,1),1184(a,1,1)),rewrite([258(5),11131(6)]),flip(b)].
% 21.99/22.25 22279 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(2(a,1),12423(g,1,2)),rewrite([13601(24),11131(24),253(29)]),flip(g)].
% 21.99/22.25 22283 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c5,B) != sk_c6 | inverse(B) != sk_c6. [para(340(a,1),22279(f,1,2)),flip(g)].
% 21.99/22.25 22285 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [resolve(22283,f,13600,a),rewrite([1184(26),11131(26)])].
% 21.99/22.25 22293 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(A),inverse(B)) != sk_c7 | multiply(B,multiply(A,sk_c6)) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(28(a,1),22285(e,1)),rewrite([1184(17)])].
% 21.99/22.25 22296 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(A)) != sk_c7 | sk_c7 != A | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(2(a,1),22293(e,1,2)),rewrite([340(18),253(22)]),flip(e)].
% 21.99/22.25 22300 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != identity | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c6),sk_c5) != sk_c6. [para(11131(a,1),22296(d,1,2)),xx(e),merge(d)].
% 21.99/22.25 22535 multiply(sk_c7,inverse(sk_c6)) = sk_c3 | multiply(sk_c7,inverse(sk_c6)) = sk_c5. [para(2990(a,1),1184(a,1,1)),rewrite([11131(8),13601(9)]),flip(b)].
% 21.99/22.25 22656 identity = sk_c5 | identity = sk_c2 | multiply(sk_c3,inverse(sk_c1)) = identity. [para(16692(b,1),12029(b,2))].
% 21.99/22.25 22994 multiply(sk_c7,sk_c7) = sk_c6 | multiply(sk_c5,inverse(sk_c6)) = sk_c7. [para(13859(a,1),1184(a,1,1)),rewrite([13601(7),11131(8)]),flip(b)].
% 21.99/22.25 23177 sk_c4 = sk_c5 | multiply(sk_c2,inverse(sk_c6)) = sk_c5. [para(14706(b,1),41(a,1,2)),rewrite([340(6)])].
% 21.99/22.25 23198 sk_c4 = sk_c5 | multiply(sk_c6,inverse(sk_c2)) = sk_c7. [para(23177(b,1),1184(a,1,1)),rewrite([13601(5),340(7)]),flip(b)].
% 21.99/22.25 24160 sk_c3 = sk_c5 | multiply(sk_c5,multiply(sk_c5,sk_c5)) = sk_c1. [para(16287(b,1),11325(b,1)),flip(c),merge(b)].
% 21.99/22.25 24299 identity = sk_c7 | identity = sk_c5 | sk_c3 = sk_c1. [para(20194(b,1),16536(b,1,2)),rewrite([253(9)]),flip(c)].
% 21.99/22.25 24323 identity = sk_c7 | sk_c3 = sk_c1. [para(24299(b,1),258(a,1,1)),rewrite([13601(8)]),flip(c),merge(c)].
% 21.99/22.25 24326 sk_c3 = sk_c1 | identity = sk_c5. [para(24323(a,1),258(a,1,1)),rewrite([11131(5)]),flip(b)].
% 21.99/22.25 24616 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(A,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c6,inverse(B)) != sk_c7 | sk_c7 != B | sk_c5 != sk_c6. [para(2(a,1),11445(g,1,2)),rewrite([340(23),253(27)]),flip(g)].
% 21.99/22.25 24644 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(A,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(11131(a,1),24616(f,1,2)),xx(g),merge(f)].
% 21.99/22.25 24645 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(A,multiply(B,sk_c7)) != sk_c5 | multiply(inverse(B),inverse(A)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(28(a,1),24644(c,1)),rewrite([1184(15)])].
% 21.99/22.25 24646 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | sk_c5 != A | multiply(sk_c7,inverse(A)) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(2(a,1),24645(c,1,2)),rewrite([253(10),11131(12),13601(12)]),flip(c)].
% 21.99/22.25 24672 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | inverse(A) != sk_c5 | multiply(sk_c7,A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(340(a,1),24646(d,1,2)),flip(c)].
% 21.99/22.25 24675 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(inverse(A),sk_c7) != sk_c5 | sk_c7 != A | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(339(a,1),24672(d,1)),rewrite([11131(10),1184(11),13601(11)]),flip(d)].
% 21.99/22.25 24676 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(inverse(A),multiply(inverse(B),sk_c7)) != sk_c5 | multiply(B,A) != sk_c7 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [para(1184(a,1),24675(c,1,1)),rewrite([28(13)]),flip(d)].
% 21.99/22.25 24678 multiply(sk_c6,sk_c5) != sk_c7 | identity != sk_c6 | multiply(sk_c7,multiply(inverse(sk_c6),sk_c7)) != sk_c5 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c5 != sk_c6. [factor(24676,a,d),rewrite([13601(10)])].
% 21.99/22.25 25432 sk_c6 = sk_c7 | multiply(sk_c7,sk_c2) = sk_c6. [para(19754(b,1),3748(b,1)),flip(c),merge(c)].
% 21.99/22.25 25440 sk_c6 = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5. [para(25432(b,1),2624(c,1)),merge(c),merge(d)].
% 21.99/22.25 25461 sk_c6 = sk_c7 | multiply(sk_c4,sk_c5) = sk_c7. [para(25440(b,1),19754(b,1,2)),merge(b)].
% 21.99/22.25 25465 sk_c6 = sk_c7 | multiply(sk_c1,sk_c7) = sk_c2. [para(25461(b,1),27(b,1)),flip(c),merge(c)].
% 21.99/22.25 25484 sk_c6 = sk_c7 | identity = sk_c2. [para(1770(b,1),25465(b,1,1)),rewrite([13599(9)]),merge(b)].
% 21.99/22.25 25494 sk_c6 = sk_c7 | inverse(sk_c2) = identity. [para(25484(b,1),258(a,1,1))].
% 21.99/22.25 25515 sk_c6 = sk_c7 | sk_c4 = sk_c5. [para(25494(b,1),23198(b,1,2)),rewrite([253(9)]),merge(c)].
% 21.99/22.25 25529 sk_c6 = sk_c7. [para(25515(b,1),19741(b,1,1)),rewrite([13601(8)]),flip(c),merge(b),merge(c)].
% 21.99/22.25 25911 identity != sk_c7 | sk_c5 != sk_c7 | multiply(sk_c7,sk_c7) != sk_c5. [back_rewrite(24678),rewrite([25529(1),13602(3),25529(5),25529(8),11131(9),13599(10),253(9),25529(10),25529(16)]),flip(c),merge(b),merge(e)].
% 21.99/22.25 26533 multiply(sk_c7,sk_c7) = sk_c7 | multiply(sk_c5,sk_c5) = sk_c7. [back_rewrite(22994),rewrite([25529(4),25529(7),11131(8)])].
% 21.99/22.25 26814 identity = sk_c3 | identity = sk_c5. [back_rewrite(22535),rewrite([25529(2),11131(3),13602(3),25529(5),11131(6),13602(6)])].
% 21.99/22.25 26919 identity != sk_c7 | multiply(sk_c7,sk_c7) != sk_c5 | multiply(sk_c5,sk_c5) != sk_c7. [back_rewrite(22300),rewrite([25529(1),13602(3),25529(5),13599(6),25529(7),25529(12),11131(13),25529(15)]),xx(b)].
% 21.99/22.25 28068 sk_c5 = sk_c7 | identity = sk_c7. [back_rewrite(14158),rewrite([25529(4),13602(6),25529(8),13599(9)]),merge(c)].
% 21.99/22.25 28960 sk_c5 = sk_c7 | identity = sk_c5. [para(14139(a,1),26814(a,2)),merge(c)].
% 21.99/22.25 29458 sk_c5 = sk_c7. [para(28960(b,1),28068(b,1)),merge(b),merge(c)].
% 21.99/22.25 30279 identity != sk_c7 | multiply(sk_c7,sk_c7) != sk_c7. [back_rewrite(26919),rewrite([29458(7),29458(9),29458(10)]),merge(c)].
% 21.99/22.25 30321 multiply(sk_c7,sk_c7) = sk_c7. [back_rewrite(26533),rewrite([29458(6),29458(7)]),merge(b)].
% 21.99/22.25 30593 identity != sk_c7. [back_rewrite(25911),rewrite([29458(4),30321(9),29458(8)]),xx(b),xx(c)].
% 21.99/22.25 30684 sk_c3 = sk_c1. [back_rewrite(24326),rewrite([29458(5)]),unit_del(b,30593)].
% 21.99/22.25 30690 sk_c1 = sk_c7. [back_rewrite(24160),rewrite([30684(1),29458(2),29458(4),29458(5),29458(6),30321(7),30321(6)]),flip(b),merge(b)].
% 21.99/22.25 30691 identity = sk_c2. [back_rewrite(22656),rewrite([29458(2),30684(7),30690(7),30690(8),11131(9),29458(8),30321(9)]),flip(c),merge(c),unit_del(a,30593)].
% 21.99/22.25 30697 sk_c2 = sk_c7. [back_rewrite(20221),rewrite([30691(1),29458(4),30684(5),30690(5),11131(6),29458(5),30321(6),30691(5)]),flip(b),merge(b)].
% 21.99/22.25 30701 $F. [back_rewrite(30279),rewrite([30691(1),30697(1),30321(6)]),xx(a),xx(b)].
% 21.99/22.25
% 21.99/22.25 % SZS output end Refutation
% 21.99/22.25 ============================== end of proof ==========================
% 21.99/22.25
% 21.99/22.25 ============================== STATISTICS ============================
% 21.99/22.25
% 21.99/22.25 Given=4311. Generated=1054912. Kept=30700. proofs=1.
% 21.99/22.25 Usable=163. Sos=1661. Demods=23. Limbo=380, Disabled=28525. Hints=0.
% 21.99/22.25 Megabytes=24.84.
% 21.99/22.25 User_CPU=20.68, System_CPU=0.59, Wall_clock=21.
% 21.99/22.25
% 21.99/22.25 ============================== end of statistics =====================
% 21.99/22.25
% 21.99/22.25 ============================== end of search =========================
% 21.99/22.25
% 21.99/22.25 THEOREM PROVED
% 21.99/22.25 % SZS status Unsatisfiable
% 21.99/22.25
% 21.99/22.25 Exiting with 1 proof.
% 21.99/22.25
% 21.99/22.25 Process 26617 exit (max_proofs) Tue Jun 14 09:01:41 2022
% 21.99/22.25 Prover9 interrupted
%------------------------------------------------------------------------------