TSTP Solution File: GRP216-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP216-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 7.61s 7.88s
% Output : Refutation 7.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP216-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 10:13:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.31/3.56 ============================== Prover9 ===============================
% 3.31/3.56 Prover9 (32) version 2009-11A, November 2009.
% 3.31/3.56 Process 21647 was started by sandbox on n022.cluster.edu,
% 3.31/3.56 Mon Jun 13 10:13:19 2022
% 3.31/3.56 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21493_n022.cluster.edu".
% 3.31/3.56 ============================== end of head ===========================
% 3.31/3.56
% 3.31/3.56 ============================== INPUT =================================
% 3.31/3.56
% 3.31/3.56 % Reading from file /tmp/Prover9_21493_n022.cluster.edu
% 3.31/3.56
% 3.31/3.56 set(prolog_style_variables).
% 3.31/3.56 set(auto2).
% 3.31/3.56 % set(auto2) -> set(auto).
% 3.31/3.56 % set(auto) -> set(auto_inference).
% 3.31/3.56 % set(auto) -> set(auto_setup).
% 3.31/3.56 % set(auto_setup) -> set(predicate_elim).
% 3.31/3.56 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.31/3.56 % set(auto) -> set(auto_limits).
% 3.31/3.56 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.31/3.56 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.31/3.56 % set(auto) -> set(auto_denials).
% 3.31/3.56 % set(auto) -> set(auto_process).
% 3.31/3.56 % set(auto2) -> assign(new_constants, 1).
% 3.31/3.56 % set(auto2) -> assign(fold_denial_max, 3).
% 3.31/3.56 % set(auto2) -> assign(max_weight, "200.000").
% 3.31/3.56 % set(auto2) -> assign(max_hours, 1).
% 3.31/3.56 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.31/3.56 % set(auto2) -> assign(max_seconds, 0).
% 3.31/3.56 % set(auto2) -> assign(max_minutes, 5).
% 3.31/3.56 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.31/3.56 % set(auto2) -> set(sort_initial_sos).
% 3.31/3.56 % set(auto2) -> assign(sos_limit, -1).
% 3.31/3.56 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.31/3.56 % set(auto2) -> assign(max_megs, 400).
% 3.31/3.56 % set(auto2) -> assign(stats, some).
% 3.31/3.56 % set(auto2) -> clear(echo_input).
% 3.31/3.56 % set(auto2) -> set(quiet).
% 3.31/3.56 % set(auto2) -> clear(print_initial_clauses).
% 3.31/3.56 % set(auto2) -> clear(print_given).
% 3.31/3.56 assign(lrs_ticks,-1).
% 3.31/3.56 assign(sos_limit,10000).
% 3.31/3.56 assign(order,kbo).
% 3.31/3.56 set(lex_order_vars).
% 3.31/3.56 clear(print_given).
% 3.31/3.56
% 3.31/3.56 % formulas(sos). % not echoed (28 formulas)
% 3.31/3.56
% 3.31/3.56 ============================== end of input ==========================
% 3.31/3.56
% 3.31/3.56 % From the command line: assign(max_seconds, 300).
% 3.31/3.56
% 3.31/3.56 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.31/3.56
% 3.31/3.56 % Formulas that are not ordinary clauses:
% 3.31/3.56
% 3.31/3.56 ============================== end of process non-clausal formulas ===
% 3.31/3.56
% 3.31/3.56 ============================== PROCESS INITIAL CLAUSES ===============
% 3.31/3.56
% 3.31/3.56 ============================== PREDICATE ELIMINATION =================
% 3.31/3.56
% 3.31/3.56 ============================== end predicate elimination =============
% 3.31/3.56
% 3.31/3.56 Auto_denials: (non-Horn, no changes).
% 3.31/3.56
% 3.31/3.56 Term ordering decisions:
% 3.31/3.56
% 3.31/3.56 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 3.31/3.56 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 3.31/3.56
% 3.31/3.56 ============================== end of process initial clauses ========
% 3.31/3.56
% 3.31/3.56 ============================== CLAUSES FOR SEARCH ====================
% 3.31/3.56
% 3.31/3.56 ============================== end of clauses for search =============
% 3.31/3.56
% 3.31/3.56 ============================== SEARCH ================================
% 3.31/3.56
% 3.31/3.56 % Starting search at 0.02 seconds.
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=46.000, iters=3409
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=44.000, iters=3382
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=43.000, iters=3570
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=42.000, iters=3432
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=41.000, iters=3388
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=40.000, iters=3542
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=39.000, iters=3407
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=38.000, iters=3346
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=37.000, iters=3350
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=36.000, iters=3442
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=35.000, iters=3460
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=34.000, iters=3424
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=33.000, iters=3409
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=32.000, iters=3358
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=31.000, iters=3341
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=30.000, iters=3361
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=29.000, iters=3373
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=28.000, iters=3342
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=27.000, iters=3411
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=26.000, iters=3375
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=25.000, iters=3346
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=24.000, iters=3340
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=23.000, iters=3349
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=22.000, iters=3411
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=21.000, iters=3379
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=20.000, iters=3395
% 3.31/3.56
% 3.31/3.56 Low Water (keep): wt=19.000, iters=3335
% 7.61/7.88
% 7.61/7.88 Low Water (keep): wt=17.000, iters=3339
% 7.61/7.88
% 7.61/7.88 Low Water (keep): wt=16.000, iters=3349
% 7.61/7.88
% 7.61/7.88 Low Water (keep): wt=15.000, iters=3339
% 7.61/7.88
% 7.61/7.88 Low Water (keep): wt=14.000, iters=3333
% 7.61/7.88
% 7.61/7.88 ============================== PROOF =================================
% 7.61/7.88 % SZS status Unsatisfiable
% 7.61/7.88 % SZS output start Refutation
% 7.61/7.88
% 7.61/7.88 % Proof 1 at 6.70 (+ 0.19) seconds.
% 7.61/7.88 % Length of proof is 153.
% 7.61/7.88 % Level of proof is 27.
% 7.61/7.88 % Maximum clause weight is 45.000.
% 7.61/7.88 % Given clauses 2122.
% 7.61/7.88
% 7.61/7.88 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 7.61/7.88 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 7.61/7.88 3 inverse(sk_c1) = sk_c7 | inverse(sk_c7) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 7.61/7.88 4 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 7.61/7.88 5 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 7.61/7.88 6 inverse(sk_c2) = sk_c6 | inverse(sk_c7) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 7.61/7.88 7 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 7.61/7.88 8 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c7 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 7.61/7.88 9 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 7.61/7.88 12 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 7.61/7.88 13 inverse(sk_c1) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 7.61/7.88 14 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 7.61/7.88 15 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c7) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 7.61/7.88 16 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 7.61/7.88 17 multiply(sk_c2,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 7.61/7.88 18 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 7.61/7.88 19 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 7.61/7.88 20 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 7.61/7.88 21 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 7.61/7.88 25 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c7,sk_c5) = sk_c6 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 7.61/7.88 26 multiply(sk_c2,sk_c6) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 7.61/7.88 27 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 7.61/7.88 28 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | multiply(sk_c7,D) != sk_c6 | multiply(E,sk_c7) != D | inverse(E) != sk_c7 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 7.61/7.88 67 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 7.61/7.88 70 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 7.61/7.88 73 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),27(a,1,1)),rewrite([1(2)]),flip(a)].
% 7.61/7.88 75 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(9(a,1),27(a,2,2)),rewrite([27(8)])].
% 7.61/7.88 80 inverse(sk_c1) = sk_c7 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(12(b,1),27(a,1,1)),flip(b)].
% 7.61/7.88 83 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c7,sk_c5)) = multiply(A,sk_c6). [para(13(b,1),27(a,2,2)),rewrite([27(8)])].
% 7.61/7.88 87 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c2,sk_c6)) = multiply(A,sk_c7). [para(15(a,1),27(a,2,2)),rewrite([27(8)])].
% 7.61/7.88 95 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c7,sk_c5)) = multiply(A,sk_c6). [para(19(b,1),27(a,2,2)),rewrite([27(8)])].
% 7.61/7.88 98 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(21(b,1),27(a,1,1)),flip(b)].
% 7.61/7.88 106 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(25(a,1),27(a,1,1)),flip(b)].
% 7.61/7.88 134 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(C) != sk_c7 | multiply(C,sk_c6) != sk_c7 | multiply(sk_c7,identity) != sk_c6 | inverse(inverse(sk_c7)) != sk_c7. [resolve(28,i,2,a)].
% 7.61/7.88 137 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | multiply(D,sk_c7) != C | inverse(D) != sk_c7. [para(1(a,1),28(a,1)),flip(a)].
% 7.61/7.88 141 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | multiply(D,sk_c7) != C | inverse(D) != sk_c7. [para(2(a,1),28(a,1))].
% 7.61/7.88 289 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(sk_c7,identity) != sk_c6 | inverse(inverse(sk_c7)) != sk_c7. [factor(134,c,g)].
% 7.61/7.88 303 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c7,B) != sk_c6 | multiply(C,sk_c7) != B | inverse(C) != sk_c7. [factor(137,b,f),rewrite([1(21)]),merge(f)].
% 7.61/7.88 315 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,C) != sk_c6 | identity != C. [factor(141,b,j),rewrite([2(34)])].
% 7.61/7.88 587 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(inverse(sk_c7)) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(sk_c7,identity) != sk_c6. [factor(289,f,h)].
% 7.61/7.88 605 sk_c6 != sk_c7 | inverse(identity) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B. [factor(303,b,h),rewrite([1(25)])].
% 7.61/7.88 618 identity != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [factor(315,a,i)].
% 7.61/7.88 1108 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),73(a,1,2))].
% 7.61/7.88 1121 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c2),sk_c7) = sk_c6. [para(16(a,1),73(a,1,2))].
% 7.61/7.88 1122 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c2),sk_c7) = sk_c6. [para(17(a,1),73(a,1,2))].
% 7.61/7.88 1123 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(18(b,1),73(a,1,2))].
% 7.61/7.88 1133 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c7),identity) = sk_c1. [para(67(b,1),73(a,1,2))].
% 7.61/7.88 1134 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(73(a,1),73(a,1,2))].
% 7.61/7.88 1135 multiply(A,identity) = A. [back_rewrite(1108),rewrite([1134(4)])].
% 7.61/7.88 1136 inverse(sk_c7) = sk_c6 | inverse(sk_c7) = sk_c1. [back_rewrite(1133),rewrite([1135(8)])].
% 7.61/7.88 1143 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(inverse(sk_c7)) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(inverse(sk_c7)) != sk_c7 | sk_c6 != sk_c7. [back_rewrite(587),rewrite([1135(30)]),flip(g)].
% 7.61/7.88 1156 inverse(identity) = identity. [para(1135(a,1),2(a,1))].
% 7.61/7.88 1194 sk_c6 != sk_c7 | identity != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | multiply(sk_c7,B) != sk_c6 | sk_c7 != B. [back_rewrite(605),rewrite([1156(5)])].
% 7.61/7.88 1215 inverse(sk_c7) = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(1136(b,1),2(a,1,1))].
% 7.61/7.88 1266 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c2. [para(70(b,1),73(a,1,2)),rewrite([1135(8)])].
% 7.61/7.88 1296 inverse(sk_c7) = sk_c6 | multiply(sk_c2,sk_c6) = identity. [para(1266(b,1),2(a,1,1))].
% 7.61/7.88 1355 multiply(A,inverse(A)) = identity. [para(1134(a,1),2(a,1))].
% 7.61/7.88 1426 multiply(A,multiply(inverse(A),B)) = B. [para(1134(a,1),73(a,1))].
% 7.61/7.88 1427 inverse(inverse(A)) = A. [para(1134(a,1),1135(a,1)),rewrite([1135(2)]),flip(a)].
% 7.61/7.88 1447 multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [back_rewrite(1143),rewrite([1427(16),1427(23)]),flip(d),xx(f),merge(f)].
% 7.61/7.88 1481 identity != sk_c6 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | inverse(sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [back_rewrite(618),rewrite([1427(6)]),xx(b)].
% 7.61/7.88 1507 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(5(b,1),1355(a,1,2))].
% 7.61/7.88 1509 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c7) = identity. [para(8(b,1),1355(a,1,2))].
% 7.61/7.88 1510 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1355(a,1),27(a,1)),flip(a)].
% 7.61/7.88 1648 multiply(A,multiply(B,sk_c7)) != sk_c6 | inverse(multiply(A,B)) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(27(a,1),1447(a,1))].
% 7.61/7.88 1719 inverse(sk_c7) = sk_c6 | multiply(A,sk_c6) = A. [para(1215(b,1),75(b,1,2)),rewrite([1135(10)]),flip(c),merge(b)].
% 7.61/7.88 1906 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),multiply(sk_c7,A)) = multiply(sk_c6,A). [para(80(b,1),73(a,1,2))].
% 7.61/7.88 2041 inverse(sk_c1) = sk_c7 | identity = sk_c5. [para(1507(b,1),14(b,1)),merge(b)].
% 7.61/7.88 2046 identity = sk_c5 | inverse(sk_c7) = sk_c1. [para(2041(a,1),1427(a,1,1))].
% 7.61/7.88 2233 multiply(A,multiply(B,multiply(C,sk_c7))) != sk_c6 | inverse(multiply(A,multiply(B,C))) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(27(a,1),1648(a,1,2))].
% 7.61/7.88 2263 inverse(sk_c2) = sk_c6 | identity = sk_c5. [para(1509(b,1),20(b,1)),merge(b)].
% 7.61/7.88 2269 identity = sk_c5 | inverse(sk_c6) = sk_c2. [para(2263(a,1),1427(a,1,1))].
% 7.61/7.88 2322 sk_c6 != sk_c7 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | multiply(sk_c7,A) != sk_c6 | sk_c7 != A. [para(2(a,1),1194(c,1)),rewrite([1427(12)]),xx(d),merge(c)].
% 7.61/7.88 2326 sk_c6 != sk_c7 | identity != sk_c7 | inverse(sk_c7) != sk_c6. [para(1135(a,1),2322(d,1)),flip(d),flip(e),merge(d),merge(e)].
% 7.61/7.88 2654 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = identity. [para(1719(b,1),2(a,1))].
% 7.61/7.88 2655 inverse(sk_c7) = sk_c6 | sk_c2 = sk_c7. [para(1719(b,1),15(a,1)),merge(c)].
% 7.61/7.88 2665 sk_c2 = sk_c7 | inverse(sk_c6) = sk_c7. [para(2655(a,1),1427(a,1,1))].
% 7.61/7.88 2734 inverse(sk_c7) = sk_c6 | multiply(A,sk_c7) = A. [para(1296(b,1),87(b,1,2)),rewrite([1135(10)]),flip(c),merge(b)].
% 7.61/7.88 2781 sk_c2 = sk_c7 | identity = sk_c5. [para(2665(b,1),2269(b,1)),flip(c),merge(c)].
% 7.61/7.88 2784 sk_c2 = sk_c7 | multiply(sk_c5,A) = A. [para(2781(b,1),1(a,1,1))].
% 7.61/7.88 2786 sk_c2 = sk_c7 | inverse(sk_c5) = identity. [para(2781(b,1),1156(a,1,1))].
% 7.61/7.88 3245 inverse(sk_c7) = sk_c6 | multiply(sk_c6,A) = A. [para(2654(b,1),73(a,1,1)),rewrite([1(8)])].
% 7.61/7.88 3588 sk_c2 = sk_c7 | multiply(inverse(sk_c5),A) = A. [para(2784(b,1),73(a,1,2))].
% 7.61/7.88 5149 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c7,inverse(sk_c6)) = sk_c3. [para(1355(a,1),98(b,1,2)),rewrite([1135(8)]),flip(b)].
% 7.61/7.88 5451 inverse(sk_c7) = sk_c6 | sk_c1 = sk_c6. [para(2734(b,1),9(a,1)),merge(c)].
% 7.61/7.88 5460 sk_c1 = sk_c6 | sk_c6 != sk_c7 | identity != sk_c7. [resolve(5451,a,2326,c)].
% 7.61/7.88 5479 sk_c1 = sk_c6 | identity = sk_c5. [para(5451(a,1),2046(b,1)),flip(c),merge(c)].
% 7.61/7.88 5617 identity != sk_c6 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [para(2(a,1),1481(b,1)),rewrite([1427(9)]),xx(c)].
% 7.61/7.88 5633 identity != sk_c6 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | inverse(multiply(A,B)) != sk_c7 | multiply(A,multiply(B,sk_c6)) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [para(27(a,1),5617(e,1))].
% 7.61/7.88 5639 identity != sk_c6 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | inverse(multiply(A,inverse(sk_c6))) != sk_c7 | sk_c7 != A | multiply(sk_c7,sk_c6) != sk_c6. [para(2(a,1),5633(e,1,2)),rewrite([1135(18)]),flip(e)].
% 7.61/7.88 5794 identity != sk_c6 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | inverse(multiply(A,multiply(B,inverse(sk_c6)))) != sk_c7 | multiply(A,B) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [para(27(a,1),5639(d,1,1)),flip(e)].
% 7.61/7.88 6905 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c6),A) = A. [para(3245(b,1),73(a,1,2))].
% 7.61/7.88 7021 sk_c6 != A | inverse(multiply(A,multiply(inverse(multiply(B,sk_c7)),B))) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(2(a,1),2233(a,1,2)),rewrite([1135(2)]),flip(a)].
% 7.61/7.88 7043 sk_c6 != A | inverse(multiply(A,multiply(inverse(multiply(B,multiply(C,sk_c7))),multiply(B,C)))) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(27(a,1),7021(b,1,1,2,1,1))].
% 7.61/7.88 7538 sk_c1 = sk_c6 | sk_c6 != sk_c7 | sk_c5 != sk_c7. [para(5479(b,1),5460(c,1)),merge(b)].
% 7.61/7.88 8019 inverse(sk_c2) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(7(b,1),1123(b,1,1)),merge(b)].
% 7.61/7.88 8045 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c7),sk_c6) = sk_c7. [para(8019(b,1),73(a,1,2))].
% 7.61/7.88 8110 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1510(a,1),73(a,1,2)),rewrite([1135(3)]),flip(a)].
% 7.61/7.88 8163 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c7,inverse(multiply(sk_c2,sk_c6))) = identity. [para(1510(a,1),106(b,1)),flip(b)].
% 7.61/7.88 8199 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c2),multiply(sk_c7,inverse(sk_c6))) = identity. [para(1121(b,1),1510(a,1,2,2,1))].
% 7.61/7.88 8200 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c2),multiply(sk_c7,inverse(sk_c6))) = identity. [para(1122(b,1),1510(a,1,2,2,1))].
% 7.61/7.88 8254 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(8110(a,1),73(a,1,2)),flip(a)].
% 7.61/7.88 8319 sk_c6 != A | multiply(sk_c7,inverse(A)) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(8110(a,1),7043(b,1,1,2,2)),rewrite([8254(4),27(7),1426(8),8254(6),1427(6),27(7),1355(6),1135(6),8254(6),1427(5)])].
% 7.61/7.88 8428 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c7,multiply(inverse(sk_c6),inverse(sk_c2))) = identity. [back_rewrite(8163),rewrite([8254(10)])].
% 7.61/7.88 8768 identity != sk_c6 | identity != sk_c7 | inverse(sk_c7) != sk_c6 | multiply(sk_c6,multiply(inverse(A),inverse(B))) != sk_c7 | multiply(B,A) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [back_rewrite(5794),rewrite([8254(15),8254(14),1427(13),27(15)])].
% 7.61/7.88 9331 inverse(A) != sk_c6 | multiply(sk_c7,A) != sk_c7 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(1427(a,1),8319(b,1,2)),flip(a)].
% 7.61/7.88 9403 multiply(inverse(A),sk_c7) != sk_c6 | sk_c7 != A | multiply(inverse(sk_c7),sk_c6) != sk_c7 | sk_c6 != sk_c7 | inverse(sk_c7) != sk_c6. [para(1426(a,1),9331(b,1)),rewrite([8254(4),1427(4)]),flip(b)].
% 7.61/7.88 12506 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c7. [para(6905(b,1),2734(b,1)),flip(c),merge(b)].
% 7.61/7.88 12542 inverse(sk_c7) = sk_c6. [para(12506(b,1),1427(a,1,1)),merge(b)].
% 7.61/7.88 13021 multiply(inverse(A),sk_c7) != sk_c6 | sk_c7 != A | multiply(sk_c6,sk_c6) != sk_c7 | sk_c6 != sk_c7. [back_rewrite(9403),rewrite([12542(9),12542(17)]),xx(e)].
% 7.61/7.88 13225 identity != sk_c6 | identity != sk_c7 | multiply(sk_c6,multiply(inverse(A),inverse(B))) != sk_c7 | multiply(B,A) != sk_c7 | multiply(sk_c7,sk_c6) != sk_c6. [back_rewrite(8768),rewrite([12542(8)]),xx(c)].
% 7.61/7.88 13420 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c6) = sk_c7. [back_rewrite(8045),rewrite([12542(6)])].
% 7.61/7.88 13800 sk_c6 != sk_c7 | identity != sk_c7. [back_rewrite(2326),rewrite([12542(8)]),xx(c)].
% 7.61/7.88 14651 multiply(sk_c6,sk_c7) = identity. [para(12542(a,1),2(a,1,1))].
% 7.61/7.88 14652 multiply(sk_c6,multiply(sk_c7,A)) = A. [para(12542(a,1),73(a,1,1))].
% 7.61/7.88 14653 inverse(sk_c6) = sk_c7. [para(12542(a,1),1427(a,1,1))].
% 7.61/7.88 14654 multiply(sk_c7,sk_c6) = identity. [para(12542(a,1),1355(a,1,2))].
% 7.61/7.88 14758 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c7,multiply(sk_c7,inverse(sk_c2))) = identity. [back_rewrite(8428),rewrite([14653(8)])].
% 7.61/7.88 14764 inverse(sk_c4) = sk_c7 | multiply(inverse(sk_c2),multiply(sk_c7,sk_c7)) = identity. [back_rewrite(8200),rewrite([14653(9)])].
% 7.61/7.88 14765 inverse(sk_c3) = sk_c7 | multiply(inverse(sk_c2),multiply(sk_c7,sk_c7)) = identity. [back_rewrite(8199),rewrite([14653(9)])].
% 7.61/7.88 14778 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c7,sk_c7) = sk_c3. [back_rewrite(5149),rewrite([14653(8)])].
% 7.61/7.88 15047 identity != sk_c6 | identity != sk_c7 | multiply(sk_c6,multiply(inverse(A),inverse(B))) != sk_c7 | multiply(B,A) != sk_c7. [back_rewrite(13225),rewrite([14654(19)]),merge(e)].
% 7.61/7.88 15326 multiply(sk_c7,sk_c7) != sk_c6 | sk_c6 != sk_c7 | multiply(sk_c6,sk_c6) != sk_c7. [para(14653(a,1),13021(a,1,1)),flip(b),merge(d)].
% 7.61/7.88 16219 inverse(sk_c2) = sk_c6 | sk_c5 = sk_c7. [para(13420(b,1),95(b,2)),rewrite([14652(13)]),merge(b)].
% 7.61/7.88 16223 sk_c5 = sk_c7 | sk_c2 = sk_c7. [para(16219(a,1),1427(a,1,1)),rewrite([14653(5)]),flip(b)].
% 7.61/7.88 16244 sk_c2 = sk_c7 | identity = sk_c7. [para(16223(a,1),2781(b,2)),merge(b)].
% 7.61/7.88 16245 sk_c2 = sk_c7 | identity = sk_c6. [para(16223(a,1),2786(b,1,1)),rewrite([12542(8)]),flip(c),merge(b)].
% 7.61/7.88 16261 sk_c2 = sk_c7 | multiply(sk_c6,A) = A. [para(16223(a,1),3588(b,1,1,1)),rewrite([12542(8)]),merge(b)].
% 7.61/7.88 16352 identity != sk_c6 | identity != sk_c7 | multiply(sk_c6,multiply(inverse(A),sk_c7)) != sk_c7 | multiply(sk_c6,A) != sk_c7. [para(14653(a,1),15047(c,1,2,2))].
% 7.61/7.88 16435 identity != sk_c6 | identity != sk_c7 | multiply(sk_c6,multiply(A,sk_c7)) != sk_c7 | multiply(sk_c6,inverse(A)) != sk_c7. [para(1427(a,1),16352(c,1,2,1))].
% 7.61/7.88 17122 sk_c2 = sk_c7 | identity != sk_c6 | identity != sk_c7. [para(16261(b,1),16435(c,1,2)),rewrite([14651(12),14653(15),14651(15)]),merge(d),merge(e)].
% 7.61/7.88 17746 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c5. [para(83(b,1),1906(b,1,2)),rewrite([14654(13),1135(12),14652(15)]),merge(b)].
% 7.61/7.88 17993 inverse(sk_c1) = sk_c7 | sk_c5 = sk_c7. [para(17746(b,1),4(b,1)),merge(b)].
% 7.61/7.88 18003 sk_c5 = sk_c7 | sk_c1 = sk_c6. [para(17993(a,1),1427(a,1,1)),rewrite([12542(5)]),flip(b)].
% 7.61/7.88 18027 sk_c1 = sk_c6 | sk_c6 != sk_c7. [resolve(18003,a,7538,c),merge(b)].
% 7.61/7.88 20442 sk_c2 = sk_c7 | identity != sk_c7. [resolve(17122,b,16245,b),merge(c)].
% 7.61/7.88 20444 sk_c2 = sk_c7. [resolve(20442,b,16244,b),merge(b)].
% 7.61/7.88 20651 inverse(sk_c3) = sk_c7 | identity = sk_c7. [back_rewrite(14765),rewrite([20444(5),12542(6),14652(9)]),flip(b)].
% 7.61/7.88 20652 inverse(sk_c4) = sk_c7 | identity = sk_c7. [back_rewrite(14764),rewrite([20444(5),12542(6),14652(9)]),flip(b)].
% 7.61/7.88 20653 multiply(sk_c7,sk_c5) = sk_c6 | identity = sk_c7. [back_rewrite(14758),rewrite([20444(8),12542(9),14654(9),1135(8)]),flip(b)].
% 7.61/7.88 20920 identity = sk_c7 | multiply(sk_c4,sk_c7) = sk_c5. [back_rewrite(26),rewrite([20444(1),14654(3)])].
% 7.61/7.88 21273 identity = sk_c7 | sk_c3 = sk_c6. [para(20651(a,1),1427(a,1,1)),rewrite([12542(5)]),flip(b)].
% 7.61/7.88 21535 sk_c3 = sk_c6 | sk_c6 != sk_c7. [resolve(21273,a,13800,b)].
% 7.61/7.88 21579 identity = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(20652(a,1),1355(a,1,2))].
% 7.61/7.88 23579 identity = sk_c7 | identity = sk_c5. [para(21579(b,1),20920(b,1)),merge(b)].
% 7.61/7.88 23581 identity = sk_c7 | multiply(A,sk_c5) = A. [para(23579(b,1),1135(a,1,2))].
% 7.61/7.88 24264 identity = sk_c7 | sk_c6 = sk_c7. [para(23581(b,1),20653(a,1)),flip(b),merge(c)].
% 7.61/7.88 24279 sk_c6 = sk_c7 | identity = sk_c6. [para(24264(a,1),1156(a,1,1)),rewrite([12542(5)]),flip(b)].
% 7.61/7.88 24309 sk_c6 = sk_c7. [para(24279(b,1),24264(a,1)),merge(b),merge(c)].
% 7.61/7.88 25359 sk_c3 = sk_c7. [back_rewrite(21535),rewrite([24309(2),24309(4)]),xx(b)].
% 7.61/7.88 25692 sk_c1 = sk_c7. [back_rewrite(18027),rewrite([24309(2),24309(4)]),xx(b)].
% 7.61/7.88 25726 multiply(sk_c7,sk_c7) != sk_c7. [back_rewrite(15326),rewrite([24309(4),24309(6),24309(9),24309(10)]),xx(b),merge(b)].
% 7.61/7.88 25754 $F. [back_rewrite(14778),rewrite([25692(1),24309(4),25359(9)]),merge(b),unit_del(a,25726)].
% 7.61/7.88
% 7.61/7.88 % SZS output end Refutation
% 7.61/7.88 ============================== end of proof ==========================
% 7.61/7.88
% 7.61/7.88 ============================== STATISTICS ============================
% 7.61/7.88
% 7.61/7.88 Given=2122. Generated=301092. Kept=25753. proofs=1.
% 7.61/7.88 Usable=359. Sos=1162. Demods=23. Limbo=1445, Disabled=22815. Hints=0.
% 7.61/7.88 Megabytes=20.01.
% 7.61/7.88 User_CPU=6.70, System_CPU=0.19, Wall_clock=7.
% 7.61/7.88
% 7.61/7.88 ============================== end of statistics =====================
% 7.61/7.88
% 7.61/7.88 ============================== end of search =========================
% 7.61/7.88
% 7.61/7.88 THEOREM PROVED
% 7.61/7.88 % SZS status Unsatisfiable
% 7.61/7.88
% 7.61/7.88 Exiting with 1 proof.
% 7.61/7.88
% 7.61/7.88 Process 21647 exit (max_proofs) Mon Jun 13 10:13:26 2022
% 7.61/7.88 Prover9 interrupted
%------------------------------------------------------------------------------