TSTP Solution File: GRP237-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP237-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 11:18:16 EDT 2022
% Result : Unsatisfiable 36.55s 36.81s
% Output : Refutation 36.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP237-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 12:23:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 7.87/8.20 ============================== Prover9 ===============================
% 7.87/8.20 Prover9 (32) version 2009-11A, November 2009.
% 7.87/8.20 Process 29976 was started by sandbox2 on n017.cluster.edu,
% 7.87/8.20 Tue Jun 14 12:23:54 2022
% 7.87/8.20 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29819_n017.cluster.edu".
% 7.87/8.20 ============================== end of head ===========================
% 7.87/8.20
% 7.87/8.20 ============================== INPUT =================================
% 7.87/8.20
% 7.87/8.20 % Reading from file /tmp/Prover9_29819_n017.cluster.edu
% 7.87/8.20
% 7.87/8.20 set(prolog_style_variables).
% 7.87/8.20 set(auto2).
% 7.87/8.20 % set(auto2) -> set(auto).
% 7.87/8.20 % set(auto) -> set(auto_inference).
% 7.87/8.20 % set(auto) -> set(auto_setup).
% 7.87/8.20 % set(auto_setup) -> set(predicate_elim).
% 7.87/8.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.87/8.20 % set(auto) -> set(auto_limits).
% 7.87/8.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.87/8.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.87/8.20 % set(auto) -> set(auto_denials).
% 7.87/8.20 % set(auto) -> set(auto_process).
% 7.87/8.20 % set(auto2) -> assign(new_constants, 1).
% 7.87/8.20 % set(auto2) -> assign(fold_denial_max, 3).
% 7.87/8.20 % set(auto2) -> assign(max_weight, "200.000").
% 7.87/8.20 % set(auto2) -> assign(max_hours, 1).
% 7.87/8.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.87/8.20 % set(auto2) -> assign(max_seconds, 0).
% 7.87/8.20 % set(auto2) -> assign(max_minutes, 5).
% 7.87/8.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.87/8.20 % set(auto2) -> set(sort_initial_sos).
% 7.87/8.20 % set(auto2) -> assign(sos_limit, -1).
% 7.87/8.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.87/8.20 % set(auto2) -> assign(max_megs, 400).
% 7.87/8.20 % set(auto2) -> assign(stats, some).
% 7.87/8.20 % set(auto2) -> clear(echo_input).
% 7.87/8.20 % set(auto2) -> set(quiet).
% 7.87/8.20 % set(auto2) -> clear(print_initial_clauses).
% 7.87/8.20 % set(auto2) -> clear(print_given).
% 7.87/8.20 assign(lrs_ticks,-1).
% 7.87/8.20 assign(sos_limit,10000).
% 7.87/8.20 assign(order,kbo).
% 7.87/8.20 set(lex_order_vars).
% 7.87/8.20 clear(print_given).
% 7.87/8.20
% 7.87/8.20 % formulas(sos). % not echoed (40 formulas)
% 7.87/8.20
% 7.87/8.20 ============================== end of input ==========================
% 7.87/8.20
% 7.87/8.20 % From the command line: assign(max_seconds, 300).
% 7.87/8.20
% 7.87/8.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.87/8.20
% 7.87/8.20 % Formulas that are not ordinary clauses:
% 7.87/8.20
% 7.87/8.20 ============================== end of process non-clausal formulas ===
% 7.87/8.20
% 7.87/8.20 ============================== PROCESS INITIAL CLAUSES ===============
% 7.87/8.20
% 7.87/8.20 ============================== PREDICATE ELIMINATION =================
% 7.87/8.20
% 7.87/8.20 ============================== end predicate elimination =============
% 7.87/8.20
% 7.87/8.20 Auto_denials: (non-Horn, no changes).
% 7.87/8.20
% 7.87/8.20 Term ordering decisions:
% 7.87/8.20
% 7.87/8.20 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 7.87/8.20 Function symbol KB weights: sk_c9=1. sk_c8=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c6=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 7.87/8.20
% 7.87/8.20 ============================== end of process initial clauses ========
% 7.87/8.20
% 7.87/8.20 ============================== CLAUSES FOR SEARCH ====================
% 7.87/8.20
% 7.87/8.20 ============================== end of clauses for search =============
% 7.87/8.20
% 7.87/8.20 ============================== SEARCH ================================
% 7.87/8.20
% 7.87/8.20 % Starting search at 0.03 seconds.
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=40.000, iters=3398
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=39.000, iters=3406
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=38.000, iters=3385
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=37.000, iters=3334
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=35.000, iters=3368
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=34.000, iters=3350
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=33.000, iters=3421
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=32.000, iters=3425
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=31.000, iters=3476
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=30.000, iters=3339
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=29.000, iters=3373
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=28.000, iters=3344
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=27.000, iters=3348
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=26.000, iters=3352
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=25.000, iters=3334
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=24.000, iters=3339
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=23.000, iters=3352
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=22.000, iters=3361
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=21.000, iters=3339
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=20.000, iters=3357
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=18.000, iters=3378
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=17.000, iters=3354
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=16.000, iters=3360
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=15.000, iters=3349
% 7.87/8.20
% 7.87/8.20 Low Water (keep): wt=14.000, iters=3348
% 7.87/8.20
% 7.87/8.20 Low Water (displace): id=3714, wt=49.000
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=3497, wt=47.000
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=3744, wt=45.000
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=3743, wt=44.000
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=4016, wt=43.000
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=16340, wt=13.000
% 36.55/36.81
% 36.55/36.81 Low Water (keep): wt=13.000, iters=3352
% 36.55/36.81
% 36.55/36.81 Low Water (displace): id=18823, wt=11.000
% 36.55/36.81
% 36.55/36.81 Low Water (keep): wt=12.000, iters=3335
% 36.55/36.81
% 36.55/36.81 ============================== PROOF =================================
% 36.55/36.81 % SZS status Unsatisfiable
% 36.55/36.81 % SZS output start Refutation
% 36.55/36.81
% 36.55/36.81 % Proof 1 at 34.76 (+ 1.04) seconds.
% 36.55/36.81 % Length of proof is 157.
% 36.55/36.81 % Level of proof is 28.
% 36.55/36.81 % Maximum clause weight is 55.000.
% 36.55/36.81 % Given clauses 4682.
% 36.55/36.81
% 36.55/36.81 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 36.55/36.81 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 36.55/36.81 3 inverse(sk_c9) = sk_c8 | inverse(sk_c4) = sk_c5 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 36.55/36.81 4 inverse(sk_c9) = sk_c8 | inverse(sk_c6) = sk_c9 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 36.55/36.81 5 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 36.55/36.81 6 inverse(sk_c1) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 36.55/36.81 7 inverse(sk_c2) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 36.55/36.81 8 inverse(sk_c2) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 36.55/36.81 9 inverse(sk_c9) = sk_c8 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 36.55/36.81 11 inverse(sk_c9) = sk_c8 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 36.55/36.81 12 inverse(sk_c9) = sk_c8 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 36.55/36.81 13 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 36.55/36.81 16 inverse(sk_c1) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 36.55/36.81 17 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c4) = sk_c5 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 36.55/36.81 20 multiply(sk_c9,sk_c3) = sk_c8 | inverse(sk_c6) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 36.55/36.81 22 multiply(sk_c2,sk_c9) = sk_c3 | inverse(sk_c6) = sk_c9 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 36.55/36.81 23 inverse(sk_c2) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 36.55/36.81 26 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_35) # label(negated_conjecture). [assumption].
% 36.55/36.81 27 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c4,sk_c5) = sk_c9 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 36.55/36.81 28 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 36.55/36.81 33 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 36.55/36.81 34 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 36.55/36.81 37 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 36.55/36.81 38 multiply(sk_c2,sk_c9) = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 36.55/36.81 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 36.55/36.81 40 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,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9 | multiply(sk_c9,F) != sk_c8 | multiply(V6,sk_c9) != F | inverse(V6) != sk_c9 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 36.55/36.81 48 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,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9. [factor(40,e,k),merge(j),merge(k)].
% 36.55/36.81 81 inverse(sk_c9) = sk_c8 | multiply(sk_c5,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 36.55/36.81 82 inverse(sk_c9) = sk_c8 | multiply(sk_c9,sk_c6) = identity. [para(4(b,1),2(a,1,1))].
% 36.55/36.81 87 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 36.55/36.81 89 inverse(sk_c9) = sk_c8 | multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c9). [para(9(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.55/36.81 93 inverse(sk_c9) = sk_c8 | multiply(A,multiply(sk_c9,sk_c7)) = multiply(A,sk_c8). [para(11(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.55/36.81 95 inverse(sk_c9) = sk_c8 | multiply(A,multiply(sk_c6,sk_c9)) = multiply(A,sk_c7). [para(12(b,1),39(a,2,2)),rewrite([39(8)])].
% 36.55/36.81 115 inverse(sk_c6) = sk_c9 | multiply(A,multiply(sk_c2,sk_c9)) = multiply(A,sk_c3). [para(22(a,1),39(a,2,2)),rewrite([39(8)])].
% 36.55/36.81 126 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(28(a,1),39(a,1,1)),flip(b)].
% 36.55/36.81 139 multiply(sk_c9,sk_c3) = sk_c8 | multiply(A,multiply(sk_c6,sk_c9)) = multiply(A,sk_c7). [para(34(b,1),39(a,2,2)),rewrite([39(9)])].
% 36.55/36.81 194 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | sk_c9 != B | inverse(identity) != sk_c9 | multiply(C,D) != sk_c9 | inverse(C) != D | multiply(D,sk_c8) != sk_c9. [para(1(a,1),48(e,1))].
% 36.55/36.81 199 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 | identity != sk_c9 | inverse(inverse(D)) != D | multiply(D,sk_c8) != sk_c9. [para(2(a,1),48(g,1))].
% 36.55/36.81 433 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | sk_c9 != B | inverse(identity) != sk_c9 | multiply(C,A) != sk_c9 | inverse(C) != A. [factor(194,c,i)].
% 36.55/36.81 453 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 | identity != sk_c9 | inverse(inverse(A)) != A. [factor(199,c,i)].
% 36.55/36.81 806 inverse(sk_c9) != sk_c8 | inverse(identity) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c9,A) != sk_c8 | sk_c9 != A | multiply(B,identity) != sk_c9 | inverse(B) != identity. [factor(433,b,f),rewrite([1(11)])].
% 36.55/36.81 1069 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),87(a,1,2))].
% 36.55/36.81 1083 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c1),sk_c9) = sk_c8. [para(17(a,1),87(a,1,2))].
% 36.55/36.81 1110 inverse(sk_c9) = sk_c8 | multiply(inverse(sk_c5),identity) = sk_c4. [para(81(b,1),87(a,1,2))].
% 36.55/36.81 1111 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(87(a,1),87(a,1,2))].
% 36.55/36.81 1115 multiply(A,identity) = A. [back_rewrite(1069),rewrite([1111(4)])].
% 36.55/36.81 1116 inverse(sk_c9) = sk_c8 | inverse(sk_c5) = sk_c4. [back_rewrite(1110),rewrite([1115(8)])].
% 36.55/36.81 1119 inverse(sk_c9) != sk_c8 | inverse(identity) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c9,A) != sk_c8 | sk_c9 != A | sk_c9 != B | inverse(B) != identity. [back_rewrite(806),rewrite([1115(19)]),flip(f)].
% 36.55/36.81 1141 inverse(sk_c9) != sk_c8 | inverse(identity) != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c9,A) != sk_c8 | sk_c9 != A | inverse(A) != identity. [factor(1119,e,f)].
% 36.55/36.81 1146 inverse(identity) = identity. [para(1115(a,1),2(a,1))].
% 36.55/36.81 1174 inverse(sk_c9) != sk_c8 | identity != sk_c9 | sk_c8 != sk_c9 | multiply(sk_c9,A) != sk_c8 | sk_c9 != A | inverse(A) != identity. [back_rewrite(1141),rewrite([1146(6)])].
% 36.55/36.81 1207 inverse(sk_c9) = sk_c8 | multiply(sk_c4,sk_c5) = identity. [para(1116(b,1),2(a,1,1))].
% 36.55/36.81 1210 inverse(sk_c9) = sk_c8 | inverse(sk_c9) = sk_c6. [para(82(b,1),87(a,1,2)),rewrite([1115(8)])].
% 36.55/36.81 1217 inverse(sk_c9) = sk_c8 | multiply(sk_c6,sk_c9) = identity. [para(1210(b,1),2(a,1,1))].
% 36.55/36.81 1266 inverse(sk_c9) != sk_c8 | identity != sk_c9 | sk_c8 != sk_c9. [para(1115(a,1),1174(d,1)),rewrite([1146(18)]),flip(d),flip(e),xx(f),merge(d),merge(e)].
% 36.55/36.81 1333 multiply(A,inverse(A)) = identity. [para(1111(a,1),2(a,1))].
% 36.55/36.81 1375 multiply(A,multiply(inverse(A),B)) = B. [para(1111(a,1),87(a,1))].
% 36.55/36.81 1376 inverse(inverse(A)) = A. [para(1111(a,1),1115(a,1)),rewrite([1115(2)]),flip(a)].
% 36.55/36.81 1418 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 | identity != sk_c9. [back_rewrite(453),rewrite([1376(26)]),xx(h)].
% 36.55/36.81 1434 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c5) = identity. [para(5(b,1),1333(a,1,2))].
% 36.55/36.81 1435 inverse(sk_c1) = sk_c9 | multiply(sk_c6,sk_c9) = identity. [para(6(b,1),1333(a,1,2))].
% 36.55/36.81 1436 inverse(sk_c2) = sk_c9 | multiply(sk_c4,sk_c5) = identity. [para(7(b,1),1333(a,1,2))].
% 36.55/36.81 1437 inverse(sk_c2) = sk_c9 | multiply(sk_c6,sk_c9) = identity. [para(8(b,1),1333(a,1,2))].
% 36.55/36.81 1438 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1333(a,1),39(a,1)),flip(a)].
% 36.55/36.81 1597 inverse(sk_c9) = sk_c8 | identity = sk_c9. [para(1207(b,1),9(b,1)),merge(b)].
% 36.55/36.81 1599 inverse(sk_c9) = sk_c8 | multiply(A,sk_c9) = A. [para(1207(b,1),89(b,1,2)),rewrite([1115(10)]),flip(c),merge(b)].
% 36.55/36.81 1709 inverse(sk_c9) = sk_c8 | identity = sk_c7. [para(1217(b,1),12(b,1)),merge(b)].
% 36.55/36.81 1931 inverse(sk_c1) = sk_c9 | identity = sk_c9. [para(1434(b,1),13(b,1)),merge(b)].
% 36.55/36.81 1943 inverse(sk_c9) = sk_c8 | multiply(A,sk_c7) = A. [para(1217(b,1),95(b,1,2)),rewrite([1115(10)]),flip(c),merge(b)].
% 36.55/36.81 2014 identity = sk_c9 | inverse(sk_c9) = sk_c1. [para(1931(a,1),1376(a,1,1))].
% 36.55/36.81 2021 identity = sk_c9 | sk_c1 = sk_c8. [para(2014(b,1),1597(a,1)),merge(c)].
% 36.55/36.81 2027 sk_c1 = sk_c8 | inverse(sk_c9) = identity. [para(2021(a,1),1146(a,1,1))].
% 36.55/36.81 2054 sk_c1 = sk_c8 | inverse(sk_c9) = sk_c9. [para(2021(a,1),2027(b,2)),merge(b)].
% 36.55/36.81 2119 sk_c1 = sk_c8 | multiply(sk_c9,sk_c9) = identity. [para(2054(b,1),2(a,1,1))].
% 36.55/36.81 2567 inverse(sk_c1) = sk_c9 | identity = sk_c7. [para(1435(b,1),16(b,1)),merge(b)].
% 36.55/36.81 2576 identity = sk_c7 | inverse(sk_c9) = sk_c1. [para(2567(a,1),1376(a,1,1))].
% 36.55/36.81 2654 identity = sk_c7 | sk_c1 = sk_c8. [para(2576(b,1),1709(a,1)),merge(c)].
% 36.55/36.81 2685 sk_c1 = sk_c8 | inverse(sk_c9) = sk_c7. [para(2654(a,1),2027(b,2)),merge(b)].
% 36.55/36.81 2686 sk_c1 = sk_c8 | multiply(sk_c9,sk_c9) = sk_c7. [para(2654(a,1),2119(b,2)),merge(b)].
% 36.55/36.81 3108 sk_c1 = sk_c8 | multiply(inverse(sk_c9),sk_c7) = sk_c9. [para(2686(b,1),87(a,1,2))].
% 36.55/36.81 3437 inverse(sk_c2) = sk_c9 | identity = sk_c9. [para(1436(b,1),23(b,1)),merge(b)].
% 36.55/36.81 3443 identity = sk_c9 | inverse(sk_c9) = sk_c2. [para(3437(a,1),1376(a,1,1))].
% 36.55/36.81 3451 identity = sk_c9 | sk_c2 = sk_c1. [para(3443(b,1),2014(b,1)),merge(b)].
% 36.55/36.81 3601 sk_c2 = sk_c1 | inverse(sk_c9) = identity. [para(3451(a,1),1146(a,1,1))].
% 36.55/36.81 3676 sk_c2 = sk_c1 | inverse(sk_c9) = sk_c9. [para(3451(a,1),3601(b,2)),merge(b)].
% 36.55/36.81 3916 sk_c2 = sk_c1 | multiply(sk_c9,sk_c9) = identity. [para(3676(b,1),2(a,1,1))].
% 36.55/36.81 4709 inverse(sk_c2) = sk_c9 | identity = sk_c7. [para(1437(b,1),26(b,1)),merge(b)].
% 36.55/36.81 4720 identity = sk_c7 | inverse(sk_c9) = sk_c2. [para(4709(a,1),1376(a,1,1))].
% 36.55/36.81 4747 identity = sk_c7 | sk_c2 = sk_c1. [para(4720(b,1),2576(b,1)),merge(b)].
% 36.55/36.81 4916 sk_c2 = sk_c1 | inverse(sk_c9) = sk_c7. [para(4747(a,1),3601(b,2)),merge(b)].
% 36.55/36.81 4920 sk_c2 = sk_c1 | multiply(sk_c9,sk_c9) = sk_c7. [para(4747(a,1),3916(b,2)),merge(b)].
% 36.55/36.81 5675 sk_c2 = sk_c1 | multiply(inverse(sk_c9),sk_c7) = sk_c9. [para(4920(b,1),87(a,1,2))].
% 36.55/36.81 6130 inverse(sk_c6) = sk_c9 | multiply(sk_c9,multiply(sk_c2,sk_c9)) = sk_c8. [para(20(a,1),115(b,2)),merge(b)].
% 36.55/36.81 6431 inverse(sk_c9) = sk_c8 | inverse(sk_c9) = identity. [para(1599(b,1),2(a,1))].
% 36.55/36.81 6617 inverse(sk_c9) = sk_c8 | multiply(sk_c9,A) = A. [para(6431(b,1),87(a,1,1)),rewrite([1(8)])].
% 36.55/36.81 7719 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c1,multiply(sk_c8,inverse(sk_c9))) = identity. [para(1333(a,1),126(b,2))].
% 36.55/36.81 8633 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(sk_c9,B) != sk_c8 | sk_c9 != B | identity != sk_c9. [para(1(a,1),1418(e,1)),rewrite([1146(19)]),merge(g)].
% 36.55/36.81 8753 inverse(sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | identity != sk_c9. [resolve(8633,d,1375,a),flip(d)].
% 36.55/36.81 8757 inverse(sk_c9) != sk_c8 | multiply(inverse(sk_c9),sk_c8) != sk_c9 | identity != sk_c9. [factor(8753,c,d),rewrite([1376(7)]),xx(b)].
% 36.55/36.81 9414 multiply(sk_c9,sk_c3) = sk_c8 | multiply(sk_c9,multiply(sk_c6,sk_c9)) = sk_c8. [para(33(b,1),139(b,2)),merge(b)].
% 36.55/36.81 10477 inverse(sk_c9) = sk_c8 | sk_c7 = sk_c8. [para(6617(b,1),11(b,1)),merge(b)].
% 36.55/36.81 10478 inverse(sk_c9) = sk_c8 | multiply(inverse(sk_c9),A) = A. [para(6617(b,1),87(a,1,2))].
% 36.55/36.81 10496 sk_c7 = sk_c8 | sk_c1 = sk_c8. [para(10477(a,1),2685(b,1)),flip(c),merge(c)].
% 36.55/36.81 10500 sk_c7 = sk_c8 | sk_c2 = sk_c1. [para(10477(a,1),4916(b,1)),flip(c),merge(c)].
% 36.55/36.81 10546 sk_c1 = sk_c8 | multiply(inverse(sk_c9),sk_c8) = sk_c9. [para(10496(a,1),3108(b,1,2)),merge(b)].
% 36.55/36.81 10610 sk_c2 = sk_c1 | multiply(inverse(sk_c9),sk_c8) = sk_c9. [para(10500(a,1),5675(b,1,2)),merge(b)].
% 36.55/36.81 12469 sk_c1 = sk_c8 | inverse(sk_c9) != sk_c8 | identity != sk_c9. [resolve(10546,b,8757,b)].
% 36.55/36.81 12505 sk_c2 = sk_c1 | inverse(sk_c9) != sk_c8 | identity != sk_c9. [resolve(10610,b,8757,b)].
% 36.55/36.81 13999 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1438(a,1),87(a,1,2)),rewrite([1115(3)]),flip(a)].
% 36.55/36.81 14305 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c1),multiply(sk_c9,inverse(sk_c8))) = identity. [para(1083(b,1),1438(a,1,2,2,1))].
% 36.55/36.81 14338 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c5,inverse(sk_c9)) = inverse(sk_c4). [para(27(b,1),13999(a,1,2,1))].
% 36.55/36.81 14339 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = inverse(sk_c1). [para(28(a,1),13999(a,1,2,1))].
% 36.55/36.81 20134 inverse(sk_c9) = sk_c8 | inverse(sk_c9) = sk_c7. [para(10478(b,1),1943(b,1)),flip(c),merge(b)].
% 36.55/36.81 20148 inverse(sk_c9) = sk_c8 | multiply(sk_c9,sk_c7) = identity. [para(20134(b,1),1333(a,1,2))].
% 36.55/36.81 20212 inverse(sk_c9) = sk_c8 | multiply(A,sk_c8) = A. [para(20148(b,1),93(b,1,2)),rewrite([1115(10)]),flip(c),merge(b)].
% 36.55/36.81 20296 inverse(sk_c9) = sk_c8. [para(20212(b,1),10478(b,1)),merge(b),merge(c)].
% 36.55/36.81 22408 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c8,sk_c8) = inverse(sk_c1). [back_rewrite(14339),rewrite([20296(8)])].
% 36.55/36.81 22409 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c5,sk_c8) = inverse(sk_c4). [back_rewrite(14338),rewrite([20296(8)])].
% 36.55/36.81 22563 sk_c2 = sk_c1 | identity != sk_c9. [back_rewrite(12505),rewrite([20296(5)]),xx(b)].
% 36.55/36.81 22565 sk_c1 = sk_c8 | identity != sk_c9. [back_rewrite(12469),rewrite([20296(5)]),xx(b)].
% 36.55/36.81 22690 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c1,multiply(sk_c8,sk_c8)) = identity. [back_rewrite(7719),rewrite([20296(9)])].
% 36.55/36.81 22834 identity != sk_c9 | sk_c8 != sk_c9. [back_rewrite(1266),rewrite([20296(2)]),xx(a)].
% 36.55/36.81 23482 multiply(sk_c8,sk_c9) = identity. [para(20296(a,1),2(a,1,1))].
% 36.55/36.81 23484 inverse(sk_c8) = sk_c9. [para(20296(a,1),1376(a,1,1))].
% 36.55/36.81 23485 multiply(sk_c9,sk_c8) = identity. [para(20296(a,1),1333(a,1,2))].
% 36.55/36.81 23720 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c1),multiply(sk_c9,sk_c9)) = identity. [back_rewrite(14305),rewrite([23484(9)])].
% 36.55/36.81 24098 sk_c2 = sk_c1. [resolve(22563,b,3451,a),merge(b)].
% 36.55/36.81 24239 inverse(sk_c6) = sk_c9 | multiply(sk_c9,multiply(sk_c1,sk_c9)) = sk_c8. [back_rewrite(6130),rewrite([24098(6)])].
% 36.55/36.81 24290 multiply(sk_c1,sk_c9) = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7. [back_rewrite(38),rewrite([24098(1)])].
% 36.55/36.81 24291 multiply(sk_c1,sk_c9) = sk_c3 | multiply(sk_c9,sk_c7) = sk_c8. [back_rewrite(37),rewrite([24098(1)])].
% 36.55/36.81 24294 multiply(sk_c1,sk_c9) = sk_c3 | inverse(sk_c6) = sk_c9. [back_rewrite(22),rewrite([24098(1)])].
% 36.55/36.81 24296 sk_c1 = sk_c8. [resolve(22565,b,2021,a),merge(b)].
% 36.55/36.81 24298 identity = sk_c3 | inverse(sk_c6) = sk_c9. [back_rewrite(24294),rewrite([24296(1),23482(3)])].
% 36.55/36.81 24301 identity = sk_c3 | multiply(sk_c9,sk_c7) = sk_c8. [back_rewrite(24291),rewrite([24296(1),23482(3)])].
% 36.55/36.81 24302 identity = sk_c3 | multiply(sk_c6,sk_c9) = sk_c7. [back_rewrite(24290),rewrite([24296(1),23482(3)])].
% 36.55/36.81 24342 inverse(sk_c6) = sk_c9 | sk_c8 = sk_c9. [back_rewrite(24239),rewrite([24296(6),23482(8),1115(7)]),flip(b)].
% 36.55/36.81 24412 inverse(sk_c4) = sk_c5 | multiply(sk_c9,multiply(sk_c9,sk_c9)) = identity. [back_rewrite(23720),rewrite([24296(5),23484(6)])].
% 36.55/36.81 24453 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c8,multiply(sk_c8,sk_c8)) = identity. [back_rewrite(22690),rewrite([24296(6)])].
% 36.55/36.81 24457 multiply(sk_c8,sk_c8) = sk_c9 | multiply(sk_c5,sk_c8) = inverse(sk_c4). [back_rewrite(22409),rewrite([24296(1)])].
% 36.55/36.82 24458 multiply(sk_c5,sk_c8) = sk_c9 | multiply(sk_c8,sk_c8) = sk_c9. [back_rewrite(22408),rewrite([24296(9),23484(10)])].
% 36.55/36.82 24575 identity = sk_c3 | multiply(sk_c6,sk_c9) = identity. [para(24298(b,1),1333(a,1,2))].
% 36.55/36.82 24603 sk_c8 = sk_c9 | sk_c6 = sk_c8. [para(24342(a,1),1376(a,1,1)),rewrite([20296(5)]),flip(b)].
% 36.55/36.82 24991 identity = sk_c3 | identity = sk_c7. [para(24575(b,1),24302(b,1)),merge(b)].
% 36.55/36.82 25038 identity = sk_c3 | multiply(A,sk_c7) = A. [para(24991(b,1),1115(a,1,2))].
% 36.55/36.82 25633 identity = sk_c3 | sk_c8 = sk_c9. [para(25038(b,1),24301(b,1)),flip(c),merge(b)].
% 36.55/36.82 25641 sk_c8 = sk_c9 | multiply(A,sk_c3) = A. [para(25633(a,1),1115(a,1,2))].
% 36.55/36.82 30862 sk_c8 = sk_c9 | multiply(sk_c9,sk_c3) = sk_c8. [para(24603(b,1),9414(b,1,2,1)),rewrite([23482(12),1115(11)]),flip(c),merge(c)].
% 36.55/36.82 31192 sk_c8 = sk_c9. [para(30862(b,1),25641(b,1)),merge(b),merge(c)].
% 36.55/36.82 33442 multiply(sk_c5,sk_c9) = sk_c9 | multiply(sk_c9,sk_c9) = sk_c9. [back_rewrite(24458),rewrite([31192(2),31192(6),31192(7)])].
% 36.55/36.82 33443 multiply(sk_c9,sk_c9) = sk_c9 | multiply(sk_c5,sk_c9) = inverse(sk_c4). [back_rewrite(24457),rewrite([31192(1),31192(2),31192(7)])].
% 36.55/36.82 33446 multiply(sk_c5,sk_c9) = sk_c9 | multiply(sk_c9,multiply(sk_c9,sk_c9)) = identity. [back_rewrite(24453),rewrite([31192(2),31192(6),31192(7),31192(8)])].
% 36.55/36.82 33684 multiply(sk_c9,sk_c9) = identity. [back_rewrite(23485),rewrite([31192(2)])].
% 36.55/36.82 33729 identity != sk_c9. [back_rewrite(22834),rewrite([31192(4)]),xx(b)].
% 36.55/36.82 34041 multiply(sk_c5,sk_c9) = sk_c9. [back_rewrite(33446),rewrite([33684(9),1115(8)]),flip(b),unit_del(b,33729)].
% 36.55/36.82 34092 inverse(sk_c4) = sk_c5. [back_rewrite(24412),rewrite([33684(8),1115(7)]),flip(b),unit_del(b,33729)].
% 36.55/36.82 34099 sk_c5 = sk_c9. [back_rewrite(33443),rewrite([33684(3),34041(6),34092(6)]),flip(b),unit_del(a,33729)].
% 36.55/36.82 34100 $F. [back_rewrite(33442),rewrite([34099(1),33684(3),33684(6)]),merge(b),unit_del(a,33729)].
% 36.55/36.82
% 36.55/36.82 % SZS output end Refutation
% 36.55/36.82 ============================== end of proof ==========================
% 36.55/36.82
% 36.55/36.82 ============================== STATISTICS ============================
% 36.55/36.82
% 36.55/36.82 Given=4682. Generated=1911796. Kept=34099. proofs=1.
% 36.55/36.82 Usable=111. Sos=1894. Demods=23. Limbo=416, Disabled=31718. Hints=0.
% 36.55/36.82 Megabytes=26.61.
% 36.55/36.82 User_CPU=34.76, System_CPU=1.04, Wall_clock=36.
% 36.55/36.82
% 36.55/36.82 ============================== end of statistics =====================
% 36.55/36.82
% 36.55/36.82 ============================== end of search =========================
% 36.55/36.82
% 36.55/36.82 THEOREM PROVED
% 36.55/36.82 % SZS status Unsatisfiable
% 36.55/36.82
% 36.55/36.82 Exiting with 1 proof.
% 36.55/36.82
% 36.55/36.82 Process 29976 exit (max_proofs) Tue Jun 14 12:24:30 2022
% 36.55/36.82 Prover9 interrupted
%------------------------------------------------------------------------------