TSTP Solution File: GRP213-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:18:11 EDT 2022
% Result : Unsatisfiable 4.19s 4.46s
% Output : Refutation 4.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP213-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 04:50:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.19/4.46 ============================== Prover9 ===============================
% 4.19/4.46 Prover9 (32) version 2009-11A, November 2009.
% 4.19/4.46 Process 10272 was started by sandbox2 on n008.cluster.edu,
% 4.19/4.46 Mon Jun 13 04:50:53 2022
% 4.19/4.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10119_n008.cluster.edu".
% 4.19/4.46 ============================== end of head ===========================
% 4.19/4.46
% 4.19/4.46 ============================== INPUT =================================
% 4.19/4.46
% 4.19/4.46 % Reading from file /tmp/Prover9_10119_n008.cluster.edu
% 4.19/4.46
% 4.19/4.46 set(prolog_style_variables).
% 4.19/4.46 set(auto2).
% 4.19/4.46 % set(auto2) -> set(auto).
% 4.19/4.46 % set(auto) -> set(auto_inference).
% 4.19/4.46 % set(auto) -> set(auto_setup).
% 4.19/4.46 % set(auto_setup) -> set(predicate_elim).
% 4.19/4.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.19/4.46 % set(auto) -> set(auto_limits).
% 4.19/4.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.19/4.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.19/4.46 % set(auto) -> set(auto_denials).
% 4.19/4.46 % set(auto) -> set(auto_process).
% 4.19/4.46 % set(auto2) -> assign(new_constants, 1).
% 4.19/4.46 % set(auto2) -> assign(fold_denial_max, 3).
% 4.19/4.46 % set(auto2) -> assign(max_weight, "200.000").
% 4.19/4.46 % set(auto2) -> assign(max_hours, 1).
% 4.19/4.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.19/4.46 % set(auto2) -> assign(max_seconds, 0).
% 4.19/4.46 % set(auto2) -> assign(max_minutes, 5).
% 4.19/4.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.19/4.46 % set(auto2) -> set(sort_initial_sos).
% 4.19/4.46 % set(auto2) -> assign(sos_limit, -1).
% 4.19/4.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.19/4.46 % set(auto2) -> assign(max_megs, 400).
% 4.19/4.46 % set(auto2) -> assign(stats, some).
% 4.19/4.46 % set(auto2) -> clear(echo_input).
% 4.19/4.46 % set(auto2) -> set(quiet).
% 4.19/4.46 % set(auto2) -> clear(print_initial_clauses).
% 4.19/4.46 % set(auto2) -> clear(print_given).
% 4.19/4.46 assign(lrs_ticks,-1).
% 4.19/4.46 assign(sos_limit,10000).
% 4.19/4.46 assign(order,kbo).
% 4.19/4.46 set(lex_order_vars).
% 4.19/4.46 clear(print_given).
% 4.19/4.46
% 4.19/4.46 % formulas(sos). % not echoed (28 formulas)
% 4.19/4.46
% 4.19/4.46 ============================== end of input ==========================
% 4.19/4.46
% 4.19/4.46 % From the command line: assign(max_seconds, 300).
% 4.19/4.46
% 4.19/4.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.19/4.46
% 4.19/4.46 % Formulas that are not ordinary clauses:
% 4.19/4.46
% 4.19/4.46 ============================== end of process non-clausal formulas ===
% 4.19/4.46
% 4.19/4.46 ============================== PROCESS INITIAL CLAUSES ===============
% 4.19/4.46
% 4.19/4.46 ============================== PREDICATE ELIMINATION =================
% 4.19/4.46
% 4.19/4.46 ============================== end predicate elimination =============
% 4.19/4.46
% 4.19/4.46 Auto_denials: (non-Horn, no changes).
% 4.19/4.46
% 4.19/4.46 Term ordering decisions:
% 4.19/4.46
% 4.19/4.46 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 4.19/4.46 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 4.19/4.46
% 4.19/4.46 ============================== end of process initial clauses ========
% 4.19/4.46
% 4.19/4.46 ============================== CLAUSES FOR SEARCH ====================
% 4.19/4.46
% 4.19/4.46 ============================== end of clauses for search =============
% 4.19/4.46
% 4.19/4.46 ============================== SEARCH ================================
% 4.19/4.46
% 4.19/4.46 % Starting search at 0.03 seconds.
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=48.000, iters=3376
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=47.000, iters=3355
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=44.000, iters=3479
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=43.000, iters=3498
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=42.000, iters=3425
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=41.000, iters=3403
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=40.000, iters=3713
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=39.000, iters=3423
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=38.000, iters=3380
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=37.000, iters=3399
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=36.000, iters=3385
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=35.000, iters=3396
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=34.000, iters=3398
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=33.000, iters=3375
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=32.000, iters=3334
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=31.000, iters=3342
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=30.000, iters=3376
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=29.000, iters=3421
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=28.000, iters=3372
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=27.000, iters=3335
% 4.19/4.46
% 4.19/4.46 Low Water (keep): wt=26.000, iters=3361
% 4.19/4.46
% 4.19/4.46 ============================== PROOF =================================
% 4.19/4.46 % SZS status Unsatisfiable
% 4.19/4.46 % SZS output start Refutation
% 4.19/4.46
% 4.19/4.46 % Proof 1 at 3.45 (+ 0.06) seconds.
% 4.19/4.46 % Length of proof is 139.
% 4.19/4.46 % Level of proof is 29.
% 4.19/4.46 % Maximum clause weight is 45.000.
% 4.19/4.46 % Given clauses 816.
% 4.19/4.46
% 4.19/4.46 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 4.19/4.46 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 4.19/4.46 3 inverse(sk_c1) = sk_c8 | inverse(sk_c8) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 4.19/4.46 4 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 4.19/4.46 5 inverse(sk_c1) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 4.19/4.46 6 inverse(sk_c2) = sk_c3 | inverse(sk_c8) = sk_c7 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 4.19/4.46 9 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c8) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 4.19/4.46 10 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 4.19/4.46 11 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c5) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 4.19/4.46 12 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 4.19/4.46 13 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 4.19/4.46 14 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 4.19/4.46 15 multiply(sk_c2,sk_c3) = sk_c8 | inverse(sk_c8) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 4.19/4.46 21 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 4.19/4.46 22 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 4.19/4.46 23 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 4.19/4.46 27 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 4.19/4.46 28 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | inverse(sk_c8) != sk_c7 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8 | multiply(sk_c8,E) != sk_c7 | multiply(F,sk_c8) != E | inverse(F) != sk_c8 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 4.19/4.46 86 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 4.19/4.46 89 inverse(sk_c8) = sk_c7 | multiply(sk_c3,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 4.19/4.46 92 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),27(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.19/4.46 94 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c1,sk_c8)) = multiply(A,sk_c7). [para(9(a,1),27(a,2,2)),rewrite([27(8)])].
% 4.19/4.46 95 inverse(sk_c4) = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(10(a,1),27(a,1,1)),flip(b)].
% 4.19/4.46 97 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(11(a,1),27(a,1,1)),flip(b)].
% 4.19/4.46 102 inverse(sk_c1) = sk_c8 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(13(b,1),27(a,2,2)),rewrite([27(8)])].
% 4.19/4.46 106 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c2,sk_c3)) = multiply(A,sk_c8). [para(15(a,1),27(a,2,2)),rewrite([27(8)])].
% 4.19/4.46 117 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(21(b,1),27(a,1,1)),flip(b)].
% 4.19/4.46 119 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c7,A). [para(22(a,1),27(a,1,1)),flip(b)].
% 4.19/4.46 139 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | inverse(identity) != sk_c8 | inverse(sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [resolve(28,c,1,a)].
% 4.19/4.46 151 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | inverse(sk_c8) != sk_c7 | inverse(D) != sk_c8 | multiply(D,sk_c7) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8. [resolve(28,i,2,a)].
% 4.19/4.46 242 sk_c7 != sk_c8 | inverse(identity) != sk_c8 | inverse(sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [factor(139,b,c),rewrite([1(3)]),flip(a)].
% 4.19/4.46 347 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c7 | inverse(sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(sk_c8,identity) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8. [factor(151,c,g)].
% 4.19/4.46 662 sk_c7 != sk_c8 | inverse(identity) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8. [factor(242,b,d),rewrite([1(14)]),merge(d)].
% 4.19/4.46 858 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | inverse(inverse(sk_c8)) != sk_c7 | inverse(sk_c8) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,identity) != sk_c7. [factor(347,f,h)].
% 4.19/4.46 1279 sk_c7 != sk_c8 | inverse(identity) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(sk_c8,A) != sk_c7 | sk_c8 != A. [factor(662,b,f),rewrite([1(18)])].
% 4.19/4.46 1686 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != inverse(inverse(B)) | inverse(sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8. [resolve(92,a,28,c),flip(c)].
% 4.19/4.46 1688 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),92(a,1,2))].
% 4.19/4.46 1697 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c4),sk_c8) = sk_c7. [para(12(b,1),92(a,1,2))].
% 4.19/4.46 1720 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),identity) = sk_c1. [para(86(b,1),92(a,1,2))].
% 4.19/4.46 1721 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(92(a,1),92(a,1,2))].
% 4.19/4.46 1726 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != inverse(inverse(B)) | inverse(sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,inverse(inverse(B))) != sk_c7 | inverse(B) != sk_c8. [factor(1686,c,h)].
% 4.19/4.46 1727 multiply(A,identity) = A. [back_rewrite(1688),rewrite([1721(4)])].
% 4.19/4.46 1728 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c1. [back_rewrite(1720),rewrite([1727(8)])].
% 4.19/4.46 1737 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | inverse(inverse(sk_c8)) != sk_c7 | inverse(sk_c8) != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(858),rewrite([1727(30)]),flip(g)].
% 4.19/4.46 1765 inverse(identity) = identity. [para(1727(a,1),2(a,1))].
% 4.19/4.46 1803 sk_c7 != sk_c8 | identity != sk_c8 | inverse(sk_c8) != sk_c7. [para(1727(a,1),1279(d,1)),rewrite([1765(5)]),flip(d),flip(e),merge(d),merge(e)].
% 4.19/4.46 1824 inverse(sk_c8) = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(1728(b,1),2(a,1,1))].
% 4.19/4.46 1896 inverse(sk_c8) = sk_c7 | inverse(sk_c3) = sk_c2. [para(89(b,1),92(a,1,2)),rewrite([1727(8)])].
% 4.19/4.46 1935 inverse(sk_c8) = sk_c7 | multiply(sk_c2,sk_c3) = identity. [para(1896(b,1),2(a,1,1))].
% 4.19/4.46 2004 multiply(A,inverse(A)) = identity. [para(1721(a,1),2(a,1))].
% 4.19/4.46 2106 inverse(inverse(A)) = A. [para(1721(a,1),1727(a,1)),rewrite([1727(2)]),flip(a)].
% 4.19/4.46 2130 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(sk_c8) != sk_c7. [back_rewrite(1737),rewrite([2106(16),2106(23)]),flip(d),xx(f),merge(f)].
% 4.19/4.46 2134 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != B | inverse(sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,B) != sk_c7 | inverse(B) != sk_c8. [back_rewrite(1726),rewrite([2106(11),2106(24)])].
% 4.19/4.46 2210 multiply(sk_c7,sk_c8) != sk_c7 | inverse(sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7. [factor(2134,a,c),merge(g)].
% 4.19/4.46 2225 inverse(sk_c1) = sk_c8 | multiply(sk_c5,sk_c8) = identity. [para(5(b,1),2004(a,1,2))].
% 4.19/4.46 2228 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(2004(a,1),27(a,1)),flip(a)].
% 4.19/4.46 2401 inverse(sk_c4) = sk_c8 | multiply(sk_c1,multiply(sk_c8,inverse(sk_c7))) = identity. [para(2004(a,1),95(b,2))].
% 4.19/4.46 2424 multiply(A,multiply(B,sk_c8)) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(sk_c8) != sk_c7. [para(27(a,1),2130(a,1))].
% 4.19/4.46 2504 inverse(sk_c8) = sk_c7 | multiply(A,sk_c7) = A. [para(1824(b,1),94(b,1,2)),rewrite([1727(10)]),flip(c),merge(b)].
% 4.19/4.46 2553 inverse(sk_c5) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = sk_c1. [para(2004(a,1),97(b,1,2)),rewrite([1727(7)]),flip(b)].
% 4.19/4.46 2554 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c8,inverse(sk_c7))) = identity. [para(2004(a,1),97(b,2))].
% 4.19/4.46 2915 inverse(sk_c1) = sk_c8 | identity = sk_c6. [para(2225(b,1),14(b,1)),merge(b)].
% 4.19/4.46 2920 identity = sk_c6 | inverse(sk_c8) = sk_c1. [para(2915(a,1),2106(a,1,1))].
% 4.19/4.46 3360 sk_c7 != A | inverse(multiply(A,inverse(sk_c8))) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(sk_c8) != sk_c7. [para(2(a,1),2424(a,1,2)),rewrite([1727(2)]),flip(a)].
% 4.19/4.46 3449 multiply(A,B) != sk_c7 | inverse(multiply(A,multiply(B,inverse(sk_c8)))) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(sk_c8) != sk_c7. [para(27(a,1),3360(b,1,1)),flip(a)].
% 4.19/4.46 3543 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = identity. [para(2504(b,1),2(a,1))].
% 4.19/4.46 3549 inverse(sk_c8) = sk_c7 | multiply(sk_c7,A) = A. [para(3543(b,1),92(a,1,1)),rewrite([1(8)])].
% 4.19/4.46 3558 inverse(sk_c8) = sk_c7 | multiply(A,sk_c8) = A. [para(1935(b,1),106(b,1,2)),rewrite([1727(10)]),flip(c),merge(b)].
% 4.19/4.46 4180 multiply(sk_c7,sk_c8) != sk_c7 | inverse(sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | multiply(A,multiply(B,sk_c7)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7. [para(27(a,1),2210(e,1))].
% 4.19/4.46 4221 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c7),A) = A. [para(3549(b,1),92(a,1,2))].
% 4.19/4.46 4225 inverse(sk_c8) = sk_c7 | sk_c1 = sk_c7. [para(3558(b,1),9(a,1)),merge(c)].
% 4.19/4.46 4258 sk_c1 = sk_c7 | identity = sk_c6. [para(4225(a,1),2920(b,1)),flip(c),merge(c)].
% 4.19/4.46 4490 sk_c1 = sk_c7 | inverse(sk_c6) = identity. [para(4258(b,1),1765(a,1,1))].
% 4.19/4.46 6195 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c8,inverse(sk_c7)) = sk_c4. [para(2004(a,1),117(b,1,2)),rewrite([1727(8)]),flip(b)].
% 4.19/4.46 7336 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(4(b,1),1697(b,1,1)),merge(b)].
% 4.19/4.46 7364 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(7336(b,1),92(a,1,2))].
% 4.19/4.46 7800 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(2228(a,1),92(a,1,2)),rewrite([1727(3)]),flip(a)].
% 4.19/4.46 7843 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,inverse(multiply(sk_c1,sk_c8))) = identity. [para(2228(a,1),119(b,1)),flip(b)].
% 4.19/4.46 7922 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(7800(a,1),92(a,1,2)),flip(a)].
% 4.19/4.46 8049 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,multiply(inverse(sk_c8),inverse(sk_c1))) = identity. [back_rewrite(7843),rewrite([7922(10)])].
% 4.19/4.46 8659 multiply(sk_c7,sk_c8) != sk_c7 | inverse(sk_c7) != sk_c8 | inverse(sk_c8) != sk_c7 | multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c7)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7. [back_rewrite(4180),rewrite([7922(15)])].
% 4.19/4.46 8702 multiply(A,B) != sk_c7 | multiply(sk_c8,multiply(inverse(B),inverse(A))) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8 | sk_c7 != sk_c8 | inverse(sk_c8) != sk_c7. [back_rewrite(3449),rewrite([7922(8),7922(7),2106(6),27(8)])].
% 4.19/4.46 10002 inverse(sk_c5) = sk_c8 | multiply(inverse(sk_c7),sk_c1) = inverse(sk_c8). [para(2553(b,1),92(a,1,2))].
% 4.19/4.46 10684 inverse(sk_c8) = sk_c7 | inverse(sk_c7) = sk_c8. [para(4221(b,1),3558(b,1)),flip(c),merge(b)].
% 4.19/4.46 10695 inverse(sk_c8) = sk_c7. [para(10684(b,1),2106(a,1,1)),merge(b)].
% 4.19/4.46 10866 inverse(sk_c5) = sk_c8 | multiply(inverse(sk_c7),sk_c1) = sk_c7. [back_rewrite(10002),rewrite([10695(10)])].
% 4.19/4.46 11710 multiply(A,B) != sk_c7 | multiply(sk_c8,multiply(inverse(B),inverse(A))) != sk_c8 | multiply(sk_c7,sk_c7) != sk_c8 | sk_c7 != sk_c8. [back_rewrite(8702),rewrite([10695(12),10695(20)]),xx(e)].
% 4.19/4.46 11748 multiply(sk_c7,sk_c8) != sk_c7 | inverse(sk_c7) != sk_c8 | multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c7)) != sk_c8 | multiply(sk_c8,sk_c7) != sk_c7. [back_rewrite(8659),rewrite([10695(11)]),xx(c)].
% 4.19/4.46 12177 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,multiply(sk_c7,inverse(sk_c1))) = identity. [back_rewrite(8049),rewrite([10695(8)])].
% 4.19/4.46 12492 inverse(sk_c1) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(7364),rewrite([10695(6)])].
% 4.19/4.46 14326 sk_c7 != sk_c8 | identity != sk_c8. [back_rewrite(1803),rewrite([10695(8)]),xx(c)].
% 4.19/4.46 15436 multiply(sk_c7,sk_c8) = identity. [para(10695(a,1),2(a,1,1))].
% 4.19/4.46 15437 multiply(sk_c7,multiply(sk_c8,A)) = A. [para(10695(a,1),92(a,1,1))].
% 4.19/4.46 15438 inverse(sk_c7) = sk_c8. [para(10695(a,1),2106(a,1,1))].
% 4.19/4.46 15439 multiply(sk_c8,sk_c7) = identity. [para(10695(a,1),2004(a,1,2))].
% 4.19/4.46 15468 identity != sk_c7 | multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c7)) != sk_c8. [back_rewrite(11748),rewrite([15436(3),15438(5),15439(19)]),xx(b),merge(d)].
% 4.19/4.46 15582 inverse(sk_c5) = sk_c8 | multiply(sk_c8,sk_c1) = sk_c7. [back_rewrite(10866),rewrite([15438(6)])].
% 4.19/4.46 15617 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c8,sk_c8) = sk_c4. [back_rewrite(6195),rewrite([15438(8)])].
% 4.19/4.46 15630 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c8,sk_c8)) = identity. [back_rewrite(2554),rewrite([15438(8)])].
% 4.19/4.46 15633 inverse(sk_c4) = sk_c8 | multiply(sk_c1,multiply(sk_c8,sk_c8)) = identity. [back_rewrite(2401),rewrite([15438(8)])].
% 4.19/4.46 15896 identity != sk_c7 | multiply(sk_c7,inverse(A)) != sk_c8 | sk_c8 != A. [para(2(a,1),15468(c,1,2)),rewrite([15438(5),10695(5),1727(10)]),flip(c)].
% 4.19/4.46 15951 identity != sk_c7 | multiply(sk_c7,A) != sk_c8 | inverse(A) != sk_c8. [para(2106(a,1),15896(b,1,2)),flip(c)].
% 4.19/4.46 16896 multiply(sk_c7,A) != sk_c7 | multiply(sk_c8,multiply(inverse(A),sk_c8)) != sk_c8 | multiply(sk_c7,sk_c7) != sk_c8 | sk_c7 != sk_c8. [para(15438(a,1),11710(b,1,2,2))].
% 4.19/4.46 16999 inverse(sk_c1) = sk_c8 | identity != sk_c7. [resolve(12492,b,15951,b),rewrite([15438(9)]),xx(c)].
% 4.19/4.46 17009 inverse(sk_c1) = sk_c8 | sk_c6 = sk_c8. [para(12492(b,1),102(b,2)),rewrite([15437(13)]),merge(b)].
% 4.19/4.46 17055 sk_c6 = sk_c8 | sk_c1 = sk_c7. [para(17009(a,1),2106(a,1,1)),rewrite([10695(5)]),flip(b)].
% 4.19/4.46 17089 sk_c1 = sk_c7 | identity = sk_c7. [para(17055(a,1),4490(b,1,1)),rewrite([10695(8)]),flip(c),merge(b)].
% 4.19/4.46 17236 sk_c1 = sk_c7 | inverse(sk_c1) = sk_c8. [resolve(17089,b,16999,b)].
% 4.19/4.46 17483 sk_c1 = sk_c7. [para(17236(b,1),2106(a,1,1)),rewrite([10695(5)]),flip(b),merge(b)].
% 4.19/4.46 17611 inverse(sk_c4) = sk_c8 | identity = sk_c8. [back_rewrite(15633),rewrite([17483(5),15437(9)]),flip(b)].
% 4.19/4.46 17612 inverse(sk_c5) = sk_c8 | identity = sk_c8. [back_rewrite(15630),rewrite([17483(5),15437(9)]),flip(b)].
% 4.19/4.46 17614 identity = sk_c7 | multiply(sk_c8,sk_c8) = sk_c4. [back_rewrite(15617),rewrite([17483(1),15436(3)])].
% 4.19/4.46 17623 inverse(sk_c5) = sk_c8 | identity = sk_c7. [back_rewrite(15582),rewrite([17483(6),15439(7)])].
% 4.19/4.46 17927 multiply(sk_c8,sk_c6) = sk_c7 | identity = sk_c7. [back_rewrite(12177),rewrite([17483(8),15438(9),15436(9),1727(8)]),flip(b)].
% 4.19/4.46 18012 identity = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6. [back_rewrite(23),rewrite([17483(1),15436(3)])].
% 4.19/4.46 18072 identity = sk_c8 | sk_c4 = sk_c7. [para(17611(a,1),2106(a,1,1)),rewrite([10695(5)]),flip(b)].
% 4.19/4.46 18091 sk_c4 = sk_c7 | sk_c7 != sk_c8. [resolve(18072,a,14326,b)].
% 4.19/4.46 18153 identity = sk_c8 | sk_c5 = sk_c7. [para(17612(a,1),2106(a,1,1)),rewrite([10695(5)]),flip(b)].
% 4.19/4.46 18172 sk_c5 = sk_c7 | sk_c7 != sk_c8. [resolve(18153,a,14326,b)].
% 4.19/4.46 18269 identity = sk_c7 | multiply(sk_c8,sk_c5) = identity. [para(17623(a,1),2(a,1,1))].
% 4.19/4.46 18271 identity = sk_c7 | multiply(sk_c5,sk_c8) = identity. [para(17623(a,1),2004(a,1,2))].
% 4.19/4.46 18375 identity = sk_c7 | multiply(sk_c7,sk_c4) = sk_c8. [para(17614(b,1),92(a,1,2)),rewrite([10695(5)])].
% 4.19/4.46 19197 identity = sk_c7 | identity = sk_c6. [para(18271(b,1),18012(b,1)),merge(b)].
% 4.19/4.46 19270 identity = sk_c7 | multiply(A,sk_c6) = A. [para(19197(b,1),1727(a,1,2))].
% 4.19/4.46 19286 identity = sk_c7 | multiply(sk_c8,sk_c5) = sk_c6. [para(19197(b,1),18269(b,2)),merge(b)].
% 4.19/4.46 19487 identity = sk_c7 | sk_c7 = sk_c8. [para(19270(b,1),17927(a,1)),flip(b),merge(c)].
% 4.19/4.46 19490 sk_c7 = sk_c8 | identity = sk_c8. [para(19487(a,1),1765(a,1,1)),rewrite([15438(5)]),flip(b)].
% 4.19/4.46 19502 sk_c7 = sk_c8. [para(19490(b,1),19487(a,1)),flip(b),merge(b),merge(c)].
% 4.19/4.46 19601 identity = sk_c8 | multiply(sk_c8,sk_c5) = sk_c6. [back_rewrite(19286),rewrite([19502(2)])].
% 4.19/4.46 20042 identity = sk_c8 | multiply(sk_c8,sk_c4) = sk_c8. [back_rewrite(18375),rewrite([19502(2),19502(4)])].
% 4.19/4.46 20151 sk_c5 = sk_c8. [back_rewrite(18172),rewrite([19502(2),19502(4)]),xx(b)].
% 4.19/4.46 20176 sk_c4 = sk_c8. [back_rewrite(18091),rewrite([19502(2),19502(4)]),xx(b)].
% 4.19/4.46 20324 multiply(sk_c8,A) != sk_c8 | multiply(sk_c8,multiply(inverse(A),sk_c8)) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c8. [back_rewrite(16896),rewrite([19502(1),19502(3),19502(12),19502(13),19502(17)]),xx(d)].
% 4.19/4.46 20420 multiply(sk_c8,sk_c8) = identity. [back_rewrite(15439),rewrite([19502(2)])].
% 4.19/4.46 20445 identity != sk_c8. [back_rewrite(14326),rewrite([19502(1)]),xx(a)].
% 4.19/4.46 20459 inverse(sk_c8) = sk_c8. [back_rewrite(10695),rewrite([19502(3)])].
% 4.19/4.46 20464 identity = sk_c6. [back_rewrite(19601),rewrite([20151(5),20420(6)]),unit_del(a,20445)].
% 4.19/4.46 20467 sk_c6 = sk_c8. [back_rewrite(20042),rewrite([20464(1),20176(5),20420(6),20464(4)]),merge(b)].
% 4.19/4.46 20468 $F. [factor(20324,a,c),rewrite([20420(3),20464(1),20467(1),20459(6),20420(7),20464(5),20467(5),20420(6),20464(4),20467(4)]),xx(a),xx(b)].
% 4.19/4.46
% 4.19/4.46 % SZS output end Refutation
% 4.19/4.46 ============================== end of proof ==========================
% 4.19/4.46
% 4.19/4.46 ============================== STATISTICS ============================
% 4.19/4.46
% 4.19/4.46 Given=816. Generated=82181. Kept=20467. proofs=1.
% 4.19/4.46 Usable=24. Sos=364. Demods=24. Limbo=144, Disabled=19963. Hints=0.
% 4.19/4.46 Megabytes=18.46.
% 4.19/4.46 User_CPU=3.45, System_CPU=0.06, Wall_clock=3.
% 4.19/4.46
% 4.19/4.46 ============================== end of statistics =====================
% 4.19/4.46
% 4.19/4.46 ============================== end of search =========================
% 4.19/4.46
% 4.19/4.46 THEOREM PROVED
% 4.19/4.46 % SZS status Unsatisfiable
% 4.19/4.46
% 4.19/4.46 Exiting with 1 proof.
% 4.19/4.46
% 4.19/4.46 Process 10272 exit (max_proofs) Mon Jun 13 04:50:56 2022
% 4.19/4.46 Prover9 interrupted
%------------------------------------------------------------------------------