TSTP Solution File: GRP305-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP305-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:18:33 EDT 2022
% Result : Unsatisfiable 26.06s 26.46s
% Output : Refutation 26.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP305-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jun 13 21:20:39 EDT 2022
% 0.10/0.31 % CPUTime :
% 26.06/26.46 ============================== Prover9 ===============================
% 26.06/26.46 Prover9 (32) version 2009-11A, November 2009.
% 26.06/26.46 Process 5041 was started by sandbox2 on n025.cluster.edu,
% 26.06/26.46 Mon Jun 13 21:20:40 2022
% 26.06/26.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4888_n025.cluster.edu".
% 26.06/26.46 ============================== end of head ===========================
% 26.06/26.46
% 26.06/26.46 ============================== INPUT =================================
% 26.06/26.46
% 26.06/26.46 % Reading from file /tmp/Prover9_4888_n025.cluster.edu
% 26.06/26.46
% 26.06/26.46 set(prolog_style_variables).
% 26.06/26.46 set(auto2).
% 26.06/26.46 % set(auto2) -> set(auto).
% 26.06/26.46 % set(auto) -> set(auto_inference).
% 26.06/26.46 % set(auto) -> set(auto_setup).
% 26.06/26.46 % set(auto_setup) -> set(predicate_elim).
% 26.06/26.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 26.06/26.46 % set(auto) -> set(auto_limits).
% 26.06/26.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 26.06/26.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 26.06/26.46 % set(auto) -> set(auto_denials).
% 26.06/26.46 % set(auto) -> set(auto_process).
% 26.06/26.46 % set(auto2) -> assign(new_constants, 1).
% 26.06/26.46 % set(auto2) -> assign(fold_denial_max, 3).
% 26.06/26.46 % set(auto2) -> assign(max_weight, "200.000").
% 26.06/26.46 % set(auto2) -> assign(max_hours, 1).
% 26.06/26.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 26.06/26.46 % set(auto2) -> assign(max_seconds, 0).
% 26.06/26.46 % set(auto2) -> assign(max_minutes, 5).
% 26.06/26.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 26.06/26.46 % set(auto2) -> set(sort_initial_sos).
% 26.06/26.46 % set(auto2) -> assign(sos_limit, -1).
% 26.06/26.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 26.06/26.46 % set(auto2) -> assign(max_megs, 400).
% 26.06/26.46 % set(auto2) -> assign(stats, some).
% 26.06/26.46 % set(auto2) -> clear(echo_input).
% 26.06/26.46 % set(auto2) -> set(quiet).
% 26.06/26.46 % set(auto2) -> clear(print_initial_clauses).
% 26.06/26.46 % set(auto2) -> clear(print_given).
% 26.06/26.46 assign(lrs_ticks,-1).
% 26.06/26.46 assign(sos_limit,10000).
% 26.06/26.46 assign(order,kbo).
% 26.06/26.46 set(lex_order_vars).
% 26.06/26.46 clear(print_given).
% 26.06/26.46
% 26.06/26.46 % formulas(sos). % not echoed (29 formulas)
% 26.06/26.46
% 26.06/26.46 ============================== end of input ==========================
% 26.06/26.46
% 26.06/26.46 % From the command line: assign(max_seconds, 300).
% 26.06/26.46
% 26.06/26.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 26.06/26.46
% 26.06/26.46 % Formulas that are not ordinary clauses:
% 26.06/26.46
% 26.06/26.46 ============================== end of process non-clausal formulas ===
% 26.06/26.46
% 26.06/26.46 ============================== PROCESS INITIAL CLAUSES ===============
% 26.06/26.46
% 26.06/26.46 ============================== PREDICATE ELIMINATION =================
% 26.06/26.46
% 26.06/26.46 ============================== end predicate elimination =============
% 26.06/26.46
% 26.06/26.46 Auto_denials: (non-Horn, no changes).
% 26.06/26.46
% 26.06/26.46 Term ordering decisions:
% 26.06/26.46
% 26.06/26.46 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 26.06/26.46 Function symbol KB weights: sk_c6=1. sk_c4=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. identity=1. multiply=1. inverse=0.
% 26.06/26.46
% 26.06/26.46 ============================== end of process initial clauses ========
% 26.06/26.46
% 26.06/26.46 ============================== CLAUSES FOR SEARCH ====================
% 26.06/26.46
% 26.06/26.46 ============================== end of clauses for search =============
% 26.06/26.46
% 26.06/26.46 ============================== SEARCH ================================
% 26.06/26.46
% 26.06/26.46 % Starting search at 0.01 seconds.
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=46.000, iters=3561
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=45.000, iters=3346
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=44.000, iters=3457
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=43.000, iters=3358
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=42.000, iters=3334
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=41.000, iters=3342
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=40.000, iters=3358
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=39.000, iters=3348
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=38.000, iters=3342
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=37.000, iters=3334
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=35.000, iters=3367
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=33.000, iters=3358
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=32.000, iters=3341
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=18.000, iters=3375
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=17.000, iters=3339
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=16.000, iters=3337
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=15.000, iters=3350
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=14.000, iters=3339
% 26.06/26.46
% 26.06/26.46 Low Water (keep): wt=13.000, iters=3340
% 26.06/26.46
% 26.06/26.46 ============================== PROOF =================================
% 26.06/26.46 % SZS status Unsatisfiable
% 26.06/26.46 % SZS output start Refutation
% 26.06/26.46
% 26.06/26.46 % Proof 1 at 24.84 (+ 0.54) seconds.
% 26.06/26.46 % Length of proof is 222.
% 26.06/26.46 % Level of proof is 34.
% 26.06/26.46 % Maximum clause weight is 48.000.
% 26.06/26.46 % Given clauses 2522.
% 26.06/26.46
% 26.06/26.46 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 26.06/26.46 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 26.06/26.46 3 inverse(sk_c6) = sk_c4 | inverse(sk_c2) = sk_c6 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 26.06/26.46 4 inverse(sk_c6) = sk_c4 | inverse(sk_c3) = sk_c5 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 26.06/26.46 5 inverse(sk_c1) = sk_c6 | inverse(sk_c2) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 26.06/26.46 6 inverse(sk_c1) = sk_c6 | inverse(sk_c3) = sk_c5 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 26.06/26.46 9 multiply(sk_c5,sk_c4) = sk_c6 | inverse(sk_c2) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 26.06/26.46 10 multiply(sk_c5,sk_c4) = sk_c6 | inverse(sk_c3) = sk_c5 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 26.06/26.46 11 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c6) = sk_c4 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 26.06/26.46 12 inverse(sk_c6) = sk_c4 | multiply(sk_c2,sk_c5) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 26.06/26.46 13 inverse(sk_c6) = sk_c4 | multiply(sk_c3,sk_c4) = sk_c5 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 26.06/26.46 14 multiply(sk_c1,sk_c6) = sk_c4 | inverse(sk_c2) = sk_c6 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 26.06/26.46 15 multiply(sk_c1,sk_c6) = sk_c4 | inverse(sk_c3) = sk_c5 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 26.06/26.46 16 inverse(sk_c1) = sk_c6 | multiply(sk_c5,sk_c6) = sk_c4 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 26.06/26.46 17 inverse(sk_c1) = sk_c6 | multiply(sk_c2,sk_c5) = sk_c6 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 26.06/26.46 18 inverse(sk_c1) = sk_c6 | multiply(sk_c3,sk_c4) = sk_c5 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 26.06/26.46 19 multiply(sk_c6,sk_c5) = sk_c4 | multiply(sk_c5,sk_c6) = sk_c4 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 26.06/26.46 22 multiply(sk_c5,sk_c4) = sk_c6 | multiply(sk_c5,sk_c6) = sk_c4 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 26.06/26.46 23 multiply(sk_c5,sk_c4) = sk_c6 | multiply(sk_c2,sk_c5) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 26.06/26.46 24 multiply(sk_c5,sk_c4) = sk_c6 | multiply(sk_c3,sk_c4) = sk_c5 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 26.06/26.46 26 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c2,sk_c5) = sk_c6 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 26.06/26.46 27 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c3,sk_c4) = sk_c5 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 26.06/26.46 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 26.06/26.46 29 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6 | inverse(C) != sk_c5 | multiply(C,sk_c4) != sk_c5 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 26.06/26.46 33 inverse(sk_c6) = sk_c4 | multiply(sk_c6,sk_c2) = identity. [para(3(b,1),2(a,1,1))].
% 26.06/26.46 34 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c3) = identity. [para(4(b,1),2(a,1,1))].
% 26.06/26.46 35 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c2) = identity. [para(5(b,1),2(a,1,1))].
% 26.06/26.46 36 inverse(sk_c1) = sk_c6 | multiply(sk_c5,sk_c3) = identity. [para(6(b,1),2(a,1,1))].
% 26.06/26.46 37 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 26.06/26.46 42 inverse(sk_c2) = sk_c6 | multiply(sk_c5,multiply(sk_c4,A)) = multiply(sk_c6,A). [para(9(a,1),28(a,1,1)),flip(b)].
% 26.06/26.46 44 inverse(sk_c3) = sk_c5 | multiply(sk_c5,multiply(sk_c4,A)) = multiply(sk_c6,A). [para(10(a,1),28(a,1,1)),flip(b)].
% 26.06/26.46 46 inverse(sk_c6) = sk_c4 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c4,A). [para(11(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 47 inverse(sk_c6) = sk_c4 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c4). [para(11(b,1),28(a,2,2)),rewrite([28(8)])].
% 26.06/26.46 48 inverse(sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(12(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 52 inverse(sk_c2) = sk_c6 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c4,A). [para(14(a,1),28(a,1,1)),flip(b)].
% 26.06/26.46 54 inverse(sk_c3) = sk_c5 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c4,A). [para(15(a,1),28(a,1,1)),flip(b)].
% 26.06/26.46 76 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(26(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 77 multiply(sk_c1,sk_c6) = sk_c4 | multiply(A,multiply(sk_c2,sk_c5)) = multiply(A,sk_c6). [para(26(b,1),28(a,2,2)),rewrite([28(9)])].
% 26.06/26.46 89 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(identity) != sk_c6 | sk_c5 != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5. [para(1(a,1),29(h,1))].
% 26.06/26.46 91 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | inverse(inverse(sk_c6)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5. [para(2(a,1),29(d,1))].
% 26.06/26.46 92 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(inverse(sk_c5)) != sk_c6 | identity != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5. [para(2(a,1),29(h,1))].
% 26.06/26.46 121 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | inverse(inverse(sk_c5)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | inverse(A) != sk_c5 | multiply(A,sk_c4) != sk_c5. [factor(92,e,g)].
% 26.06/26.46 159 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),37(a,1,2))].
% 26.06/26.46 167 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c5),sk_c4) = sk_c6. [para(11(b,1),37(a,1,2))].
% 26.06/26.46 168 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c2),sk_c6) = sk_c5. [para(12(b,1),37(a,1,2))].
% 26.06/26.46 169 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c3),sk_c5) = sk_c4. [para(13(b,1),37(a,1,2))].
% 26.06/26.46 172 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c5),sk_c4) = sk_c6. [para(16(b,1),37(a,1,2))].
% 26.06/26.46 173 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c2),sk_c6) = sk_c5. [para(17(b,1),37(a,1,2))].
% 26.06/26.46 174 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c3),sk_c5) = sk_c4. [para(18(b,1),37(a,1,2))].
% 26.06/26.46 175 multiply(sk_c6,sk_c5) = sk_c4 | multiply(inverse(sk_c5),sk_c4) = sk_c6. [para(19(b,1),37(a,1,2))].
% 26.06/26.46 178 multiply(sk_c5,sk_c6) = sk_c4 | multiply(inverse(sk_c5),sk_c6) = sk_c4. [para(22(a,1),37(a,1,2))].
% 26.06/26.46 179 multiply(sk_c5,sk_c4) = sk_c6 | multiply(inverse(sk_c2),sk_c6) = sk_c5. [para(23(b,1),37(a,1,2))].
% 26.06/26.46 186 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(37(a,1),37(a,1,2))].
% 26.06/26.46 187 multiply(A,identity) = A. [back_rewrite(159),rewrite([186(4)])].
% 26.06/26.46 190 inverse(identity) = identity. [para(187(a,1),2(a,1))].
% 26.06/26.46 208 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5. [back_rewrite(89),rewrite([190(28)])].
% 26.06/26.46 212 inverse(sk_c6) = sk_c4 | multiply(A,multiply(sk_c5,sk_c3)) = A. [para(34(b,1),28(a,2,2)),rewrite([28(8),187(10)])].
% 26.06/26.46 213 inverse(sk_c6) = sk_c4 | inverse(sk_c5) = sk_c3. [para(34(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 216 inverse(sk_c6) = sk_c4 | multiply(sk_c3,sk_c5) = identity. [para(213(b,1),2(a,1,1))].
% 26.06/26.46 219 inverse(sk_c1) = sk_c6 | inverse(sk_c6) = sk_c2. [para(35(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 223 inverse(sk_c1) = sk_c6 | inverse(sk_c5) = sk_c3. [para(36(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 252 multiply(A,inverse(A)) = identity. [para(186(a,1),2(a,1))].
% 26.06/26.46 265 multiply(A,multiply(inverse(A),B)) = B. [para(186(a,1),37(a,1))].
% 26.06/26.46 266 inverse(inverse(A)) = A. [para(186(a,1),187(a,1)),rewrite([187(2)]),flip(a)].
% 26.06/26.46 269 inverse(sk_c6) = sk_c2 | multiply(inverse(sk_c6),A) = multiply(sk_c1,A). [para(219(a,1),186(a,1,1,1))].
% 26.06/26.46 271 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | inverse(A) != sk_c5 | multiply(A,sk_c4) != sk_c5. [back_rewrite(121),rewrite([266(23)])].
% 26.06/26.46 273 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(B) != sk_c5 | multiply(B,sk_c4) != sk_c5. [back_rewrite(91),rewrite([266(20)]),xx(e)].
% 26.06/26.46 278 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(252(a,1),28(a,1)),flip(a)].
% 26.06/26.46 279 inverse(sk_c6) = sk_c2 | multiply(sk_c1,sk_c6) = identity. [para(219(a,1),252(a,1,2))].
% 26.06/26.46 334 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | inverse(multiply(A,B)) != sk_c5 | multiply(A,multiply(B,sk_c4)) != sk_c5. [para(28(a,1),271(i,1))].
% 26.06/26.46 349 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | inverse(multiply(B,C)) != sk_c5 | multiply(B,multiply(C,sk_c4)) != sk_c5. [para(28(a,1),273(i,1))].
% 26.06/26.46 361 inverse(sk_c6) = sk_c4 | multiply(A,multiply(sk_c3,sk_c5)) = A. [para(216(b,1),28(a,2,2)),rewrite([28(8),187(10)])].
% 26.06/26.46 403 inverse(sk_c6) = sk_c2 | identity = sk_c4 | inverse(sk_c2) = sk_c6. [para(279(b,1),14(a,1))].
% 26.06/26.46 412 inverse(sk_c2) = sk_c6 | multiply(sk_c6,inverse(sk_c4)) = sk_c5. [para(252(a,1),42(b,1,2)),rewrite([187(7)]),flip(b)].
% 26.06/26.46 539 inverse(sk_c3) = sk_c5 | multiply(sk_c6,inverse(sk_c4)) = sk_c5. [para(252(a,1),44(b,1,2)),rewrite([187(7)]),flip(b)].
% 26.06/26.46 578 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c5),multiply(sk_c4,A)) = multiply(sk_c6,A). [para(167(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 580 inverse(sk_c6) = sk_c4 | multiply(sk_c3,sk_c4) = sk_c6. [para(213(b,1),167(b,1,1)),merge(b)].
% 26.06/26.46 581 inverse(sk_c6) = sk_c4 | sk_c5 = sk_c6. [para(580(b,1),13(b,1)),flip(c),merge(b)].
% 26.06/26.46 591 sk_c5 = sk_c6 | multiply(sk_c6,multiply(sk_c4,A)) = A. [para(581(a,1),265(a,1,2,1))].
% 26.06/26.46 659 inverse(sk_c6) = sk_c4 | multiply(sk_c6,sk_c6) = sk_c5. [para(3(b,1),168(b,1,1)),merge(b)].
% 26.06/26.46 663 inverse(sk_c6) = sk_c4 | multiply(sk_c4,sk_c2) = sk_c5. [para(33(b,1),46(b,1,2)),rewrite([187(11)]),flip(c),merge(b)].
% 26.06/26.46 690 inverse(sk_c6) = sk_c4 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(659(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 693 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c5) = multiply(sk_c4,sk_c6). [para(659(b,1),46(b,1,2)),merge(b)].
% 26.06/26.46 694 inverse(sk_c6) = sk_c4 | multiply(sk_c4,multiply(sk_c2,A)) = multiply(sk_c5,A). [para(663(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 696 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c4),sk_c5) = sk_c2. [para(663(b,1),37(a,1,2))].
% 26.06/26.46 697 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c5) = sk_c4. [para(4(b,1),169(b,1,1)),merge(b)].
% 26.06/26.46 700 inverse(sk_c6) = sk_c4 | multiply(sk_c5,multiply(sk_c5,A)) = multiply(sk_c4,A). [para(697(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 702 inverse(sk_c6) = sk_c4 | multiply(inverse(sk_c5),sk_c4) = sk_c5. [para(697(b,1),37(a,1,2))].
% 26.06/26.46 705 inverse(sk_c6) = sk_c4 | multiply(sk_c3,multiply(sk_c5,sk_c6)) = sk_c5. [para(13(b,1),47(b,2)),merge(b)].
% 26.06/26.46 759 inverse(sk_c1) = sk_c6 | multiply(sk_c6,sk_c6) = sk_c5. [para(5(b,1),173(b,1,1)),merge(b)].
% 26.06/26.46 765 inverse(sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c5,sk_c2)) = identity. [para(33(b,1),48(b,2)),merge(b)].
% 26.06/26.46 792 inverse(sk_c1) = sk_c6 | multiply(sk_c6,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(759(b,1),28(a,1,1)),flip(b)].
% 26.06/26.46 801 inverse(sk_c1) = sk_c6 | multiply(sk_c5,sk_c5) = sk_c4. [para(6(b,1),174(b,1,1)),merge(b)].
% 26.06/26.46 821 inverse(sk_c1) = sk_c6 | multiply(inverse(sk_c5),sk_c4) = sk_c5. [para(801(b,1),37(a,1,2))].
% 26.06/26.46 869 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(278(a,1),37(a,1,2)),rewrite([187(3)]),flip(a)].
% 26.06/26.46 925 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(869(a,1),37(a,1,2)),flip(a)].
% 26.06/26.46 929 inverse(sk_c6) = sk_c4 | multiply(sk_c5,inverse(sk_c4)) = sk_c3. [para(169(b,1),869(a,1,2,1)),rewrite([266(11)])].
% 26.06/26.46 1131 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | multiply(inverse(B),inverse(C)) != sk_c5 | multiply(C,multiply(B,sk_c4)) != sk_c5. [back_rewrite(349),rewrite([925(31)])].
% 26.06/26.46 1133 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(inverse(A),inverse(B)) != sk_c5 | multiply(B,multiply(A,sk_c4)) != sk_c5. [back_rewrite(334),rewrite([925(33)])].
% 26.06/26.46 1279 inverse(sk_c2) = sk_c6 | multiply(sk_c1,sk_c5) = identity. [para(412(b,1),52(b,1,2)),rewrite([252(15)]),merge(b)].
% 26.06/26.46 1320 inverse(sk_c2) = sk_c6 | inverse(sk_c1) = sk_c5. [para(1279(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 1327 inverse(sk_c1) = sk_c5 | inverse(sk_c6) = sk_c2. [para(1320(a,1),266(a,1,1))].
% 26.06/26.46 1337 inverse(sk_c6) = sk_c2 | sk_c5 = sk_c6. [para(1327(a,1),219(a,1)),merge(c)].
% 26.06/26.46 1339 inverse(sk_c6) = sk_c2 | multiply(sk_c1,sk_c5) = identity. [para(1327(a,1),252(a,1,2))].
% 26.06/26.46 1347 sk_c5 = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = A. [para(1337(a,1),37(a,1,1))].
% 26.06/26.46 1353 sk_c5 = sk_c6 | sk_c2 = sk_c4. [para(1337(a,1),581(a,1)),merge(c)].
% 26.06/26.46 1416 inverse(sk_c3) = sk_c5 | multiply(sk_c1,sk_c5) = identity. [para(539(b,1),54(b,1,2)),rewrite([252(15)]),merge(b)].
% 26.06/26.46 1512 inverse(sk_c3) = sk_c5 | inverse(sk_c1) = sk_c5. [para(1416(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 1519 inverse(sk_c1) = sk_c5 | inverse(sk_c5) = sk_c3. [para(1512(a,1),266(a,1,1))].
% 26.06/26.46 1531 inverse(sk_c5) = sk_c3 | sk_c5 = sk_c6. [para(1519(a,1),223(a,1)),merge(c)].
% 26.06/26.46 2084 inverse(sk_c1) = sk_c6 | sk_c5 = sk_c6. [para(821(b,1),172(b,1)),merge(b)].
% 26.06/26.46 2181 sk_c5 = sk_c6 | multiply(sk_c1,sk_c6) = identity. [para(2084(a,1),252(a,1,2))].
% 26.06/26.46 2309 sk_c5 = sk_c6 | multiply(A,multiply(sk_c1,sk_c6)) = A. [para(2181(b,1),28(a,2,2)),rewrite([28(7),187(9)])].
% 26.06/26.46 3515 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(inverse(B),inverse(C)) != sk_c5 | multiply(C,multiply(B,sk_c4)) != sk_c5. [para(28(a,1),208(j,1)),rewrite([925(34)])].
% 26.06/26.46 3604 sk_c5 = sk_c6 | multiply(sk_c2,A) = multiply(sk_c4,A). [para(591(b,1),1347(b,1,2)),merge(b)].
% 26.06/26.46 4218 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | multiply(sk_c4,inverse(B)) != sk_c5 | sk_c5 != B. [para(2(a,1),1131(i,1,2)),rewrite([266(32),187(36)]),flip(i)].
% 26.06/26.46 4262 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | multiply(sk_c4,B) != sk_c5 | inverse(B) != sk_c5. [para(266(a,1),4218(h,1,2)),flip(i)].
% 26.06/26.46 4355 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(A,sk_c5) != sk_c6 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [resolve(4262,h,265,a),rewrite([925(34),266(34)])].
% 26.06/26.46 4373 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(inverse(A),inverse(B)) != sk_c6 | multiply(B,multiply(A,sk_c5)) != sk_c6 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [para(28(a,1),4355(g,1)),rewrite([925(24)])].
% 26.06/26.46 4418 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(sk_c5,inverse(A)) != sk_c6 | sk_c6 != A | multiply(inverse(sk_c5),sk_c4) != sk_c5. [para(2(a,1),4373(g,1,2)),rewrite([266(25),187(29)]),flip(g)].
% 26.06/26.46 4496 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(sk_c5,A) != sk_c6 | inverse(A) != sk_c6 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [para(266(a,1),4418(f,1,2)),flip(g)].
% 26.06/26.46 4515 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [factor(4496,b,f)].
% 26.06/26.46 4581 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c5,multiply(sk_c2,sk_c5))) = multiply(sk_c6,sk_c6). [para(77(b,1),76(b,2)),merge(b)].
% 26.06/26.46 4655 sk_c5 = sk_c6 | multiply(sk_c4,multiply(sk_c1,sk_c6)) = sk_c2. [para(3604(b,1),2309(b,1)),merge(b)].
% 26.06/26.46 5521 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(sk_c4,inverse(A)) != sk_c5 | sk_c5 != A. [para(2(a,1),1133(i,1,2)),rewrite([266(34),187(38)]),flip(i)].
% 26.06/26.46 5531 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(sk_c4,A) != sk_c5 | inverse(A) != sk_c5. [para(266(a,1),5521(h,1,2)),flip(i)].
% 26.06/26.46 5579 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != A | multiply(inverse(A),sk_c4) != sk_c5. [para(265(a,1),5531(h,1)),rewrite([925(37),266(37)]),flip(h)].
% 26.06/26.46 5580 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(inverse(sk_c6),sk_c4) != sk_c5. [factor(5579,e,h)].
% 26.06/26.46 6121 multiply(sk_c6,sk_c5) = sk_c4 | multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6). [para(175(b,1),925(a,1,1)),rewrite([266(12)]),flip(b)].
% 26.06/26.46 6763 inverse(sk_c6) = sk_c2 | identity = sk_c4. [para(403(c,1),266(a,1,1)),merge(c)].
% 26.06/26.46 7360 inverse(sk_c6) = sk_c4 | multiply(sk_c4,sk_c6) = sk_c4. [para(693(b,1),697(b,1)),merge(b)].
% 26.06/26.46 7368 inverse(sk_c6) = sk_c4 | identity = sk_c6. [para(7360(b,1),37(a,1,2)),rewrite([2(8)])].
% 26.06/26.46 7375 identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(7368(a,1),266(a,1,1))].
% 26.06/26.46 7398 identity = sk_c6 | sk_c2 = sk_c4 | identity = sk_c4. [para(7368(a,1),6763(a,1)),flip(b)].
% 26.06/26.46 7481 identity = sk_c6 | sk_c2 = sk_c4 | inverse(sk_c4) = identity. [para(7398(c,1),190(a,1,1))].
% 26.06/26.46 7827 identity = sk_c6 | sk_c2 = sk_c4. [para(7481(c,1),7375(b,1)),merge(c),merge(d)].
% 26.06/26.46 7831 sk_c2 = sk_c4 | inverse(sk_c6) = identity. [para(7827(a,1),190(a,1,1))].
% 26.06/26.46 7912 sk_c2 = sk_c4 | inverse(sk_c6) = sk_c6. [para(7827(a,1),7831(b,2)),merge(b)].
% 26.06/26.46 7913 sk_c2 = sk_c4 | multiply(sk_c6,sk_c6) = identity. [para(7912(b,1),2(a,1,1))].
% 26.06/26.46 8082 inverse(sk_c6) = sk_c2 | multiply(inverse(sk_c6),sk_c5) = identity. [para(1339(b,1),269(b,2)),merge(b)].
% 26.06/26.46 8100 sk_c2 = sk_c4 | inverse(sk_c6) = sk_c4 | identity = sk_c5. [para(7913(b,1),659(b,1))].
% 26.06/26.46 9193 sk_c2 = sk_c4 | inverse(sk_c6) = sk_c2 | identity = sk_c5. [para(7831(b,1),8082(b,1,1)),rewrite([1(10)]),flip(c)].
% 26.06/26.46 10265 sk_c2 = sk_c4 | identity = sk_c5. [para(9193(b,1),8100(b,1)),merge(c),merge(d),merge(e)].
% 26.06/26.46 10269 sk_c2 = sk_c4 | inverse(sk_c5) = identity. [para(10265(b,1),190(a,1,1))].
% 26.06/26.46 10297 sk_c2 = sk_c4 | inverse(sk_c6) = sk_c5. [para(10265(b,1),7831(b,2)),merge(b)].
% 26.06/26.46 10339 sk_c2 = sk_c4 | inverse(sk_c5) = sk_c5. [para(10265(b,1),10269(b,2)),merge(b)].
% 26.06/26.46 10349 sk_c2 = sk_c4 | multiply(sk_c5,sk_c6) = identity. [para(10297(b,1),2(a,1,1))].
% 26.06/26.46 10421 sk_c2 = sk_c4 | multiply(sk_c5,sk_c6) = sk_c4. [para(10339(b,1),178(b,1,1)),merge(c)].
% 26.06/26.46 10716 sk_c2 = sk_c4 | identity = sk_c4. [para(10421(b,1),10349(b,1)),flip(c),merge(b)].
% 26.06/26.46 10823 sk_c2 = sk_c4 | inverse(sk_c5) = sk_c4. [para(10716(b,1),10269(b,2)),merge(b)].
% 26.06/26.46 11107 sk_c2 = sk_c4 | multiply(sk_c5,sk_c4) = identity. [para(10823(b,1),252(a,1,2))].
% 26.06/26.46 11719 sk_c2 = sk_c4 | multiply(sk_c5,sk_c4) = sk_c6. [para(7827(a,1),11107(b,2)),merge(b)].
% 26.06/26.46 12137 sk_c2 = sk_c4 | multiply(inverse(sk_c5),sk_c6) = sk_c4. [para(11719(b,1),37(a,1,2))].
% 26.06/26.46 13256 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c4,inverse(B)) != sk_c5 | sk_c5 != B. [para(2(a,1),3515(j,1,2)),rewrite([266(35),187(39)]),flip(j)].
% 26.06/26.46 13296 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c4,B) != sk_c5 | inverse(B) != sk_c5. [para(266(a,1),13256(i,1,2)),flip(j)].
% 26.06/26.46 13300 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | sk_c5 != B | multiply(inverse(B),sk_c4) != sk_c5. [para(265(a,1),13296(i,1)),rewrite([925(38),266(38)]),flip(i)].
% 26.06/26.46 13301 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,sk_c6) != sk_c4 | inverse(A) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(inverse(sk_c6),sk_c4) != sk_c5. [factor(13300,h,i)].
% 26.06/26.46 13338 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | inverse(sk_c6) != sk_c4 | multiply(A,multiply(B,sk_c6)) != sk_c4 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(inverse(sk_c6),sk_c4) != sk_c5. [para(28(a,1),13301(d,1)),rewrite([925(21)])].
% 26.06/26.46 14413 inverse(sk_c6) = sk_c4 | multiply(sk_c4,sk_c3) = sk_c5. [para(34(b,1),700(b,1,2)),rewrite([187(11)]),flip(c),merge(b)].
% 26.06/26.46 14441 inverse(sk_c6) = sk_c4 | multiply(sk_c6,sk_c3) = identity. [para(14413(b,1),578(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 26.06/26.46 14453 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c3) = sk_c6. [para(14441(b,1),690(b,1,2)),rewrite([187(11)]),flip(c),merge(b)].
% 26.06/26.46 14587 inverse(sk_c6) = sk_c4 | multiply(A,sk_c6) = A. [para(14453(b,1),212(b,1,2)),merge(b)].
% 26.06/26.46 14679 inverse(sk_c6) = sk_c4 | multiply(sk_c3,sk_c5) = sk_c5. [para(14587(b,1),705(b,1,2)),merge(b)].
% 26.06/26.46 14958 inverse(sk_c6) = sk_c4 | multiply(A,sk_c5) = A. [para(14679(b,1),361(b,1,2)),merge(b)].
% 26.06/26.46 15175 inverse(sk_c6) = sk_c4 | inverse(sk_c4) = sk_c2. [para(14958(b,1),696(b,1)),merge(b)].
% 26.06/26.46 15285 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c2) = sk_c3. [para(15175(b,1),929(b,1,2)),merge(b)].
% 26.06/26.46 15730 inverse(sk_c6) = sk_c4 | multiply(sk_c2,sk_c3) = identity. [para(15285(b,1),765(b,1,2)),merge(b)].
% 26.06/26.46 15761 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c3) = sk_c4. [para(15730(b,1),694(b,1,2)),rewrite([187(11)]),flip(c),merge(b)].
% 26.06/26.46 15786 inverse(sk_c6) = sk_c4 | multiply(A,sk_c4) = A. [para(15761(b,1),212(b,1,2)),merge(b)].
% 26.06/26.46 15843 inverse(sk_c6) = sk_c4 | inverse(sk_c5) = sk_c5. [para(15786(b,1),702(b,1)),merge(b)].
% 26.06/26.46 15883 inverse(sk_c6) = sk_c4 | multiply(sk_c5,sk_c5) = identity. [para(15843(b,1),2(a,1,1))].
% 26.06/26.46 16002 inverse(sk_c6) = sk_c4 | multiply(sk_c4,sk_c6) = identity. [para(15883(b,1),693(b,1)),flip(c),merge(b)].
% 26.06/26.46 16064 inverse(sk_c6) = sk_c4 | inverse(sk_c4) = sk_c6. [para(16002(b,1),37(a,1,2)),rewrite([187(8)])].
% 26.06/26.46 16075 inverse(sk_c6) = sk_c4. [para(16064(b,1),266(a,1,1)),merge(b)].
% 26.06/26.46 16716 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c4 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c4,sk_c4) != sk_c5. [back_rewrite(13338),rewrite([16075(12),16075(36)]),xx(c)].
% 26.06/26.46 17771 multiply(sk_c6,sk_c5) = sk_c4 | multiply(inverse(sk_c4),sk_c5) = sk_c4. [back_rewrite(6121),rewrite([16075(11)])].
% 26.06/26.46 17872 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(sk_c4,sk_c4) != sk_c5. [back_rewrite(5580),rewrite([16075(12),16075(32)]),xx(c)].
% 26.06/26.46 17946 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | inverse(sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [back_rewrite(4515),rewrite([16075(12)]),xx(c)].
% 26.06/26.46 18437 multiply(sk_c4,sk_c6) = identity. [para(16075(a,1),2(a,1,1))].
% 26.06/26.46 18439 inverse(sk_c4) = sk_c6. [para(16075(a,1),266(a,1,1))].
% 26.06/26.46 18440 multiply(sk_c6,sk_c4) = identity. [para(16075(a,1),252(a,1,2))].
% 26.06/26.46 18533 multiply(sk_c6,sk_c5) != sk_c4 | multiply(sk_c5,sk_c4) != sk_c6 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [back_rewrite(17946),rewrite([18439(20)]),xx(e)].
% 26.06/26.46 18584 multiply(sk_c6,sk_c5) = sk_c4. [back_rewrite(17771),rewrite([18439(7)]),merge(b)].
% 26.06/26.46 18990 multiply(sk_c5,sk_c4) != sk_c6 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(inverse(sk_c5),sk_c4) != sk_c5. [back_rewrite(18533),rewrite([18584(3)]),xx(a)].
% 26.06/26.46 19126 multiply(sk_c5,sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | multiply(sk_c4,sk_c4) != sk_c5. [back_rewrite(17872),rewrite([18584(3)]),xx(a)].
% 26.06/26.46 19243 multiply(sk_c5,sk_c4) != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c4 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c4,sk_c4) != sk_c5. [back_rewrite(16716),rewrite([18584(3)]),xx(a)].
% 26.06/26.46 19373 inverse(sk_c1) = sk_c6 | identity = sk_c4. [para(801(b,1),792(b,2)),rewrite([18584(12),18440(11)]),merge(b)].
% 26.06/26.46 19415 multiply(sk_c4,sk_c4) = sk_c5. [para(18584(a,1),37(a,1,2)),rewrite([16075(2)])].
% 26.06/26.46 19419 multiply(inverse(sk_c5),sk_c4) = sk_c6. [para(18584(a,1),925(a,1,1)),rewrite([18439(2),16075(5)]),flip(a)].
% 26.06/26.46 19476 multiply(sk_c5,sk_c4) != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c4 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6 | sk_c5 != sk_c6. [back_rewrite(19243),rewrite([19415(29)]),xx(g)].
% 26.06/26.46 19478 multiply(sk_c5,sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | multiply(sk_c5,sk_c6) != sk_c4 | identity != sk_c6. [back_rewrite(19126),rewrite([19415(25)]),xx(f)].
% 26.06/26.46 19523 multiply(sk_c5,sk_c4) != sk_c6 | identity != sk_c4 | multiply(sk_c5,sk_c6) != sk_c4 | sk_c5 != sk_c6. [back_rewrite(18990),rewrite([19419(17)]),flip(d)].
% 26.06/26.46 19528 multiply(sk_c6,sk_c6) = inverse(sk_c5). [para(19415(a,1),925(a,1,1)),rewrite([18439(4),18439(5)]),flip(a)].
% 26.06/26.46 19597 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c5,multiply(sk_c2,sk_c5))) = inverse(sk_c5). [back_rewrite(4581),rewrite([19528(15)])].
% 26.06/26.46 19656 multiply(sk_c5,sk_c6) = sk_c4. [para(19419(a,1),37(a,1,2)),rewrite([266(3)])].
% 26.06/26.46 19659 sk_c5 = sk_c6 | multiply(sk_c3,sk_c4) = sk_c6. [para(1531(a,1),19419(a,1,1))].
% 26.06/26.46 19682 multiply(sk_c5,sk_c4) != sk_c6 | identity != sk_c4 | sk_c5 != sk_c6. [back_rewrite(19523),rewrite([19656(11)]),xx(c)].
% 26.06/26.46 19698 multiply(sk_c5,sk_c4) != sk_c6 | multiply(inverse(sk_c5),sk_c6) != sk_c4 | sk_c5 != sk_c6 | identity != sk_c6. [back_rewrite(19478),rewrite([19656(17)]),xx(d)].
% 26.06/26.46 19700 multiply(sk_c5,sk_c4) != sk_c6 | multiply(A,multiply(B,sk_c6)) != sk_c4 | multiply(inverse(B),inverse(A)) != sk_c6 | identity != sk_c6 | sk_c5 != sk_c6. [back_rewrite(19476),rewrite([19656(18)]),xx(d)].
% 26.06/26.46 20283 multiply(sk_c5,sk_c4) != sk_c6 | sk_c5 != sk_c6 | identity != sk_c6 | sk_c2 = sk_c4. [resolve(19698,b,12137,b)].
% 26.06/26.46 20334 identity = sk_c4 | sk_c1 = sk_c4. [para(19373(a,1),266(a,1,1)),rewrite([16075(5)]),flip(b)].
% 26.06/26.46 20340 sk_c1 = sk_c4 | multiply(A,sk_c4) = A. [para(20334(a,1),187(a,1,2))].
% 26.06/26.46 21143 sk_c5 = sk_c6 | multiply(sk_c5,sk_c4) = sk_c6. [para(19659(b,1),24(b,1)),flip(c),merge(c)].
% 26.06/26.46 21144 sk_c5 = sk_c6 | multiply(sk_c1,sk_c6) = sk_c4. [para(19659(b,1),27(b,1)),flip(c),merge(c)].
% 26.06/26.46 22948 sk_c1 = sk_c4 | sk_c5 != sk_c6 | identity != sk_c4. [para(20340(b,1),19682(a,1)),merge(d)].
% 26.06/26.46 23311 sk_c5 = sk_c6 | sk_c2 = sk_c5. [para(21144(b,1),4655(b,1,2)),rewrite([19415(9)]),flip(c),merge(b)].
% 26.06/26.46 23342 multiply(sk_c5,sk_c4) != sk_c6 | multiply(A,sk_c4) != sk_c4 | multiply(inverse(sk_c5),inverse(A)) != sk_c6 | identity != sk_c6 | sk_c5 != sk_c6. [para(19656(a,1),19700(b,1,2))].
% 26.06/26.46 23346 multiply(sk_c5,sk_c4) != sk_c6 | sk_c5 != sk_c4 | multiply(inverse(sk_c5),sk_c6) != sk_c6 | identity != sk_c6 | sk_c5 != sk_c6. [para(18439(a,1),23342(c,1,2)),rewrite([19415(8)])].
% 26.06/26.46 23375 sk_c5 = sk_c6 | sk_c5 = sk_c4. [para(23311(b,1),1353(b,1)),merge(b)].
% 26.06/26.46 23474 sk_c5 = sk_c6. [para(23375(b,1),21143(b,1,1)),rewrite([19415(9)]),merge(b),merge(c)].
% 26.06/26.46 23489 identity != sk_c6 | sk_c4 != sk_c6. [back_rewrite(23346),rewrite([23474(1),18440(3),23474(4),23474(7),16075(8),18437(9),23474(13)]),flip(b),xx(e),merge(c),merge(d)].
% 26.06/26.46 23638 sk_c1 = sk_c4 | identity != sk_c4. [back_rewrite(22948),rewrite([23474(4)]),xx(b)].
% 26.06/26.46 24123 identity != sk_c6 | sk_c2 = sk_c4. [back_rewrite(20283),rewrite([23474(1),18440(3),23474(4)]),xx(b),merge(b)].
% 26.06/26.46 24294 multiply(sk_c1,sk_c6) = sk_c4 | multiply(sk_c2,multiply(sk_c6,multiply(sk_c2,sk_c6))) = sk_c4. [back_rewrite(19597),rewrite([23474(7),23474(9),23474(13),16075(14)])].
% 26.06/26.46 24315 multiply(sk_c6,sk_c6) = sk_c4. [back_rewrite(19528),rewrite([23474(4),16075(5)])].
% 26.06/26.46 24617 identity = sk_c6 | multiply(inverse(sk_c2),sk_c6) = sk_c6. [back_rewrite(179),rewrite([23474(1),18440(3),23474(8)])].
% 26.06/26.46 24658 sk_c1 = sk_c4. [resolve(23638,b,20334,a),merge(b)].
% 26.06/26.46 24701 identity = sk_c4 | multiply(sk_c2,multiply(sk_c6,multiply(sk_c2,sk_c6))) = sk_c4. [back_rewrite(24294),rewrite([24658(1),18437(3)])].
% 26.06/26.46 24811 sk_c2 = sk_c4. [resolve(24123,a,7827,a),merge(b)].
% 26.06/26.46 24813 identity = sk_c4. [back_rewrite(24701),rewrite([24811(4),24811(6),18437(8),187(7),18437(6)]),merge(b)].
% 26.06/26.46 24815 sk_c4 = sk_c6. [back_rewrite(24617),rewrite([24813(1),24811(4),18439(5),24315(6)]),merge(b)].
% 26.06/26.46 24843 $F. [back_rewrite(23489),rewrite([24813(1),24815(1),24815(4)]),xx(a),xx(b)].
% 26.06/26.46
% 26.06/26.46 % SZS output end Refutation
% 26.06/26.46 ============================== end of proof ==========================
% 26.06/26.46
% 26.06/26.46 ============================== STATISTICS ============================
% 26.06/26.46
% 26.06/26.46 Given=2522. Generated=585619. Kept=24842. proofs=1.
% 26.06/26.46 Usable=23. Sos=7. Demods=26. Limbo=30, Disabled=24811. Hints=0.
% 26.06/26.46 Megabytes=21.19.
% 26.06/26.46 User_CPU=24.84, System_CPU=0.54, Wall_clock=25.
% 26.06/26.46
% 26.06/26.46 ============================== end of statistics =====================
% 26.06/26.46
% 26.06/26.46 ============================== end of search =========================
% 26.06/26.46
% 26.06/26.46 THEOREM PROVED
% 26.06/26.46 % SZS status Unsatisfiable
% 26.06/26.46
% 26.06/26.46 Exiting with 1 proof.
% 26.06/26.46
% 26.06/26.46 Process 5041 exit (max_proofs) Mon Jun 13 21:21:05 2022
% 26.06/26.46 Prover9 interrupted
%------------------------------------------------------------------------------