TSTP Solution File: GRP239-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP239-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:18:17 EDT 2022
% Result : Unsatisfiable 99.54s 99.90s
% Output : Refutation 99.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP239-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 12:45:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.58/3.86 ============================== Prover9 ===============================
% 3.58/3.86 Prover9 (32) version 2009-11A, November 2009.
% 3.58/3.86 Process 17435 was started by sandbox on n026.cluster.edu,
% 3.58/3.86 Tue Jun 14 12:45:07 2022
% 3.58/3.86 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17268_n026.cluster.edu".
% 3.58/3.86 ============================== end of head ===========================
% 3.58/3.86
% 3.58/3.86 ============================== INPUT =================================
% 3.58/3.86
% 3.58/3.86 % Reading from file /tmp/Prover9_17268_n026.cluster.edu
% 3.58/3.86
% 3.58/3.86 set(prolog_style_variables).
% 3.58/3.86 set(auto2).
% 3.58/3.86 % set(auto2) -> set(auto).
% 3.58/3.86 % set(auto) -> set(auto_inference).
% 3.58/3.86 % set(auto) -> set(auto_setup).
% 3.58/3.86 % set(auto_setup) -> set(predicate_elim).
% 3.58/3.86 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.58/3.86 % set(auto) -> set(auto_limits).
% 3.58/3.86 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.58/3.86 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.58/3.86 % set(auto) -> set(auto_denials).
% 3.58/3.86 % set(auto) -> set(auto_process).
% 3.58/3.86 % set(auto2) -> assign(new_constants, 1).
% 3.58/3.86 % set(auto2) -> assign(fold_denial_max, 3).
% 3.58/3.86 % set(auto2) -> assign(max_weight, "200.000").
% 3.58/3.86 % set(auto2) -> assign(max_hours, 1).
% 3.58/3.86 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.58/3.86 % set(auto2) -> assign(max_seconds, 0).
% 3.58/3.86 % set(auto2) -> assign(max_minutes, 5).
% 3.58/3.86 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.58/3.86 % set(auto2) -> set(sort_initial_sos).
% 3.58/3.86 % set(auto2) -> assign(sos_limit, -1).
% 3.58/3.86 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.58/3.86 % set(auto2) -> assign(max_megs, 400).
% 3.58/3.86 % set(auto2) -> assign(stats, some).
% 3.58/3.86 % set(auto2) -> clear(echo_input).
% 3.58/3.86 % set(auto2) -> set(quiet).
% 3.58/3.86 % set(auto2) -> clear(print_initial_clauses).
% 3.58/3.86 % set(auto2) -> clear(print_given).
% 3.58/3.86 assign(lrs_ticks,-1).
% 3.58/3.86 assign(sos_limit,10000).
% 3.58/3.86 assign(order,kbo).
% 3.58/3.86 set(lex_order_vars).
% 3.58/3.86 clear(print_given).
% 3.58/3.86
% 3.58/3.86 % formulas(sos). % not echoed (46 formulas)
% 3.58/3.86
% 3.58/3.86 ============================== end of input ==========================
% 3.58/3.86
% 3.58/3.86 % From the command line: assign(max_seconds, 300).
% 3.58/3.86
% 3.58/3.86 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.58/3.86
% 3.58/3.86 % Formulas that are not ordinary clauses:
% 3.58/3.86
% 3.58/3.86 ============================== end of process non-clausal formulas ===
% 3.58/3.86
% 3.58/3.86 ============================== PROCESS INITIAL CLAUSES ===============
% 3.58/3.86
% 3.58/3.86 ============================== PREDICATE ELIMINATION =================
% 3.58/3.86
% 3.58/3.86 ============================== end predicate elimination =============
% 3.58/3.86
% 3.58/3.86 Auto_denials: (non-Horn, no changes).
% 3.58/3.86
% 3.58/3.86 Term ordering decisions:
% 3.58/3.86
% 3.58/3.86 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 3.58/3.86 Function symbol KB weights: sk_c9=1. 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.
% 3.58/3.86
% 3.58/3.86 ============================== end of process initial clauses ========
% 3.58/3.86
% 3.58/3.86 ============================== CLAUSES FOR SEARCH ====================
% 3.58/3.86
% 3.58/3.86 ============================== end of clauses for search =============
% 3.58/3.86
% 3.58/3.86 ============================== SEARCH ================================
% 3.58/3.86
% 3.58/3.86 % Starting search at 0.06 seconds.
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=48.000, iters=3374
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=47.000, iters=3380
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=46.000, iters=3506
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=44.000, iters=3334
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=43.000, iters=3360
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=42.000, iters=3341
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=41.000, iters=3466
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=40.000, iters=3343
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=39.000, iters=3400
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=38.000, iters=3369
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=37.000, iters=3390
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=36.000, iters=3350
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=35.000, iters=3409
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=34.000, iters=3337
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=33.000, iters=3343
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=32.000, iters=3371
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=31.000, iters=3355
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=30.000, iters=3381
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=29.000, iters=3333
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=28.000, iters=3337
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=27.000, iters=3413
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=26.000, iters=3384
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=25.000, iters=3388
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=24.000, iters=3343
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=23.000, iters=3422
% 3.58/3.86
% 3.58/3.86 Low Water (keep): wt=22.000, iters=3390
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=21.000, iters=3341
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=20.000, iters=3402
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=18.000, iters=3343
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=16.000, iters=3379
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=15.000, iters=3385
% 99.54/99.90
% 99.54/99.90 Low Water (displace): id=13436, wt=14.000
% 99.54/99.90
% 99.54/99.90 Low Water (displace): id=13443, wt=12.000
% 99.54/99.90
% 99.54/99.90 Low Water (displace): id=13455, wt=10.000
% 99.54/99.90
% 99.54/99.90 Low Water (displace): id=15205, wt=9.000
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=14.000, iters=3350
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=13.000, iters=3350
% 99.54/99.90
% 99.54/99.90 Low Water (keep): wt=12.000, iters=3348
% 99.54/99.90
% 99.54/99.90 ============================== PROOF =================================
% 99.54/99.90 % SZS status Unsatisfiable
% 99.54/99.90 % SZS output start Refutation
% 99.54/99.90
% 99.54/99.90 % Proof 1 at 96.35 (+ 2.51) seconds.
% 99.54/99.90 % Length of proof is 130.
% 99.54/99.90 % Level of proof is 24.
% 99.54/99.90 % Maximum clause weight is 59.000.
% 99.54/99.90 % Given clauses 7295.
% 99.54/99.90
% 99.54/99.90 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 99.54/99.90 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 99.54/99.90 4 inverse(sk_c9) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 99.54/99.90 5 inverse(sk_c9) = sk_c8 | inverse(sk_c6) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 99.54/99.90 7 inverse(sk_c1) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 99.54/99.90 10 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_39) # label(negated_conjecture). [assumption].
% 99.54/99.90 11 inverse(sk_c2) = sk_c9 | inverse(sk_c6) = sk_c7 # label(prove_this_41) # label(negated_conjecture). [assumption].
% 99.54/99.90 13 inverse(sk_c9) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 99.54/99.90 14 inverse(sk_c9) = sk_c8 | multiply(sk_c6,sk_c7) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 99.54/99.90 17 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 99.54/99.90 20 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c4) = sk_c9 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 99.54/99.90 21 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 99.54/99.90 23 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c4) = sk_c9 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 99.54/99.90 24 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 99.54/99.90 27 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c5) = sk_c8 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 99.54/99.90 30 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_38) # label(negated_conjecture). [assumption].
% 99.54/99.90 31 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c7) = sk_c8 # label(prove_this_40) # label(negated_conjecture). [assumption].
% 99.54/99.90 33 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c4,sk_c8) = sk_c9 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 99.54/99.90 38 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 99.54/99.90 42 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 99.54/99.90 45 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 99.54/99.90 46 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | inverse(D) != sk_c9 | multiply(D,sk_c8) != sk_c9 | multiply(E,sk_c8) != sk_c9 | inverse(E) != sk_c8 | multiply(F,V6) != sk_c8 | inverse(F) != V6 | multiply(V6,sk_c9) != sk_c8 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 99.54/99.90 50 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | multiply(C,sk_c9) != B | inverse(C) != sk_c9 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | multiply(E,F) != sk_c8 | inverse(E) != F | multiply(F,sk_c9) != sk_c8. [factor(46,b,g),merge(g)].
% 99.54/99.90 159 inverse(sk_c9) = sk_c8 | multiply(sk_c8,sk_c5) = identity. [para(4(b,1),2(a,1,1))].
% 99.54/99.90 160 inverse(sk_c9) = sk_c8 | multiply(sk_c7,sk_c6) = identity. [para(5(b,1),2(a,1,1))].
% 99.54/99.90 167 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),45(a,1,1)),rewrite([1(2)]),flip(a)].
% 99.54/99.90 171 inverse(sk_c9) = sk_c8 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c9). [para(13(b,1),45(a,2,2)),rewrite([45(8)])].
% 99.54/99.90 173 inverse(sk_c9) = sk_c8 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c8). [para(14(b,1),45(a,2,2)),rewrite([45(8)])].
% 99.54/99.90 184 inverse(sk_c4) = sk_c9 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(20(a,1),45(a,1,1)),flip(b)].
% 99.54/99.90 186 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(21(a,1),45(a,1,1)),flip(b)].
% 99.54/99.90 191 inverse(sk_c4) = sk_c9 | multiply(A,multiply(sk_c9,sk_c3)) = multiply(A,sk_c8). [para(23(a,1),45(a,2,2)),rewrite([45(8)])].
% 99.54/99.90 193 inverse(sk_c5) = sk_c8 | multiply(A,multiply(sk_c9,sk_c3)) = multiply(A,sk_c8). [para(24(a,1),45(a,2,2)),rewrite([45(8)])].
% 99.54/99.90 259 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(C,D) != sk_c8 | inverse(C) != D | multiply(D,sk_c9) != sk_c8. [resolve(50,e,2,a)].
% 99.54/99.90 261 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,multiply(B,sk_c9)) != sk_c8 | inverse(B) != sk_c9 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(D,E) != sk_c8 | inverse(D) != E | multiply(E,sk_c9) != sk_c8. [resolve(50,e,1,a(flip)),rewrite([1(16)])].
% 99.54/99.90 297 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | identity != B | inverse(inverse(sk_c9)) != sk_c9 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(D,E) != sk_c8 | inverse(D) != E | multiply(E,sk_c9) != sk_c8. [para(2(a,1),50(e,1))].
% 99.54/99.90 574 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,identity) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,sk_c9) != sk_c8. [factor(259,c,f)].
% 99.54/99.90 590 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,multiply(A,sk_c9)) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(C,D) != sk_c8 | inverse(C) != D | multiply(D,sk_c9) != sk_c8. [factor(261,b,e)].
% 99.54/99.90 844 inverse(sk_c9) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(C,D) != sk_c8 | inverse(C) != D | multiply(D,sk_c9) != sk_c8. [factor(297,b,f)].
% 99.54/99.90 1626 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,multiply(A,sk_c9)) != sk_c8 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,sk_c9) != sk_c8. [factor(590,c,e)].
% 99.54/99.90 2051 inverse(sk_c9) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,A) != sk_c8 | identity != A | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | inverse(sk_c9) != A | multiply(A,sk_c9) != sk_c8. [factor(844,d,h)].
% 99.54/99.90 2829 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,multiply(A,sk_c9)) != sk_c8 | inverse(A) != sk_c8 | multiply(A,sk_c9) != inverse(sk_c9) | multiply(A,multiply(sk_c9,sk_c9)) != sk_c8. [factor(1626,d,f),rewrite([45(29)]),flip(f)].
% 99.54/99.90 3021 inverse(sk_c9) != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c8. [factor(2051,g,h),merge(g)].
% 99.54/99.90 4082 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),167(a,1,2))].
% 99.54/99.90 4117 multiply(sk_c9,sk_c3) = sk_c8 | multiply(inverse(sk_c5),sk_c9) = sk_c8. [para(38(b,1),167(a,1,2))].
% 99.54/99.90 4121 multiply(sk_c2,sk_c9) = sk_c3 | multiply(inverse(sk_c5),sk_c9) = sk_c8. [para(42(b,1),167(a,1,2))].
% 99.54/99.90 4141 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(167(a,1),167(a,1,2))].
% 99.54/99.90 4166 multiply(A,identity) = A. [back_rewrite(4082),rewrite([4141(4)])].
% 99.54/99.90 4220 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(inverse(sk_c9)) != sk_c9 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,sk_c9) != sk_c8. [back_rewrite(574),rewrite([4166(14)]),flip(d)].
% 99.54/99.90 4251 inverse(identity) = identity. [para(4166(a,1),2(a,1))].
% 99.54/99.90 4426 inverse(sk_c9) = sk_c8 | inverse(sk_c8) = sk_c5. [para(159(b,1),167(a,1,2)),rewrite([4166(8)])].
% 99.54/99.90 4427 inverse(sk_c9) = sk_c8 | multiply(sk_c5,sk_c8) = identity. [para(4426(b,1),2(a,1,1))].
% 99.54/99.90 4430 inverse(sk_c9) = sk_c8 | inverse(sk_c7) = sk_c6. [para(160(b,1),167(a,1,2)),rewrite([4166(8)])].
% 99.54/99.90 4431 inverse(sk_c9) = sk_c8 | multiply(sk_c6,sk_c7) = identity. [para(4430(b,1),2(a,1,1))].
% 99.54/99.90 4636 multiply(A,inverse(A)) = identity. [para(4141(a,1),2(a,1))].
% 99.54/99.90 4842 inverse(inverse(A)) = A. [para(4141(a,1),4166(a,1)),rewrite([4166(2)]),flip(a)].
% 99.54/99.90 4866 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c8 != sk_c9 | inverse(A) != sk_c8 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,sk_c9) != sk_c8. [back_rewrite(4220),rewrite([4842(17)]),xx(e)].
% 99.54/99.90 4983 inverse(sk_c9) != sk_c8 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c8. [back_rewrite(3021),rewrite([4842(7)]),xx(b)].
% 99.54/99.90 5089 inverse(sk_c1) = sk_c9 | multiply(sk_c5,sk_c8) = identity. [para(7(b,1),4636(a,1,2))].
% 99.54/99.90 5092 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c8) = identity. [para(10(b,1),4636(a,1,2))].
% 99.54/99.90 5093 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c7) = identity. [para(11(b,1),4636(a,1,2))].
% 99.54/99.90 5094 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(4636(a,1),45(a,1)),flip(a)].
% 99.54/99.90 5334 inverse(sk_c9) = sk_c8 | identity = sk_c9. [para(4427(b,1),13(b,1)),merge(b)].
% 99.54/99.90 5336 inverse(sk_c9) = sk_c8 | multiply(A,sk_c9) = A. [para(4427(b,1),171(b,1,2)),rewrite([4166(10)]),flip(c),merge(b)].
% 99.54/99.90 5457 inverse(sk_c9) = sk_c8 | identity = sk_c8. [para(4431(b,1),14(b,1)),merge(b)].
% 99.54/99.90 5459 inverse(sk_c9) = sk_c8 | multiply(A,sk_c8) = A. [para(4431(b,1),173(b,1,2)),rewrite([4166(10)]),flip(c),merge(b)].
% 99.54/99.90 5914 inverse(sk_c1) = sk_c9 | identity = sk_c9. [para(5089(b,1),17(b,1)),merge(b)].
% 99.54/99.90 5918 identity = sk_c9 | inverse(sk_c9) = sk_c1. [para(5914(a,1),4842(a,1,1))].
% 99.54/99.90 5926 identity = sk_c9 | sk_c1 = sk_c8. [para(5918(b,1),5334(a,1)),merge(c)].
% 99.54/99.90 5938 sk_c1 = sk_c8 | inverse(sk_c9) = identity. [para(5926(a,1),4251(a,1,1))].
% 99.54/99.90 6044 sk_c1 = sk_c8 | identity = sk_c8. [para(5938(b,1),5457(a,1)),merge(c)].
% 99.54/99.90 6050 sk_c1 = sk_c8 | inverse(sk_c9) = sk_c9. [para(5926(a,1),5938(b,2)),merge(b)].
% 99.54/99.90 6514 sk_c1 = sk_c8 | inverse(sk_c9) != sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c8,sk_c9) != sk_c8. [para(6050(b,1),4983(b,1,1)),merge(f)].
% 99.54/99.90 7154 inverse(sk_c2) = sk_c9 | identity = sk_c9. [para(5092(b,1),30(b,1)),merge(b)].
% 99.54/99.90 7161 identity = sk_c9 | inverse(sk_c9) = sk_c2. [para(7154(a,1),4842(a,1,1))].
% 99.54/99.90 7243 identity = sk_c9 | sk_c2 = sk_c8. [para(7161(b,1),5334(a,1)),merge(c)].
% 99.54/99.90 7268 sk_c2 = sk_c8 | inverse(sk_c9) = identity. [para(7243(a,1),4251(a,1,1))].
% 99.54/99.90 7334 sk_c2 = sk_c8 | identity = sk_c8. [para(7268(b,1),5457(a,1)),merge(c)].
% 99.54/99.90 7346 sk_c2 = sk_c8 | inverse(sk_c9) = sk_c9. [para(7243(a,1),7268(b,2)),merge(b)].
% 99.54/99.90 7667 sk_c2 = sk_c8 | inverse(sk_c9) != sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c8,sk_c9) != sk_c8. [para(7346(b,1),4983(b,1,1)),merge(f)].
% 99.54/99.90 8243 inverse(sk_c4) = sk_c9 | multiply(sk_c1,multiply(sk_c8,multiply(sk_c9,sk_c3))) = multiply(sk_c9,sk_c8). [para(191(b,1),184(b,2)),merge(b)].
% 99.54/99.90 8762 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c8,multiply(sk_c9,sk_c3))) = multiply(sk_c9,sk_c8). [para(193(b,1),186(b,2)),merge(b)].
% 99.54/99.90 9217 inverse(sk_c2) = sk_c9 | identity = sk_c8. [para(5093(b,1),31(b,1)),merge(b)].
% 99.54/99.90 9227 identity = sk_c8 | multiply(sk_c2,sk_c9) = identity. [para(9217(a,1),4636(a,1,2))].
% 99.54/99.90 9381 identity = sk_c8 | identity = sk_c3 | inverse(sk_c5) = sk_c8. [para(9227(b,1),27(a,1))].
% 99.54/99.90 10193 inverse(sk_c9) = sk_c8 | inverse(sk_c9) = identity. [para(5336(b,1),2(a,1))].
% 99.54/99.90 10329 inverse(sk_c9) = sk_c8 | multiply(sk_c9,A) = A. [para(10193(b,1),167(a,1,1)),rewrite([1(8)])].
% 99.54/99.90 13371 inverse(sk_c9) = sk_c8 | multiply(inverse(sk_c9),A) = A. [para(10329(b,1),167(a,1,2))].
% 99.54/99.90 15584 inverse(sk_c9) != sk_c8 | sk_c8 != sk_c9 | identity != sk_c9 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c9) != sk_c8. [para(2(a,1),4866(c,1)),rewrite([4842(7),4842(16)]),xx(e),merge(d)].
% 99.54/99.90 15605 inverse(sk_c9) != sk_c8 | sk_c8 != sk_c9 | identity != sk_c9 | sk_c8 != A | inverse(A) != identity. [para(1(a,1),15584(f,1)),rewrite([4166(12)]),flip(d),flip(f),merge(f)].
% 99.54/99.90 15636 inverse(sk_c9) != sk_c8 | sk_c8 != sk_c9 | identity != sk_c9 | inverse(A) != sk_c8 | identity != A. [para(4842(a,1),15605(e,1)),flip(d),flip(e)].
% 99.54/99.90 15637 inverse(sk_c9) != sk_c8 | sk_c8 != sk_c9 | identity != sk_c9. [factor(15636,a,d),merge(d)].
% 99.54/99.90 20966 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(5094(a,1),167(a,1,2)),rewrite([4166(3)]),flip(a)].
% 99.54/99.90 21691 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(20966(a,1),167(a,1,2)),flip(a)].
% 99.54/99.90 29753 inverse(sk_c9) != sk_c8 | multiply(inverse(A),inverse(B)) != sk_c9 | multiply(B,multiply(A,sk_c8)) != sk_c9 | multiply(sk_c9,multiply(B,multiply(A,sk_c9))) != sk_c8 | multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c9)) != inverse(sk_c9) | multiply(B,multiply(A,multiply(sk_c9,sk_c9))) != sk_c8. [para(45(a,1),2829(d,1,2)),rewrite([21691(6),45(12),21691(23),45(29),45(37)])].
% 99.54/99.90 29754 inverse(sk_c9) != sk_c8 | multiply(inverse(sk_c9),inverse(sk_c9)) != sk_c9 | multiply(sk_c9,multiply(sk_c9,sk_c8)) != sk_c9 | multiply(sk_c9,multiply(sk_c9,multiply(sk_c9,sk_c9))) != sk_c8 | multiply(inverse(sk_c9),inverse(sk_c9)) != sk_c8 | multiply(sk_c9,multiply(sk_c9,sk_c9)) != inverse(sk_c9). [factor(29753,d,g)].
% 99.54/99.90 30653 inverse(sk_c9) = sk_c8. [para(13371(b,1),5459(b,1)),flip(c),merge(b),merge(c)].
% 99.54/99.90 31025 multiply(sk_c8,sk_c8) != sk_c9 | multiply(sk_c9,multiply(sk_c9,sk_c8)) != sk_c9 | multiply(sk_c9,multiply(sk_c9,multiply(sk_c9,sk_c9))) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c8 | multiply(sk_c9,multiply(sk_c9,sk_c9)) != sk_c8. [back_rewrite(29754),rewrite([30653(2),30653(5),30653(6),30653(26),30653(27),30653(36)]),xx(a)].
% 99.54/99.90 32988 sk_c8 != sk_c9 | identity != sk_c9. [back_rewrite(15637),rewrite([30653(2)]),xx(a)].
% 99.54/99.90 33732 sk_c2 = sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c8,sk_c9) != sk_c8. [back_rewrite(7667),rewrite([30653(5)]),xx(b)].
% 99.54/99.90 34026 sk_c1 = sk_c8 | multiply(sk_c9,sk_c8) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c8 | identity != sk_c8 | multiply(sk_c8,sk_c9) != sk_c8. [back_rewrite(6514),rewrite([30653(5)]),xx(b)].
% 99.54/99.90 36396 multiply(sk_c8,sk_c9) = identity. [para(30653(a,1),2(a,1,1))].
% 99.54/99.90 36397 multiply(sk_c8,multiply(sk_c9,A)) = A. [para(30653(a,1),167(a,1,1))].
% 99.54/99.90 36398 inverse(sk_c8) = sk_c9. [para(30653(a,1),4842(a,1,1))].
% 99.54/99.90 36399 multiply(sk_c9,sk_c8) = identity. [para(30653(a,1),4636(a,1,2))].
% 99.54/99.90 36402 sk_c1 = sk_c8 | identity != sk_c9 | identity != sk_c8. [back_rewrite(34026),rewrite([36399(6),36399(9),36396(15)]),merge(d),merge(e)].
% 99.54/99.90 36404 sk_c2 = sk_c8 | identity != sk_c9 | identity != sk_c8. [back_rewrite(33732),rewrite([36399(6),36399(9),36396(15)]),merge(d),merge(e)].
% 99.54/99.90 36464 inverse(sk_c5) = sk_c8 | multiply(sk_c1,sk_c3) = identity. [back_rewrite(8762),rewrite([36397(10),36399(10)])].
% 99.54/99.90 36466 inverse(sk_c4) = sk_c9 | multiply(sk_c1,sk_c3) = identity. [back_rewrite(8243),rewrite([36397(10),36399(10)])].
% 99.54/99.90 36697 multiply(sk_c8,sk_c8) != sk_c9 | multiply(sk_c9,multiply(sk_c9,multiply(sk_c9,sk_c9))) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c8 | multiply(sk_c9,multiply(sk_c9,sk_c9)) != sk_c8. [back_rewrite(31025),rewrite([36399(9),4166(8)]),xx(b)].
% 99.54/99.90 37248 identity = sk_c8 | identity = sk_c3 | multiply(sk_c2,sk_c9) = sk_c3. [para(9381(c,1),4121(b,1,1)),rewrite([36396(14)]),merge(d)].
% 99.54/99.90 37474 sk_c1 = sk_c8 | identity != sk_c9. [resolve(36402,c,6044,b),merge(c)].
% 99.54/99.90 37477 sk_c1 = sk_c8. [resolve(37474,b,5926,a),merge(b)].
% 99.54/99.90 37531 inverse(sk_c4) = sk_c9 | multiply(sk_c8,sk_c3) = identity. [back_rewrite(36466),rewrite([37477(5)])].
% 99.54/99.90 37532 inverse(sk_c5) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [back_rewrite(36464),rewrite([37477(5)])].
% 99.54/99.90 37957 multiply(sk_c8,sk_c8) = sk_c9 | multiply(sk_c4,sk_c8) = sk_c9. [back_rewrite(33),rewrite([37477(1)])].
% 99.54/99.90 38793 sk_c2 = sk_c8 | identity != sk_c9. [resolve(36404,c,7334,b),merge(c)].
% 99.54/99.90 38794 sk_c2 = sk_c8. [resolve(38793,b,7243,a),merge(b)].
% 99.54/99.90 38880 identity = sk_c8 | identity = sk_c3. [back_rewrite(37248),rewrite([38794(7),36396(9)]),merge(c)].
% 99.54/99.90 39256 identity = sk_c8 | multiply(A,sk_c3) = A. [para(38880(b,1),4166(a,1,2))].
% 99.54/99.90 42566 inverse(sk_c4) = sk_c9 | identity = sk_c8. [para(37531(b,1),39256(b,1)),merge(c)].
% 99.54/99.90 42621 identity = sk_c8 | sk_c4 = sk_c8. [para(42566(a,1),4842(a,1,1)),rewrite([30653(5)]),flip(b)].
% 99.54/99.90 42651 sk_c4 = sk_c8 | sk_c8 != sk_c9. [para(42621(a,1),32988(b,1)),merge(c)].
% 99.54/99.90 43452 inverse(sk_c5) = sk_c8 | identity = sk_c8. [para(37532(b,1),39256(b,1)),merge(c)].
% 99.54/99.90 43467 identity = sk_c8 | multiply(sk_c9,sk_c3) = sk_c8. [para(43452(a,1),4117(b,1,1)),rewrite([36396(11)]),merge(c)].
% 99.54/99.90 43602 identity = sk_c8 | sk_c8 = sk_c9. [para(43467(b,1),39256(b,1)),merge(b)].
% 99.54/99.90 43606 sk_c8 = sk_c9 | identity = sk_c9. [para(43602(a,1),4251(a,1,1)),rewrite([36398(5)]),flip(b)].
% 99.54/99.90 43655 sk_c8 = sk_c9. [para(43606(b,1),43602(a,1)),flip(b),merge(b),merge(c)].
% 99.54/99.90 44047 sk_c4 = sk_c9. [back_rewrite(42651),rewrite([43655(2),43655(4)]),xx(b)].
% 99.54/99.90 44344 multiply(sk_c9,sk_c9) = sk_c9. [back_rewrite(37957),rewrite([43655(1),43655(2),44047(6),43655(7)]),merge(b)].
% 99.54/99.90 44379 $F. [back_rewrite(36697),rewrite([43655(1),43655(2),44344(3),44344(8),44344(7),44344(6),43655(5),43655(7),43655(8),44344(9),43655(8),44344(13),44344(12),43655(11)]),xx(a),xx(b),xx(c),xx(d)].
% 99.54/99.90
% 99.54/99.90 % SZS output end Refutation
% 99.54/99.90 ============================== end of proof ==========================
% 99.54/99.90
% 99.54/99.90 ============================== STATISTICS ============================
% 99.54/99.90
% 99.54/99.90 Given=7295. Generated=4705898. Kept=44378. proofs=1.
% 99.54/99.90 Usable=259. Sos=963. Demods=24. Limbo=724, Disabled=42478. Hints=0.
% 99.54/99.90 Megabytes=36.00.
% 99.54/99.90 User_CPU=96.35, System_CPU=2.51, Wall_clock=99.
% 99.54/99.90
% 99.54/99.90 ============================== end of statistics =====================
% 99.54/99.90
% 99.54/99.90 ============================== end of search =========================
% 99.54/99.90
% 99.54/99.90 THEOREM PROVED
% 99.54/99.90 % SZS status Unsatisfiable
% 99.54/99.90
% 99.54/99.90 Exiting with 1 proof.
% 99.54/99.90
% 99.54/99.90 Process 17435 exit (max_proofs) Tue Jun 14 12:46:46 2022
% 99.54/99.90 Prover9 interrupted
%------------------------------------------------------------------------------