TSTP Solution File: GRP383-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP383-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 11:18:51 EDT 2022
% Result : Unsatisfiable 99.37s 99.79s
% Output : Refutation 99.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP383-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 22:57:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 26.35/26.69 ============================== Prover9 ===============================
% 26.35/26.69 Prover9 (32) version 2009-11A, November 2009.
% 26.35/26.69 Process 19153 was started by sandbox2 on n024.cluster.edu,
% 26.35/26.69 Mon Jun 13 22:57:04 2022
% 26.35/26.69 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19000_n024.cluster.edu".
% 26.35/26.69 ============================== end of head ===========================
% 26.35/26.69
% 26.35/26.69 ============================== INPUT =================================
% 26.35/26.69
% 26.35/26.69 % Reading from file /tmp/Prover9_19000_n024.cluster.edu
% 26.35/26.69
% 26.35/26.69 set(prolog_style_variables).
% 26.35/26.69 set(auto2).
% 26.35/26.69 % set(auto2) -> set(auto).
% 26.35/26.69 % set(auto) -> set(auto_inference).
% 26.35/26.69 % set(auto) -> set(auto_setup).
% 26.35/26.69 % set(auto_setup) -> set(predicate_elim).
% 26.35/26.69 % set(auto_setup) -> assign(eq_defs, unfold).
% 26.35/26.69 % set(auto) -> set(auto_limits).
% 26.35/26.69 % set(auto_limits) -> assign(max_weight, "100.000").
% 26.35/26.69 % set(auto_limits) -> assign(sos_limit, 20000).
% 26.35/26.69 % set(auto) -> set(auto_denials).
% 26.35/26.69 % set(auto) -> set(auto_process).
% 26.35/26.69 % set(auto2) -> assign(new_constants, 1).
% 26.35/26.69 % set(auto2) -> assign(fold_denial_max, 3).
% 26.35/26.69 % set(auto2) -> assign(max_weight, "200.000").
% 26.35/26.69 % set(auto2) -> assign(max_hours, 1).
% 26.35/26.69 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 26.35/26.69 % set(auto2) -> assign(max_seconds, 0).
% 26.35/26.69 % set(auto2) -> assign(max_minutes, 5).
% 26.35/26.69 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 26.35/26.69 % set(auto2) -> set(sort_initial_sos).
% 26.35/26.69 % set(auto2) -> assign(sos_limit, -1).
% 26.35/26.69 % set(auto2) -> assign(lrs_ticks, 3000).
% 26.35/26.69 % set(auto2) -> assign(max_megs, 400).
% 26.35/26.69 % set(auto2) -> assign(stats, some).
% 26.35/26.69 % set(auto2) -> clear(echo_input).
% 26.35/26.69 % set(auto2) -> set(quiet).
% 26.35/26.69 % set(auto2) -> clear(print_initial_clauses).
% 26.35/26.69 % set(auto2) -> clear(print_given).
% 26.35/26.69 assign(lrs_ticks,-1).
% 26.35/26.69 assign(sos_limit,10000).
% 26.35/26.69 assign(order,kbo).
% 26.35/26.69 set(lex_order_vars).
% 26.35/26.69 clear(print_given).
% 26.35/26.69
% 26.35/26.69 % formulas(sos). % not echoed (39 formulas)
% 26.35/26.69
% 26.35/26.69 ============================== end of input ==========================
% 26.35/26.69
% 26.35/26.69 % From the command line: assign(max_seconds, 300).
% 26.35/26.69
% 26.35/26.69 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 26.35/26.69
% 26.35/26.69 % Formulas that are not ordinary clauses:
% 26.35/26.69
% 26.35/26.69 ============================== end of process non-clausal formulas ===
% 26.35/26.69
% 26.35/26.69 ============================== PROCESS INITIAL CLAUSES ===============
% 26.35/26.69
% 26.35/26.69 ============================== PREDICATE ELIMINATION =================
% 26.35/26.69
% 26.35/26.69 ============================== end predicate elimination =============
% 26.35/26.69
% 26.35/26.69 Auto_denials: (non-Horn, no changes).
% 26.35/26.69
% 26.35/26.69 Term ordering decisions:
% 26.35/26.69
% 26.35/26.69 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 26.35/26.69 Function symbol KB weights: sk_c7=1. sk_c8=1. sk_c6=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c1=1. sk_c2=1. identity=1. multiply=1. inverse=0.
% 26.35/26.69
% 26.35/26.69 ============================== end of process initial clauses ========
% 26.35/26.69
% 26.35/26.69 ============================== CLAUSES FOR SEARCH ====================
% 26.35/26.69
% 26.35/26.69 ============================== end of clauses for search =============
% 26.35/26.69
% 26.35/26.69 ============================== SEARCH ================================
% 26.35/26.69
% 26.35/26.69 % Starting search at 0.02 seconds.
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=47.000, iters=3568
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=43.000, iters=3404
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=42.000, iters=3466
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=41.000, iters=3339
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=40.000, iters=3334
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=39.000, iters=3636
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=38.000, iters=3379
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=37.000, iters=3422
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=36.000, iters=3346
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=35.000, iters=3348
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=34.000, iters=3384
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=33.000, iters=3376
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=32.000, iters=3369
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=31.000, iters=3336
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=30.000, iters=3575
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=28.000, iters=3425
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=27.000, iters=3381
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=17.000, iters=3377
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=16.000, iters=3344
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=15.000, iters=3337
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=14.000, iters=3351
% 26.35/26.69
% 26.35/26.69 Low Water (keep): wt=13.000, iters=3370
% 26.35/26.69
% 26.35/26.69 Low Water (displace): id=4886, wt=54.000
% 26.35/26.69
% 26.35/26.69 Low Water (displace): id=15735, wt=12.000
% 26.35/26.69
% 26.35/26.69 Low Water (displace): id=15825, wt=11.000
% 26.35/26.69
% 26.35/26.69 Low Water (displace): id=20188, wt=10.000
% 99.37/99.79
% 99.37/99.79 Low Water (keep): wt=12.000, iters=3333
% 99.37/99.79
% 99.37/99.79 Low Water (keep): wt=11.000, iters=3333
% 99.37/99.79
% 99.37/99.79 ============================== PROOF =================================
% 99.37/99.79 % SZS status Unsatisfiable
% 99.37/99.79 % SZS output start Refutation
% 99.37/99.79
% 99.37/99.79 % Proof 1 at 96.30 (+ 2.38) seconds.
% 99.37/99.79 % Length of proof is 213.
% 99.37/99.79 % Level of proof is 35.
% 99.37/99.79 % Maximum clause weight is 55.000.
% 99.37/99.79 % Given clauses 6762.
% 99.37/99.79
% 99.37/99.79 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 99.37/99.79 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 99.37/99.79 3 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 99.37/99.79 4 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 99.37/99.79 5 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 99.37/99.79 6 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 99.37/99.79 7 inverse(sk_c2) = sk_c3 | inverse(sk_c4) = sk_c8 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 99.37/99.79 8 inverse(sk_c2) = sk_c3 | inverse(sk_c5) = sk_c7 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 99.37/99.79 9 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 99.37/99.79 10 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 99.37/99.79 11 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 99.37/99.79 15 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 99.37/99.79 16 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 99.37/99.79 17 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 99.37/99.79 18 multiply(sk_c1,sk_c7) = sk_c8 | inverse(sk_c5) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 99.37/99.79 19 multiply(sk_c2,sk_c3) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 99.37/99.79 20 multiply(sk_c2,sk_c3) = sk_c7 | inverse(sk_c5) = sk_c7 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 99.37/99.79 21 inverse(sk_c2) = sk_c3 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 99.37/99.79 24 multiply(sk_c3,sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 99.37/99.79 26 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 99.37/99.79 28 multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c5,sk_c6) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 99.37/99.79 30 multiply(sk_c1,sk_c7) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 99.37/99.79 32 multiply(sk_c2,sk_c3) = sk_c7 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 99.37/99.79 35 multiply(sk_c3,sk_c8) = sk_c7 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 99.37/99.79 36 multiply(sk_c3,sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_33) # label(negated_conjecture). [assumption].
% 99.37/99.79 38 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 99.37/99.79 39 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(B,C) != sk_c7 | inverse(B) != C | multiply(C,sk_c8) != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8 | inverse(E) != sk_c7 | multiply(E,sk_c6) != sk_c7 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 99.37/99.79 43 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(B,C) != sk_c7 | inverse(B) != C | multiply(C,sk_c8) != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(D) != sk_c7 | multiply(D,sk_c6) != sk_c7. [factor(39,c,i),merge(i)].
% 99.37/99.79 58 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 99.37/99.79 59 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c5) = identity. [para(4(b,1),2(a,1,1))].
% 99.37/99.79 61 inverse(sk_c5) = sk_c7 | multiply(sk_c8,sk_c1) = identity. [para(6(a,1),2(a,1,1))].
% 99.37/99.79 64 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),38(a,1,1)),rewrite([1(2)]),flip(a)].
% 99.37/99.79 65 inverse(sk_c8) = sk_c7 | multiply(sk_c7,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(9(b,1),38(a,1,1)),flip(b)].
% 99.37/99.79 66 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c7,sk_c8)) = multiply(A,sk_c6). [para(9(b,1),38(a,2,2)),rewrite([38(8)])].
% 99.37/99.79 67 inverse(sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(10(b,1),38(a,1,1)),flip(b)].
% 99.37/99.79 69 inverse(sk_c8) = sk_c7 | multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(11(b,1),38(a,1,1)),flip(b)].
% 99.37/99.79 77 inverse(sk_c1) = sk_c8 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(15(b,1),38(a,1,1)),flip(b)].
% 99.37/99.79 88 inverse(sk_c5) = sk_c7 | multiply(A,multiply(sk_c2,sk_c3)) = multiply(A,sk_c7). [para(20(a,1),38(a,2,2)),rewrite([38(8)])].
% 99.37/99.79 95 inverse(sk_c4) = sk_c8 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(24(a,1),38(a,1,1)),flip(b)].
% 99.37/99.79 100 multiply(sk_c7,sk_c8) = sk_c6 | multiply(A,multiply(sk_c7,sk_c6)) = multiply(A,sk_c8). [para(26(a,1),38(a,2,2)),rewrite([38(9)])].
% 99.37/99.79 111 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c2,multiply(sk_c3,A)) = multiply(sk_c7,A). [para(32(a,1),38(a,1,1)),flip(b)].
% 99.37/99.79 117 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(35(a,1),38(a,1,1)),flip(b)].
% 99.37/99.79 120 multiply(sk_c3,sk_c8) = sk_c7 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c8). [para(36(b,1),38(a,2,2)),rewrite([38(9)])].
% 99.37/99.79 149 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(B,identity) != sk_c7 | inverse(B) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7. [para(1(a,1),43(g,1))].
% 99.37/99.79 401 inverse(sk_c8) = sk_c7 | multiply(sk_c8,multiply(sk_c4,A)) = A. [para(58(b,1),38(a,1,1)),rewrite([1(6)]),flip(b)].
% 99.37/99.79 402 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c8,sk_c4)) = multiply(A,identity). [para(58(b,1),38(a,2,2)),rewrite([38(8)])].
% 99.37/99.79 422 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),64(a,1,2))].
% 99.37/99.79 423 inverse(sk_c8) = sk_c7 | multiply(sk_c7,multiply(sk_c5,A)) = A. [para(4(b,1),64(a,1,1))].
% 99.37/99.79 430 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(11(b,1),64(a,1,2))].
% 99.37/99.79 435 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c5),sk_c7) = sk_c6. [para(16(b,1),64(a,1,2))].
% 99.37/99.79 436 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c1),sk_c8) = sk_c7. [para(17(a,1),64(a,1,2))].
% 99.37/99.79 451 multiply(sk_c7,sk_c8) = sk_c6 | multiply(inverse(sk_c2),sk_c7) = sk_c3. [para(32(a,1),64(a,1,2))].
% 99.37/99.79 460 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),identity) = sk_c4. [para(58(b,1),64(a,1,2))].
% 99.37/99.79 461 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(64(a,1),64(a,1,2))].
% 99.37/99.79 462 multiply(A,identity) = A. [back_rewrite(422),rewrite([461(4)])].
% 99.37/99.79 463 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c4. [back_rewrite(460),rewrite([462(8)])].
% 99.37/99.79 464 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c8,sk_c4)) = A. [back_rewrite(402),rewrite([462(10)])].
% 99.37/99.79 466 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | sk_c7 != B | inverse(B) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7. [back_rewrite(149),rewrite([462(18)]),flip(e)].
% 99.37/99.79 469 inverse(identity) = identity. [para(462(a,1),2(a,1))].
% 99.37/99.79 506 inverse(sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(463(b,1),64(a,1,1))].
% 99.37/99.79 508 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = sk_c5. [para(59(b,1),64(a,1,2)),rewrite([462(8)])].
% 99.37/99.79 509 inverse(sk_c7) = sk_c5 | multiply(sk_c7,sk_c8) = identity. [para(508(a,1),2(a,1,1))].
% 99.37/99.79 520 inverse(sk_c5) = sk_c7 | inverse(sk_c8) = sk_c1. [para(61(b,1),64(a,1,2)),rewrite([462(8)])].
% 99.37/99.79 544 inverse(sk_c8) = sk_c7 | multiply(sk_c6,sk_c4) = sk_c7. [para(58(b,1),65(b,1,2)),rewrite([462(11)]),flip(c),merge(b)].
% 99.37/99.79 545 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c7),multiply(sk_c6,A)) = multiply(sk_c8,A). [para(65(b,1),64(a,1,2))].
% 99.37/99.79 555 multiply(A,inverse(A)) = identity. [para(461(a,1),2(a,1))].
% 99.37/99.79 584 multiply(A,multiply(inverse(A),B)) = B. [para(461(a,1),64(a,1))].
% 99.37/99.79 585 inverse(inverse(A)) = A. [para(461(a,1),462(a,1)),rewrite([462(2)]),flip(a)].
% 99.37/99.79 606 inverse(sk_c8) = sk_c1 | inverse(sk_c7) = sk_c5. [para(520(a,1),585(a,1,1))].
% 99.37/99.79 609 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c7) = identity. [para(4(b,1),555(a,1,2))].
% 99.37/99.79 612 inverse(sk_c4) = sk_c8 | multiply(sk_c2,sk_c3) = identity. [para(7(a,1),555(a,1,2))].
% 99.37/99.79 613 inverse(sk_c5) = sk_c7 | multiply(sk_c2,sk_c3) = identity. [para(8(a,1),555(a,1,2))].
% 99.37/99.79 614 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(555(a,1),38(a,1)),flip(a)].
% 99.37/99.79 622 inverse(sk_c8) = sk_c7 | multiply(sk_c5,multiply(sk_c7,A)) = A. [para(4(b,1),584(a,1,2,1))].
% 99.37/99.79 637 inverse(sk_c8) = sk_c7 | multiply(sk_c5,multiply(sk_c7,sk_c8)) = sk_c7. [para(11(b,1),66(b,2)),merge(b)].
% 99.37/99.79 667 inverse(sk_c7) = sk_c5 | sk_c1 = sk_c7. [para(606(a,1),508(a,1)),merge(c)].
% 99.37/99.79 679 inverse(sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c7,sk_c4)) = identity. [para(58(b,1),67(b,2)),merge(b)].
% 99.37/99.79 683 inverse(sk_c8) = sk_c7 | multiply(sk_c8,inverse(sk_c7)) = sk_c4. [para(555(a,1),67(b,1,2)),rewrite([462(7)]),flip(b)].
% 99.37/99.79 776 inverse(sk_c8) = sk_c7 | multiply(sk_c5,multiply(sk_c6,sk_c5)) = identity. [para(59(b,1),69(b,2)),merge(b)].
% 99.37/99.79 927 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c7) = multiply(sk_c7,sk_c4). [para(544(b,1),69(b,1,2)),merge(b)].
% 99.37/99.79 928 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c5,sk_c7)) = A. [para(609(b,1),38(a,2,2)),rewrite([38(8),462(10)])].
% 99.37/99.79 966 inverse(sk_c4) = sk_c8 | identity = sk_c7. [para(612(b,1),19(a,1)),merge(c)].
% 99.37/99.79 968 identity = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(966(a,1),2(a,1,1))].
% 99.37/99.79 969 identity = sk_c7 | multiply(sk_c8,multiply(sk_c4,A)) = A. [para(966(a,1),64(a,1,1))].
% 99.37/99.79 972 identity = sk_c7 | multiply(sk_c4,multiply(sk_c8,A)) = A. [para(966(a,1),584(a,1,2,1))].
% 99.37/99.79 976 identity = sk_c7 | multiply(A,multiply(sk_c8,sk_c4)) = A. [para(968(b,1),38(a,2,2)),rewrite([38(7),462(9)])].
% 99.37/99.79 1022 inverse(sk_c5) = sk_c7 | identity = sk_c7. [para(613(b,1),20(a,1)),merge(c)].
% 99.37/99.79 1028 identity = sk_c7 | multiply(sk_c5,multiply(sk_c7,A)) = A. [para(1022(a,1),584(a,1,2,1))].
% 99.37/99.79 1403 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c4),multiply(sk_c8,A)) = multiply(sk_c7,A). [para(77(b,1),64(a,1,2))].
% 99.37/99.79 1653 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c7) = sk_c6. [para(4(b,1),430(b,1,1)),merge(b)].
% 99.37/99.79 1657 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(1653(b,1),64(a,1,2))].
% 99.37/99.79 1797 identity = sk_c7 | inverse(sk_c1) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c6. [para(1022(a,1),435(b,1,1))].
% 99.37/99.79 1965 inverse(sk_c4) = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(5(a,1),436(b,1,1)),merge(b)].
% 99.37/99.79 2584 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(614(a,1),64(a,1,2)),rewrite([462(3)]),flip(a)].
% 99.37/99.79 2651 multiply(sk_c4,sk_c7) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = inverse(sk_c1). [para(30(a,1),2584(a,1,2,1))].
% 99.37/99.79 2664 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(2584(a,1),64(a,1,2)),flip(a)].
% 99.37/99.79 3531 inverse(sk_c5) = sk_c7 | multiply(A,sk_c7) = A. [para(613(b,1),88(b,1,2)),rewrite([462(10)]),flip(c),merge(b)].
% 99.37/99.79 4086 inverse(sk_c5) = sk_c7 | inverse(sk_c7) = identity. [para(3531(b,1),2(a,1))].
% 99.37/99.79 4087 inverse(sk_c5) = sk_c7 | sk_c1 = sk_c8. [para(3531(b,1),18(a,1)),merge(c)].
% 99.37/99.79 4132 sk_c1 = sk_c8 | inverse(sk_c7) = sk_c5. [para(4087(a,1),585(a,1,1))].
% 99.37/99.79 4167 inverse(sk_c7) = identity | inverse(sk_c7) = sk_c5. [para(4086(a,1),585(a,1,1))].
% 99.37/99.79 4313 inverse(sk_c7) = sk_c5 | multiply(sk_c7,A) = A. [para(4167(a,1),64(a,1,1)),rewrite([1(8)])].
% 99.37/99.79 4898 inverse(sk_c4) = sk_c8 | multiply(sk_c3,sk_c7) = multiply(sk_c7,sk_c8). [para(1965(b,1),95(b,1,2)),merge(b)].
% 99.37/99.79 5483 inverse(sk_c7) = sk_c5 | identity = sk_c8. [para(4313(b,1),509(b,1)),flip(c),merge(b)].
% 99.37/99.79 5538 identity = sk_c8 | multiply(sk_c5,sk_c7) = identity. [para(5483(a,1),2(a,1,1))].
% 99.37/99.79 6146 identity = sk_c7 | multiply(inverse(sk_c4),A) = multiply(sk_c8,A). [para(584(a,1),969(b,1,2)),flip(b)].
% 99.37/99.79 6210 identity = sk_c7 | multiply(sk_c4,sk_c8) = multiply(sk_c8,sk_c4). [para(976(b,1),972(b,1,2)),merge(b)].
% 99.37/99.79 6382 identity = sk_c7 | multiply(sk_c5,sk_c7) = multiply(sk_c8,sk_c4). [para(976(b,1),1028(b,1,2)),merge(b)].
% 99.37/99.79 6714 inverse(sk_c8) = sk_c7 | sk_c8 = sk_c7. [para(1657(b,1),66(b,2)),rewrite([64(14)]),merge(b)].
% 99.37/99.79 6845 sk_c8 = sk_c7 | inverse(sk_c7) = sk_c8. [para(6714(a,1),585(a,1,1))].
% 99.37/99.79 6867 sk_c8 = sk_c7 | sk_c5 = sk_c8 | sk_c1 = sk_c7. [para(6845(b,1),667(a,1)),flip(b)].
% 99.37/99.79 6879 sk_c8 = sk_c7 | sk_c1 = sk_c8 | sk_c5 = sk_c8. [para(6845(b,1),4132(b,1)),flip(c)].
% 99.37/99.79 7279 sk_c8 = sk_c7 | sk_c5 = sk_c8. [para(6879(b,1),6867(c,1)),merge(c),merge(d),merge(e)].
% 99.37/99.79 7282 sk_c8 = sk_c7 | multiply(sk_c7,sk_c6) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7. [para(7279(b,1),28(b,1,1))].
% 99.37/99.79 7611 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c8). [para(35(a,1),111(b,1,2)),merge(b)].
% 99.37/99.79 8252 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c3,multiply(sk_c8,multiply(sk_c7,sk_c6))) = multiply(sk_c7,sk_c8). [para(100(b,1),117(b,2)),merge(b)].
% 99.37/99.79 8538 multiply(sk_c3,sk_c8) = sk_c7 | multiply(inverse(sk_c8),multiply(sk_c4,sk_c7)) = identity. [para(2(a,1),120(b,2))].
% 99.37/99.79 8853 multiply(sk_c7,sk_c8) = sk_c6 | multiply(inverse(sk_c8),inverse(sk_c3)) = inverse(sk_c7). [para(35(a,1),2664(a,1,1)),flip(b)].
% 99.37/99.79 9955 identity = sk_c7 | multiply(inverse(sk_c4),multiply(sk_c8,sk_c4)) = sk_c8. [para(6210(b,1),64(a,1,2))].
% 99.37/99.79 10953 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(B) != sk_c7 | identity != B | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7. [para(585(a,1),466(f,1)),flip(e),flip(f)].
% 99.37/99.79 10956 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(B) != sk_c7 | identity != B | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | multiply(B,sk_c6) != sk_c7. [factor(10953,e,i)].
% 99.37/99.79 11139 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c7)) != sk_c8 | inverse(C) != sk_c7 | identity != C | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | multiply(C,sk_c6) != sk_c7. [para(38(a,1),10956(d,1)),rewrite([2664(11)])].
% 99.37/99.79 11595 multiply(sk_c7,sk_c8) = sk_c6 | multiply(inverse(sk_c7),sk_c2) = inverse(sk_c3). [para(451(b,1),2664(a,1,1)),rewrite([585(12)]),flip(b)].
% 99.37/99.79 11649 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c4) = inverse(sk_c7). [para(683(b,1),506(b,1,2)),merge(b)].
% 99.37/99.79 12263 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c6) = sk_c8. [para(9(b,1),622(b,1,2)),merge(b)].
% 99.37/99.79 12271 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c5),sk_c8) = sk_c6. [para(12263(b,1),64(a,1,2))].
% 99.37/99.79 12955 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c7,inverse(A)) != sk_c8 | sk_c8 != A | inverse(B) != sk_c7 | identity != B | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | multiply(B,sk_c6) != sk_c7. [para(2(a,1),11139(d,1,2)),rewrite([585(12),462(16)]),flip(d)].
% 99.37/99.79 12958 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c7,inverse(A)) != sk_c8 | sk_c8 != A | multiply(inverse(B),inverse(C)) != sk_c7 | multiply(C,B) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | multiply(C,multiply(B,sk_c6)) != sk_c7. [para(38(a,1),12955(i,1)),rewrite([2664(18)]),flip(f)].
% 99.37/99.79 14844 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c4) = inverse(sk_c4). [para(679(b,1),64(a,1,2)),rewrite([462(8)]),flip(b)].
% 99.37/99.79 14851 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c4) = sk_c8. [para(679(b,1),401(b,1,2)),rewrite([462(11)]),flip(c),merge(b)].
% 99.37/99.79 14870 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c4. [para(14851(b,1),622(b,1,2)),merge(b)].
% 99.37/99.79 14873 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c5),sk_c4) = sk_c8. [para(14870(b,1),64(a,1,2))].
% 99.37/99.79 14927 inverse(sk_c8) = sk_c7 | multiply(sk_c6,sk_c5) = inverse(sk_c5). [para(776(b,1),64(a,1,2)),rewrite([462(8)]),flip(b)].
% 99.37/99.79 14938 inverse(sk_c8) = sk_c7 | multiply(sk_c6,sk_c5) = sk_c7. [para(776(b,1),423(b,1,2)),rewrite([462(11)]),flip(c),merge(b)].
% 99.37/99.79 15649 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = identity. [para(14938(b,1),545(b,1,2)),rewrite([2(12)]),flip(c),merge(b)].
% 99.37/99.79 15666 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c5. [para(15649(b,1),64(a,1,2)),rewrite([462(8)])].
% 99.37/99.79 15826 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c8. [para(15666(b,1),585(a,1,1))].
% 99.37/99.79 15866 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = sk_c8. [para(15826(b,1),14873(b,1,1)),merge(b)].
% 99.37/99.79 20182 inverse(sk_c8) = sk_c7 | multiply(A,sk_c8) = A. [para(15866(b,1),464(b,1,2)),merge(b)].
% 99.37/99.79 20746 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c7,inverse(A)) != sk_c8 | sk_c8 != A | multiply(sk_c6,inverse(B)) != sk_c7 | multiply(B,inverse(sk_c6)) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | sk_c7 != B. [para(2(a,1),12958(i,1,2)),rewrite([585(19),462(36)]),flip(i)].
% 99.37/99.79 20750 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | multiply(sk_c7,A) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c6,inverse(B)) != sk_c7 | multiply(B,inverse(sk_c6)) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | sk_c7 != B. [para(585(a,1),20746(c,1,2)),flip(d)].
% 99.37/99.79 20756 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | sk_c8 != A | multiply(inverse(A),sk_c7) != sk_c8 | multiply(sk_c6,inverse(B)) != sk_c7 | multiply(B,inverse(sk_c6)) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | sk_c7 != B. [para(584(a,1),20750(c,1)),rewrite([2664(15),585(15)]),flip(c)].
% 99.37/99.79 20778 inverse(sk_c8) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c8 | sk_c8 != A | multiply(inverse(A),sk_c7) != sk_c8 | multiply(sk_c6,B) != sk_c7 | multiply(inverse(B),inverse(sk_c6)) != identity | sk_c8 != sk_c7 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(B) != sk_c7. [para(585(a,1),20756(e,1,2)),flip(i)].
% 99.37/99.79 21702 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c6. [para(20182(b,1),12271(b,1)),merge(b)].
% 99.37/99.79 21705 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c7) = sk_c7. [para(20182(b,1),637(b,1,2)),merge(b)].
% 99.37/99.79 21869 inverse(sk_c8) = sk_c7 | multiply(sk_c6,sk_c5) = identity. [para(21702(b,1),2(a,1,1))].
% 99.37/99.79 24576 inverse(sk_c8) = sk_c7 | multiply(A,sk_c7) = A. [para(21705(b,1),928(b,1,2)),merge(b)].
% 99.37/99.79 24625 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = identity. [para(21869(b,1),14927(b,1)),flip(c),merge(b)].
% 99.37/99.79 24649 inverse(sk_c8) = sk_c7 | identity = sk_c6. [para(24625(b,1),21702(b,1)),merge(b)].
% 99.37/99.79 24650 identity = sk_c6 | multiply(sk_c7,sk_c8) = identity. [para(24649(a,1),2(a,1,1))].
% 99.37/99.79 24662 identity = sk_c6 | inverse(sk_c2) = sk_c3. [para(24650(b,1),21(b,1)),merge(c)].
% 99.37/99.79 24681 identity = sk_c6 | inverse(sk_c3) = sk_c2. [para(24662(b,1),585(a,1,1))].
% 99.37/99.79 26024 inverse(sk_c8) = sk_c7 | multiply(sk_c7,sk_c4) = sk_c5. [para(24576(b,1),927(b,1)),flip(c),merge(b)].
% 99.37/99.79 26786 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c5. [para(26024(b,1),14844(b,1)),flip(c),merge(b)].
% 99.37/99.79 26804 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c4. [para(26786(b,1),585(a,1,1))].
% 99.37/99.79 26816 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c4) = sk_c8. [para(26804(b,1),14873(b,1,1)),merge(b)].
% 99.37/99.79 27175 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = sk_c8. [para(26816(b,1),11649(b,1)),flip(c),merge(b)].
% 99.37/99.79 27181 inverse(sk_c7) = sk_c8. [para(27175(a,1),585(a,1,1)),merge(b)].
% 99.37/99.79 27799 multiply(sk_c7,sk_c8) = sk_c6 | multiply(sk_c8,sk_c2) = inverse(sk_c3). [back_rewrite(11595),rewrite([27181(7)])].
% 99.37/99.79 27966 multiply(sk_c7,sk_c8) = sk_c6 | multiply(inverse(sk_c8),inverse(sk_c3)) = sk_c8. [back_rewrite(8853),rewrite([27181(12)])].
% 99.37/99.79 28105 multiply(sk_c8,sk_c7) = identity. [para(27181(a,1),2(a,1,1))].
% 99.37/99.79 28106 multiply(sk_c8,multiply(sk_c7,A)) = A. [para(27181(a,1),64(a,1,1))].
% 99.37/99.79 28107 inverse(sk_c8) = sk_c7. [para(27181(a,1),585(a,1,1))].
% 99.37/99.79 28108 multiply(sk_c7,sk_c8) = identity. [para(27181(a,1),555(a,1,2))].
% 99.37/99.79 29151 multiply(sk_c7,sk_c6) != sk_c8 | sk_c8 != A | multiply(inverse(A),sk_c7) != sk_c8 | multiply(sk_c6,sk_c7) != sk_c7 | multiply(sk_c8,inverse(sk_c6)) != identity | sk_c8 != sk_c7 | identity != sk_c6. [para(27181(a,1),20778(f,1,1)),rewrite([28107(2),28108(32),27181(34)]),xx(a),merge(h)].
% 99.37/99.79 29847 identity = sk_c6 | multiply(sk_c3,sk_c6) = identity. [back_rewrite(8252),rewrite([28108(3),28106(9),28108(9)])].
% 99.37/99.79 29888 identity = sk_c6 | multiply(sk_c7,inverse(sk_c3)) = sk_c8. [back_rewrite(27966),rewrite([28108(3),28107(5)])].
% 99.37/99.79 31953 multiply(sk_c3,sk_c8) = sk_c7 | multiply(sk_c7,multiply(sk_c4,sk_c7)) = identity. [back_rewrite(8538),rewrite([28107(7)])].
% 99.37/99.79 32176 multiply(sk_c4,sk_c7) = sk_c8 | multiply(sk_c7,sk_c7) = inverse(sk_c1). [back_rewrite(2651),rewrite([28107(8)])].
% 99.37/99.79 32575 identity = sk_c6 | multiply(sk_c8,sk_c2) = inverse(sk_c3). [back_rewrite(27799),rewrite([28108(3)])].
% 99.37/99.79 32776 identity = sk_c6 | multiply(sk_c2,sk_c7) = identity. [back_rewrite(7611),rewrite([28108(3),28108(9)])].
% 99.37/99.79 32861 inverse(sk_c4) = sk_c8 | multiply(sk_c3,sk_c7) = identity. [back_rewrite(4898),rewrite([28108(10)])].
% 99.37/99.79 33236 identity = sk_c6 | inverse(sk_c3) = sk_c6. [para(29847(b,1),64(a,1,2)),rewrite([462(7)])].
% 99.37/99.79 33507 identity = sk_c6 | inverse(sk_c2) = sk_c7. [para(32776(b,1),64(a,1,2)),rewrite([462(7)])].
% 99.37/99.79 33511 identity = sk_c6 | multiply(sk_c7,sk_c2) = identity. [para(33507(b,1),2(a,1,1))].
% 99.37/99.79 34136 identity = sk_c7 | inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c6. [para(1797(c,1),1403(b,2)),rewrite([28105(16),462(15)]),merge(c)].
% 99.37/99.79 35394 identity = sk_c6 | multiply(sk_c7,sk_c2) = sk_c8. [para(24681(b,1),29888(b,1,2)),merge(b)].
% 99.37/99.79 35409 identity = sk_c6 | identity = sk_c8. [para(35394(b,1),33511(b,1)),flip(c),merge(b)].
% 99.37/99.79 35420 identity = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6. [para(35409(a,1),5538(b,2)),merge(b)].
% 99.37/99.79 35868 multiply(sk_c7,sk_c6) != sk_c8 | multiply(A,B) != sk_c8 | multiply(inverse(B),multiply(inverse(A),sk_c7)) != sk_c8 | multiply(sk_c6,sk_c7) != sk_c7 | multiply(sk_c8,inverse(sk_c6)) != identity | sk_c8 != sk_c7 | identity != sk_c6. [para(2664(a,1),29151(c,1,1)),rewrite([38(13)]),flip(b)].
% 99.37/99.79 36169 identity = sk_c6 | multiply(sk_c8,sk_c2) = sk_c2. [para(24681(b,1),32575(b,2)),merge(b)].
% 99.37/99.79 36173 identity = sk_c6 | multiply(sk_c7,sk_c2) = sk_c2. [para(36169(b,1),64(a,1,2)),rewrite([28107(5)])].
% 99.37/99.79 36223 identity = sk_c6 | identity = sk_c2. [para(36173(b,1),33511(b,1)),flip(c),merge(b)].
% 99.37/99.79 36226 identity = sk_c6 | inverse(sk_c2) = identity. [para(36223(b,1),469(a,1,1))].
% 99.37/99.79 36303 identity = sk_c6 | identity = sk_c3. [para(36226(b,1),24662(b,1)),merge(b)].
% 99.37/99.79 36309 identity = sk_c6 | inverse(sk_c3) = identity. [para(36303(b,1),469(a,1,1))].
% 99.37/99.79 36358 identity = sk_c6. [para(36309(b,1),33236(b,1)),merge(b),merge(c)].
% 99.37/99.79 36450 multiply(sk_c7,sk_c6) != sk_c8 | multiply(A,B) != sk_c8 | multiply(inverse(B),multiply(inverse(A),sk_c7)) != sk_c8 | multiply(sk_c6,sk_c7) != sk_c7 | multiply(sk_c8,inverse(sk_c6)) != sk_c6 | sk_c8 != sk_c7. [back_rewrite(35868),rewrite([36358(25),36358(30)]),xx(g)].
% 99.37/99.79 36550 sk_c6 = sk_c8 | multiply(sk_c5,sk_c7) = sk_c6. [back_rewrite(35420),rewrite([36358(1)])].
% 99.37/99.79 36749 sk_c6 = sk_c7 | inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c6. [back_rewrite(34136),rewrite([36358(1)])].
% 99.37/99.79 36840 inverse(sk_c4) = sk_c8 | multiply(sk_c3,sk_c7) = sk_c6. [back_rewrite(32861),rewrite([36358(8)])].
% 99.37/99.79 36915 multiply(sk_c3,sk_c8) = sk_c7 | multiply(sk_c7,multiply(sk_c4,sk_c7)) = sk_c6. [back_rewrite(31953),rewrite([36358(11)])].
% 99.37/99.79 40081 multiply(sk_c8,sk_c7) = sk_c6. [back_rewrite(28105),rewrite([36358(4)])].
% 99.37/99.79 40300 sk_c6 = sk_c7 | multiply(inverse(sk_c4),multiply(sk_c8,sk_c4)) = sk_c8. [back_rewrite(9955),rewrite([36358(1)])].
% 99.37/99.79 40597 sk_c6 = sk_c7 | multiply(sk_c5,sk_c7) = multiply(sk_c8,sk_c4). [back_rewrite(6382),rewrite([36358(1)])].
% 99.37/99.79 40637 sk_c6 = sk_c7 | multiply(sk_c4,sk_c8) = multiply(sk_c8,sk_c4). [back_rewrite(6210),rewrite([36358(1)])].
% 99.37/99.79 40661 sk_c6 = sk_c7 | multiply(inverse(sk_c4),A) = multiply(sk_c8,A). [back_rewrite(6146),rewrite([36358(1)])].
% 99.37/99.79 40763 inverse(sk_c6) = sk_c6. [back_rewrite(469),rewrite([36358(1),36358(3)])].
% 99.37/99.79 40764 multiply(A,sk_c6) = A. [back_rewrite(462),rewrite([36358(1)])].
% 99.37/99.79 40769 multiply(sk_c6,A) = A. [back_rewrite(1),rewrite([36358(1)])].
% 99.37/99.79 40772 sk_c8 != sk_c7 | sk_c6 != sk_c8. [factor(36450,a,b),rewrite([40764(3),40763(5),27181(6),40081(7),40764(6),40769(9),40763(12),40764(12)]),flip(a),flip(d),xx(c),merge(c),merge(d)].
% 99.37/99.79 41751 sk_c8 = sk_c7. [back_rewrite(7282),rewrite([40764(6),40764(9)]),flip(b),merge(b),merge(c)].
% 99.37/99.79 42397 sk_c6 != sk_c7. [back_rewrite(40772),rewrite([41751(1),41751(5)]),xx(a)].
% 99.37/99.79 42421 multiply(inverse(sk_c4),A) = multiply(sk_c7,A). [back_rewrite(40661),rewrite([41751(7)]),unit_del(a,42397)].
% 99.37/99.79 42433 multiply(sk_c4,sk_c7) = multiply(sk_c7,sk_c4). [back_rewrite(40637),rewrite([41751(5),41751(7)]),unit_del(a,42397)].
% 99.37/99.79 42439 multiply(sk_c5,sk_c7) = multiply(sk_c7,sk_c4). [back_rewrite(40597),rewrite([41751(7)]),unit_del(a,42397)].
% 99.37/99.79 42475 multiply(sk_c7,multiply(sk_c7,sk_c4)) = sk_c7. [back_rewrite(40300),rewrite([41751(6),42421(9),41751(9)]),unit_del(a,42397)].
% 99.37/99.79 42528 multiply(sk_c7,sk_c7) = sk_c6. [back_rewrite(40081),rewrite([41751(1)])].
% 99.37/99.79 42537 multiply(sk_c3,sk_c7) = sk_c7. [back_rewrite(36915),rewrite([41751(2),42433(9),42475(10)]),flip(b),unit_del(b,42397)].
% 99.37/99.79 42544 inverse(sk_c4) = sk_c7. [back_rewrite(36840),rewrite([41751(3),42537(7)]),flip(b),unit_del(b,42397)].
% 99.37/99.79 42548 inverse(sk_c1) = sk_c7. [back_rewrite(36749),rewrite([41751(6),42544(9)]),flip(c),merge(c),unit_del(a,42397)].
% 99.37/99.79 42554 multiply(sk_c7,sk_c4) = sk_c6. [back_rewrite(36550),rewrite([41751(2),42439(6)]),unit_del(a,42397)].
% 99.37/99.79 42575 $F. [back_rewrite(32176),rewrite([42433(3),42554(3),41751(2),42528(6),42548(6)]),merge(b),unit_del(a,42397)].
% 99.37/99.79
% 99.37/99.79 % SZS output end Refutation
% 99.37/99.79 ============================== end of proof ==========================
% 99.37/99.79
% 99.37/99.79 ============================== STATISTICS ============================
% 99.37/99.79
% 99.37/99.79 Given=6762. Generated=3928895. Kept=42574. proofs=1.
% 99.37/99.79 Usable=994. Sos=1783. Demods=44. Limbo=824, Disabled=39012. Hints=0.
% 99.37/99.79 Megabytes=34.75.
% 99.37/99.79 User_CPU=96.30, System_CPU=2.38, Wall_clock=99.
% 99.37/99.79
% 99.37/99.79 ============================== end of statistics =====================
% 99.37/99.79
% 99.37/99.79 ============================== end of search =========================
% 99.37/99.79
% 99.37/99.79 THEOREM PROVED
% 99.37/99.79 % SZS status Unsatisfiable
% 99.37/99.79
% 99.37/99.79 Exiting with 1 proof.
% 99.37/99.79
% 99.37/99.79 Process 19153 exit (max_proofs) Mon Jun 13 22:58:43 2022
% 99.37/99.79 Prover9 interrupted
%------------------------------------------------------------------------------