TSTP Solution File: GRP231-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP231-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:18:15 EDT 2022
% Result : Unsatisfiable 30.18s 30.46s
% Output : Refutation 30.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP231-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.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 : Mon Jun 13 05:08:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 10.68/10.96 ============================== Prover9 ===============================
% 10.68/10.96 Prover9 (32) version 2009-11A, November 2009.
% 10.68/10.96 Process 5772 was started by sandbox2 on n020.cluster.edu,
% 10.68/10.96 Mon Jun 13 05:08:21 2022
% 10.68/10.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5619_n020.cluster.edu".
% 10.68/10.96 ============================== end of head ===========================
% 10.68/10.96
% 10.68/10.96 ============================== INPUT =================================
% 10.68/10.96
% 10.68/10.96 % Reading from file /tmp/Prover9_5619_n020.cluster.edu
% 10.68/10.96
% 10.68/10.96 set(prolog_style_variables).
% 10.68/10.96 set(auto2).
% 10.68/10.96 % set(auto2) -> set(auto).
% 10.68/10.96 % set(auto) -> set(auto_inference).
% 10.68/10.96 % set(auto) -> set(auto_setup).
% 10.68/10.96 % set(auto_setup) -> set(predicate_elim).
% 10.68/10.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.68/10.96 % set(auto) -> set(auto_limits).
% 10.68/10.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.68/10.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.68/10.96 % set(auto) -> set(auto_denials).
% 10.68/10.96 % set(auto) -> set(auto_process).
% 10.68/10.96 % set(auto2) -> assign(new_constants, 1).
% 10.68/10.96 % set(auto2) -> assign(fold_denial_max, 3).
% 10.68/10.96 % set(auto2) -> assign(max_weight, "200.000").
% 10.68/10.96 % set(auto2) -> assign(max_hours, 1).
% 10.68/10.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.68/10.96 % set(auto2) -> assign(max_seconds, 0).
% 10.68/10.96 % set(auto2) -> assign(max_minutes, 5).
% 10.68/10.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.68/10.96 % set(auto2) -> set(sort_initial_sos).
% 10.68/10.96 % set(auto2) -> assign(sos_limit, -1).
% 10.68/10.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.68/10.96 % set(auto2) -> assign(max_megs, 400).
% 10.68/10.96 % set(auto2) -> assign(stats, some).
% 10.68/10.96 % set(auto2) -> clear(echo_input).
% 10.68/10.96 % set(auto2) -> set(quiet).
% 10.68/10.96 % set(auto2) -> clear(print_initial_clauses).
% 10.68/10.96 % set(auto2) -> clear(print_given).
% 10.68/10.96 assign(lrs_ticks,-1).
% 10.68/10.96 assign(sos_limit,10000).
% 10.68/10.96 assign(order,kbo).
% 10.68/10.96 set(lex_order_vars).
% 10.68/10.96 clear(print_given).
% 10.68/10.96
% 10.68/10.96 % formulas(sos). % not echoed (34 formulas)
% 10.68/10.96
% 10.68/10.96 ============================== end of input ==========================
% 10.68/10.96
% 10.68/10.96 % From the command line: assign(max_seconds, 300).
% 10.68/10.96
% 10.68/10.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.68/10.96
% 10.68/10.96 % Formulas that are not ordinary clauses:
% 10.68/10.96
% 10.68/10.96 ============================== end of process non-clausal formulas ===
% 10.68/10.96
% 10.68/10.96 ============================== PROCESS INITIAL CLAUSES ===============
% 10.68/10.96
% 10.68/10.96 ============================== PREDICATE ELIMINATION =================
% 10.68/10.96
% 10.68/10.96 ============================== end predicate elimination =============
% 10.68/10.96
% 10.68/10.96 Auto_denials: (non-Horn, no changes).
% 10.68/10.96
% 10.68/10.96 Term ordering decisions:
% 10.68/10.96
% 10.68/10.96 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 10.68/10.96 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c2=1. sk_c4=1. sk_c5=1. sk_c6=1. sk_c1=1. sk_c3=1. identity=1. multiply=1. inverse=0.
% 10.68/10.96
% 10.68/10.96 ============================== end of process initial clauses ========
% 10.68/10.96
% 10.68/10.96 ============================== CLAUSES FOR SEARCH ====================
% 10.68/10.96
% 10.68/10.96 ============================== end of clauses for search =============
% 10.68/10.96
% 10.68/10.96 ============================== SEARCH ================================
% 10.68/10.96
% 10.68/10.96 % Starting search at 0.03 seconds.
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=40.000, iters=3357
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=39.000, iters=3435
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=38.000, iters=3389
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=37.000, iters=3379
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=36.000, iters=3459
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=35.000, iters=3448
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=34.000, iters=3335
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=33.000, iters=3472
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=32.000, iters=3334
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=31.000, iters=3386
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=30.000, iters=3379
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=29.000, iters=3342
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=28.000, iters=3367
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=27.000, iters=3341
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=26.000, iters=3334
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=25.000, iters=3363
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=24.000, iters=3333
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=23.000, iters=3387
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=22.000, iters=3351
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=21.000, iters=3412
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=20.000, iters=3340
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=19.000, iters=3337
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=17.000, iters=3377
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=16.000, iters=3381
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=15.000, iters=3355
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=14.000, iters=3438
% 10.68/10.96
% 10.68/10.96 Low Water (keep): wt=13.000, iters=3333
% 30.18/30.46
% 30.18/30.46 ============================== PROOF =================================
% 30.18/30.46 % SZS status Unsatisfiable
% 30.18/30.46 % SZS output start Refutation
% 30.18/30.46
% 30.18/30.46 % Proof 1 at 28.66 (+ 0.80) seconds.
% 30.18/30.46 % Length of proof is 177.
% 30.18/30.46 % Level of proof is 28.
% 30.18/30.46 % Maximum clause weight is 50.000.
% 30.18/30.46 % Given clauses 4196.
% 30.18/30.46
% 30.18/30.46 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 30.18/30.46 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 30.18/30.46 3 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 30.18/30.46 4 inverse(sk_c8) = sk_c7 | inverse(sk_c5) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 30.18/30.46 5 inverse(sk_c1) = sk_c2 | inverse(sk_c4) = sk_c8 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 30.18/30.46 6 inverse(sk_c1) = sk_c2 | inverse(sk_c5) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 30.18/30.46 7 inverse(sk_c3) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 30.18/30.46 9 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 30.18/30.46 10 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 30.18/30.46 11 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 30.18/30.46 12 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 30.18/30.46 13 multiply(sk_c1,sk_c2) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 30.18/30.46 15 inverse(sk_c1) = sk_c2 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 30.18/30.46 16 inverse(sk_c1) = sk_c2 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 30.18/30.46 19 inverse(sk_c3) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 30.18/30.46 20 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 30.18/30.46 21 inverse(sk_c3) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 30.18/30.46 22 multiply(sk_c3,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 30.18/30.46 25 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 30.18/30.46 26 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 30.18/30.46 30 multiply(sk_c3,sk_c7) = sk_c8 | multiply(sk_c4,sk_c7) = sk_c8 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 30.18/30.46 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 30.18/30.46 34 inverse(sk_c8) != sk_c7 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | 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_31) # label(negated_conjecture). [assumption].
% 30.18/30.46 41 inverse(sk_c8) != sk_c7 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | 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. [factor(34,d,f)].
% 30.18/30.46 42 inverse(sk_c8) != sk_c7 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | 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. [factor(34,e,g),merge(g)].
% 30.18/30.46 52 inverse(sk_c8) != sk_c7 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(B) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [factor(41,d,g),merge(f)].
% 30.18/30.46 71 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(3(b,1),2(a,1,1))].
% 30.18/30.46 72 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = identity. [para(4(b,1),2(a,1,1))].
% 30.18/30.46 75 inverse(sk_c4) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(7(a,1),2(a,1,1))].
% 30.18/30.46 77 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 30.18/30.46 79 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c8). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 30.18/30.46 81 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 30.18/30.46 83 inverse(sk_c8) = sk_c7 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(11(b,1),33(a,2,2)),rewrite([33(8)])].
% 30.18/30.46 85 inverse(sk_c4) = sk_c8 | multiply(A,multiply(sk_c1,sk_c2)) = multiply(A,sk_c8). [para(12(a,1),33(a,2,2)),rewrite([33(8)])].
% 30.18/30.46 93 inverse(sk_c1) = sk_c2 | multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6). [para(16(b,1),33(a,2,2)),rewrite([33(8)])].
% 30.18/30.46 98 inverse(sk_c3) = sk_c8 | multiply(sk_c4,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(19(b,1),33(a,1,1)),flip(b)].
% 30.18/30.46 100 inverse(sk_c3) = sk_c8 | multiply(sk_c8,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(20(b,1),33(a,1,1)),flip(b)].
% 30.18/30.46 102 inverse(sk_c3) = sk_c8 | multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c6,A). [para(21(b,1),33(a,1,1)),flip(b)].
% 30.18/30.46 178 inverse(sk_c8) != sk_c7 | identity != sk_c8 | inverse(inverse(A)) != A | multiply(A,sk_c7) != sk_c8 | 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. [para(2(a,1),42(b,1))].
% 30.18/30.46 181 inverse(sk_c8) != sk_c7 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,sk_c7) != sk_c8 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(sk_c8,D) != sk_c7 | identity != D | inverse(inverse(sk_c8)) != sk_c8. [para(2(a,1),42(h,1))].
% 30.18/30.46 379 inverse(sk_c8) != sk_c7 | identity != sk_c8 | inverse(inverse(A)) != A | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [factor(178,d,f)].
% 30.18/30.46 390 inverse(sk_c8) != sk_c7 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | identity != B | inverse(inverse(sk_c8)) != sk_c8. [factor(181,b,f)].
% 30.18/30.46 768 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),77(a,1,2))].
% 30.18/30.46 775 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(10(b,1),77(a,1,2))].
% 30.18/30.46 787 inverse(sk_c4) = sk_c8 | multiply(inverse(sk_c3),sk_c8) = sk_c7. [para(22(a,1),77(a,1,2))].
% 30.18/30.46 803 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),identity) = sk_c4. [para(71(b,1),77(a,1,2))].
% 30.18/30.46 804 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(77(a,1),77(a,1,2))].
% 30.18/30.46 808 multiply(A,identity) = A. [back_rewrite(768),rewrite([804(4)])].
% 30.18/30.46 809 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c4. [back_rewrite(803),rewrite([808(8)])].
% 30.18/30.46 839 inverse(identity) = identity. [para(808(a,1),2(a,1))].
% 30.18/30.46 903 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c5. [para(72(b,1),77(a,1,2)),rewrite([808(8)])].
% 30.18/30.46 907 inverse(sk_c8) = sk_c7 | multiply(sk_c5,sk_c8) = identity. [para(903(b,1),2(a,1,1))].
% 30.18/30.46 909 inverse(sk_c8) = sk_c7 | sk_c5 = sk_c4. [para(903(b,1),809(b,1)),merge(b)].
% 30.18/30.46 1039 inverse(sk_c4) = sk_c8 | inverse(sk_c8) = sk_c3. [para(75(b,1),77(a,1,2)),rewrite([808(8)])].
% 30.18/30.46 1092 multiply(A,inverse(A)) = identity. [para(804(a,1),2(a,1))].
% 30.18/30.46 1134 multiply(A,multiply(inverse(A),B)) = B. [para(804(a,1),77(a,1))].
% 30.18/30.46 1135 inverse(inverse(A)) = A. [para(804(a,1),808(a,1)),rewrite([808(2)]),flip(a)].
% 30.18/30.46 1183 inverse(sk_c8) != sk_c7 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | identity != B. [back_rewrite(390),rewrite([1135(28)]),xx(h)].
% 30.18/30.46 1186 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [back_rewrite(379),rewrite([1135(9)]),xx(c)].
% 30.18/30.46 1200 inverse(sk_c8) = sk_c3 | inverse(sk_c8) = sk_c4. [para(1039(a,1),1135(a,1,1))].
% 30.18/30.46 1202 inverse(sk_c4) = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(5(a,1),1092(a,1,2))].
% 30.18/30.46 1203 inverse(sk_c5) = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(6(a,1),1092(a,1,2))].
% 30.18/30.46 1206 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(1092(a,1),33(a,1)),flip(a)].
% 30.18/30.46 1213 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(inverse(A),sk_c7) != sk_c8 | sk_c8 != A | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [para(1092(a,1),52(b,1)),rewrite([1135(17)]),flip(e),xx(c)].
% 30.18/30.46 1589 inverse(sk_c8) = sk_c7 | multiply(A,sk_c6) = A. [para(907(b,1),83(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 30.18/30.46 1669 inverse(sk_c4) = sk_c8 | identity = sk_c8. [para(1202(b,1),12(a,1)),merge(c)].
% 30.18/30.46 1673 identity = sk_c8 | inverse(sk_c8) = sk_c4. [para(1669(a,1),1135(a,1,1))].
% 30.18/30.46 1785 inverse(sk_c5) = sk_c8 | identity = sk_c8. [para(1203(b,1),13(a,1)),merge(c)].
% 30.18/30.46 1837 inverse(sk_c4) = sk_c8 | multiply(A,sk_c8) = A. [para(1202(b,1),85(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 30.18/30.46 1866 identity = sk_c8 | inverse(sk_c8) = sk_c5. [para(1785(a,1),1135(a,1,1))].
% 30.18/30.46 1878 identity = sk_c8 | sk_c5 = sk_c4. [para(1866(b,1),1673(b,1)),merge(b)].
% 30.18/30.46 1883 sk_c5 = sk_c4 | inverse(sk_c8) = identity. [para(1878(a,1),839(a,1,1))].
% 30.18/30.46 1994 sk_c5 = sk_c4 | identity = sk_c7. [para(1883(b,1),909(a,1)),merge(c)].
% 30.18/30.46 2000 sk_c5 = sk_c4 | inverse(sk_c8) = sk_c8. [para(1878(a,1),1883(b,2)),merge(b)].
% 30.18/30.46 2027 sk_c5 = sk_c4 | multiply(sk_c8,sk_c8) = identity. [para(2000(b,1),2(a,1,1))].
% 30.18/30.46 2746 sk_c5 = sk_c4 | multiply(sk_c8,sk_c8) = sk_c7. [para(1994(b,1),2027(b,2)),merge(b)].
% 30.18/30.46 2798 sk_c5 = sk_c4 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(2746(b,1),77(a,1,2))].
% 30.18/30.46 3298 inverse(sk_c1) = sk_c2 | multiply(inverse(multiply(sk_c5,sk_c8)),sk_c6) = identity. [para(93(b,1),2(a,1))].
% 30.18/30.46 3300 inverse(sk_c1) = sk_c2 | multiply(sk_c8,multiply(sk_c5,sk_c8)) = sk_c7. [para(15(b,1),93(b,2)),merge(b)].
% 30.18/30.46 3603 inverse(sk_c8) = sk_c7 | inverse(sk_c6) = identity. [para(1589(b,1),2(a,1))].
% 30.18/30.46 3805 inverse(sk_c8) = sk_c7 | multiply(sk_c6,A) = A. [para(3603(b,1),77(a,1,1)),rewrite([1(8)])].
% 30.18/30.46 4091 inverse(sk_c4) = sk_c8 | inverse(sk_c8) = identity. [para(1837(b,1),2(a,1))].
% 30.18/30.46 4375 inverse(sk_c8) = identity | inverse(sk_c8) = sk_c4. [para(4091(a,1),1135(a,1,1))].
% 30.18/30.46 4431 inverse(sk_c8) = sk_c4 | multiply(sk_c8,A) = A. [para(4375(a,1),77(a,1,1)),rewrite([1(8)])].
% 30.18/30.46 4475 inverse(sk_c3) = sk_c8 | multiply(sk_c8,inverse(sk_c7)) = sk_c4. [para(1092(a,1),98(b,1,2)),rewrite([808(7)]),flip(b)].
% 30.18/30.46 5250 inverse(sk_c3) = sk_c8 | multiply(sk_c6,inverse(sk_c8)) = sk_c5. [para(1092(a,1),102(b,1,2)),rewrite([808(7)]),flip(b)].
% 30.18/30.46 6404 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c6),A) = A. [para(3805(b,1),77(a,1,2))].
% 30.18/30.46 6714 inverse(sk_c8) = sk_c4 | multiply(inverse(sk_c8),A) = A. [para(4431(b,1),77(a,1,2))].
% 30.18/30.46 7354 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = sk_c6. [para(809(b,1),775(b,1,1)),merge(b)].
% 30.18/30.46 7536 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c7. [para(7354(b,1),77(a,1,2))].
% 30.18/30.46 9419 inverse(sk_c4) = sk_c8 | inverse(sk_c3) = sk_c7. [para(787(b,1),1837(b,1)),flip(c),merge(b)].
% 30.18/30.46 9432 inverse(sk_c4) = sk_c8 | inverse(sk_c7) = sk_c3. [para(9419(b,1),1135(a,1,1))].
% 30.18/30.46 9492 inverse(sk_c7) = sk_c3 | inverse(sk_c8) = sk_c4. [para(9432(a,1),1135(a,1,1))].
% 30.18/30.46 9536 inverse(sk_c8) = sk_c4 | multiply(sk_c3,sk_c7) = identity. [para(9492(a,1),2(a,1,1))].
% 30.18/30.46 10065 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,B) != sk_c7 | sk_c8 != B. [para(1(a,1),1186(f,1)),rewrite([839(22)]),merge(g)].
% 30.18/30.46 10126 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [resolve(10065,e,1134,a),flip(e)].
% 30.18/30.46 10130 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(inverse(sk_c8),sk_c7) != sk_c8. [factor(10126,c,e),rewrite([1135(16)]),xx(d)].
% 30.18/30.46 10131 inverse(sk_c8) != sk_c7 | identity != sk_c8 | sk_c5 = sk_c4. [resolve(10130,c,2798,b)].
% 30.18/30.46 10782 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(inverse(A),sk_c7) != sk_c8 | sk_c8 != A | multiply(sk_c8,B) != sk_c7 | sk_c8 != B. [para(1(a,1),1213(f,1)),rewrite([839(22)]),merge(g)].
% 30.18/30.46 10799 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(inverse(A),sk_c7) != sk_c8 | sk_c8 != A | sk_c7 != B | multiply(inverse(sk_c8),B) != sk_c8. [para(1134(a,1),10782(e,1)),flip(e),flip(f)].
% 30.18/30.46 12805 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1206(a,1),77(a,1,2)),rewrite([808(3)]),flip(a)].
% 30.18/30.46 13045 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(12805(a,1),77(a,1,2)),flip(a)].
% 30.18/30.46 13118 inverse(sk_c8) != sk_c7 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | inverse(A) != sk_c8 | inverse(B) != sk_c7 | multiply(inverse(sk_c8),inverse(B)) != identity. [para(12805(a,1),1183(f,1)),rewrite([13045(26)]),flip(g)].
% 30.18/30.46 14043 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),multiply(inverse(sk_c5),sk_c6)) = identity. [back_rewrite(3298),rewrite([13045(8),33(11)])].
% 30.18/30.46 14155 inverse(sk_c8) != sk_c7 | multiply(A,sk_c7) != sk_c8 | inverse(A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | inverse(A) != sk_c8 | multiply(inverse(sk_c8),inverse(A)) != identity. [factor(13118,c,f)].
% 30.18/30.46 16861 inverse(sk_c8) != sk_c7 | multiply(inverse(A),sk_c7) != sk_c8 | sk_c7 != A | multiply(sk_c7,sk_c7) != sk_c8 | sk_c8 != A | multiply(inverse(sk_c8),A) != identity. [para(1135(a,1),14155(f,1,2)),rewrite([1135(11),1135(18)]),flip(c),flip(e)].
% 30.18/30.46 16910 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c4) = inverse(sk_c7). [para(4475(b,1),77(a,1,2))].
% 30.18/30.46 17274 inverse(sk_c3) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = multiply(sk_c8,sk_c5). [para(5250(b,1),100(b,1,2)),flip(c),merge(b)].
% 30.18/30.46 17378 inverse(sk_c8) = sk_c4 | multiply(sk_c3,A) = A. [para(1200(a,1),6714(b,1,1)),merge(b)].
% 30.18/30.46 17390 inverse(sk_c8) = sk_c4 | identity = sk_c7. [para(17378(b,1),9536(b,1)),flip(c),merge(b)].
% 30.18/30.46 17484 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c7. [para(7536(b,1),1589(b,1)),flip(c),merge(b)].
% 30.18/30.46 17488 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c7) = identity. [para(17484(b,1),1092(a,1,2))].
% 30.18/30.46 17502 inverse(sk_c8) = sk_c7 | identity = sk_c8. [para(17488(b,1),9(b,1)),merge(b)].
% 30.18/30.46 17504 inverse(sk_c8) = sk_c7 | multiply(A,sk_c8) = A. [para(17488(b,1),79(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 30.18/30.46 17511 identity = sk_c8 | sk_c4 = sk_c7. [para(17502(a,1),1673(b,1)),flip(c),merge(b)].
% 30.18/30.46 17527 sk_c4 = sk_c7 | inverse(sk_c8) = identity. [para(17511(a,1),839(a,1,1))].
% 30.18/30.46 17701 sk_c4 = sk_c7 | inverse(sk_c8) = sk_c8. [para(17511(a,1),17527(b,2)),merge(b)].
% 30.18/30.46 17734 sk_c4 = sk_c7 | multiply(sk_c8,sk_c8) = identity. [para(17701(b,1),2(a,1,1))].
% 30.18/30.46 17928 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = identity. [para(17504(b,1),2(a,1))].
% 30.18/30.46 17943 inverse(sk_c8) = sk_c7 | inverse(sk_c6) = sk_c8. [para(17504(b,1),6404(b,1)),merge(b)].
% 30.18/30.46 18008 inverse(sk_c8) = sk_c7 | multiply(sk_c8,A) = A. [para(17928(b,1),77(a,1,1)),rewrite([1(8)])].
% 30.18/30.46 18049 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c6) = identity. [para(17943(b,1),2(a,1,1))].
% 30.18/30.46 18550 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c8),A) = A. [para(18008(b,1),77(a,1,2))].
% 30.18/30.46 18631 inverse(sk_c8) = sk_c7 | identity = sk_c7. [para(18049(b,1),10(b,1)),merge(b)].
% 30.18/30.46 18634 inverse(sk_c8) = sk_c7 | multiply(A,sk_c7) = A. [para(18049(b,1),81(b,1,2)),rewrite([808(10)]),flip(c),merge(b)].
% 30.18/30.46 18664 identity = sk_c7 | sk_c4 = sk_c7. [para(18631(a,1),17390(a,1)),flip(b),merge(c)].
% 30.18/30.46 18736 sk_c4 = sk_c7 | multiply(sk_c8,sk_c8) = sk_c7. [para(18664(a,1),17734(b,2)),merge(b)].
% 30.18/30.46 19563 sk_c4 = sk_c7 | multiply(inverse(sk_c8),sk_c7) = sk_c8. [para(18736(b,1),77(a,1,2))].
% 30.18/30.46 20260 sk_c4 = sk_c7 | inverse(sk_c8) != sk_c7 | identity != sk_c8. [resolve(19563,b,10130,c)].
% 30.18/30.46 20699 identity != sk_c8 | sk_c5 = sk_c4. [resolve(10131,a,909,a),merge(c)].
% 30.18/30.46 20702 sk_c5 = sk_c4. [resolve(20699,a,1878,a),merge(b)].
% 30.18/30.46 20772 inverse(sk_c3) = sk_c8 | multiply(sk_c7,inverse(sk_c8)) = multiply(sk_c8,sk_c4). [back_rewrite(17274),rewrite([20702(10)])].
% 30.18/30.46 20785 inverse(sk_c1) = sk_c2 | multiply(inverse(sk_c8),multiply(inverse(sk_c4),sk_c6)) = identity. [back_rewrite(14043),rewrite([20702(7)])].
% 30.18/30.46 21022 inverse(sk_c1) = sk_c2 | multiply(sk_c8,multiply(sk_c4,sk_c8)) = sk_c7. [back_rewrite(3300),rewrite([20702(6)])].
% 30.18/30.46 21239 multiply(sk_c1,sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c6. [back_rewrite(26),rewrite([20702(6)])].
% 30.18/30.46 21980 inverse(sk_c8) != sk_c7 | identity != sk_c8 | multiply(inverse(A),multiply(inverse(B),sk_c7)) != sk_c8 | multiply(B,A) != sk_c8 | sk_c7 != C | multiply(inverse(sk_c8),C) != sk_c8. [para(13045(a,1),10799(c,1,1)),rewrite([33(12)]),flip(d)].
% 30.18/30.46 22124 inverse(sk_c8) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c7)) != sk_c8 | multiply(B,A) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | multiply(B,A) != sk_c8 | multiply(inverse(sk_c8),multiply(B,A)) != identity. [para(13045(a,1),16861(b,1,1)),rewrite([33(9)]),flip(c),flip(e)].
% 30.18/30.46 22703 inverse(sk_c8) != sk_c7 | inverse(sk_c7) != sk_c8 | multiply(sk_c7,sk_c7) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | multiply(inverse(sk_c8),multiply(sk_c7,sk_c7)) != identity. [factor(22124,d,e),rewrite([2(10),808(8)])].
% 30.18/30.46 27194 inverse(sk_c8) = sk_c7. [para(18550(b,1),18634(b,1)),flip(c),merge(b),merge(c)].
% 30.18/30.46 28243 inverse(sk_c7) != sk_c8 | multiply(sk_c7,sk_c7) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | multiply(sk_c7,multiply(sk_c7,sk_c7)) != identity. [back_rewrite(22703),rewrite([27194(2),27194(19)]),xx(a)].
% 30.18/30.46 28671 identity != sk_c8 | multiply(inverse(A),multiply(inverse(B),sk_c7)) != sk_c8 | multiply(B,A) != sk_c8 | sk_c7 != C | multiply(sk_c7,C) != sk_c8. [back_rewrite(21980),rewrite([27194(2),27194(20)]),xx(a)].
% 30.18/30.46 28778 inverse(sk_c1) = sk_c2 | multiply(sk_c7,multiply(inverse(sk_c4),sk_c6)) = identity. [back_rewrite(20785),rewrite([27194(6)])].
% 30.18/30.46 28783 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c7) = multiply(sk_c8,sk_c4). [back_rewrite(20772),rewrite([27194(7)])].
% 30.18/30.46 28961 sk_c4 = sk_c7 | identity != sk_c8. [back_rewrite(20260),rewrite([27194(5)]),xx(b)].
% 30.18/30.46 29513 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c4) = inverse(sk_c7). [back_rewrite(16910),rewrite([27194(6)])].
% 30.18/30.46 30646 identity != sk_c8 | multiply(sk_c7,sk_c7) != sk_c8. [back_rewrite(10130),rewrite([27194(2),27194(8)]),xx(a)].
% 30.18/30.46 31467 identity != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c7,A) != sk_c8 | sk_c7 != A. [factor(28671,c,e),rewrite([2(8),808(6)])].
% 30.18/30.46 31506 multiply(sk_c7,sk_c8) = identity. [para(27194(a,1),2(a,1,1))].
% 30.18/30.46 31507 multiply(sk_c7,multiply(sk_c8,A)) = A. [para(27194(a,1),77(a,1,1))].
% 30.18/30.46 31508 inverse(sk_c7) = sk_c8. [para(27194(a,1),1135(a,1,1))].
% 30.18/30.46 31509 multiply(sk_c8,sk_c7) = identity. [para(27194(a,1),1092(a,1,2))].
% 30.18/30.46 31656 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c4) = sk_c8. [back_rewrite(29513),rewrite([31508(9)])].
% 30.18/30.46 31731 multiply(sk_c7,sk_c7) != sk_c7 | multiply(sk_c7,sk_c7) != sk_c8 | multiply(sk_c7,multiply(sk_c7,sk_c7)) != identity. [back_rewrite(28243),rewrite([31508(2)]),xx(a)].
% 30.18/30.46 32107 sk_c4 = sk_c7. [resolve(28961,b,17511,a),merge(b)].
% 30.18/30.46 32162 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(31656),rewrite([32107(6)])].
% 30.18/30.46 32268 inverse(sk_c3) = sk_c8 | multiply(sk_c7,sk_c7) = identity. [back_rewrite(28783),rewrite([32107(9),31509(10)])].
% 30.18/30.46 32273 inverse(sk_c1) = sk_c2 | identity = sk_c6. [back_rewrite(28778),rewrite([32107(6),31508(7),31507(9)]),flip(b)].
% 30.18/30.46 32312 multiply(sk_c1,sk_c2) = sk_c8 | identity = sk_c6. [back_rewrite(21239),rewrite([32107(6),31506(8)])].
% 30.18/30.46 32333 inverse(sk_c1) = sk_c2 | sk_c7 = sk_c8. [back_rewrite(21022),rewrite([32107(6),31506(8),808(7)]),flip(b)].
% 30.18/30.46 32433 multiply(sk_c3,sk_c7) = sk_c8 | multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(30),rewrite([32107(6)])].
% 30.18/30.46 32473 identity = sk_c6 | multiply(sk_c1,sk_c2) = identity. [para(32273(a,1),1092(a,1,2))].
% 30.18/30.46 32498 sk_c7 = sk_c8 | multiply(sk_c1,sk_c2) = identity. [para(32333(a,1),1092(a,1,2))].
% 30.18/30.46 32766 identity = sk_c6 | identity = sk_c8. [para(32473(b,1),32312(a,1)),merge(c)].
% 30.18/30.46 32975 sk_c7 = sk_c8 | identity = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7. [para(32498(b,1),25(a,1))].
% 30.18/30.46 32976 sk_c7 = sk_c8 | multiply(A,multiply(sk_c1,sk_c2)) = A. [para(32498(b,1),33(a,2,2)),rewrite([33(7),808(9)])].
% 30.18/30.46 32979 identity = sk_c8 | sk_c7 = sk_c8 | multiply(sk_c1,sk_c2) = sk_c6. [para(32766(a,1),32498(b,2))].
% 30.18/30.46 33484 inverse(sk_c3) = sk_c8 | identity != sk_c8. [resolve(32162,b,31467,c),rewrite([31508(9)]),xx(c),xx(d)].
% 30.18/30.47 33713 inverse(sk_c3) = sk_c8 | identity = sk_c8. [para(32268(b,1),32162(b,1)),merge(b)].
% 30.18/30.47 33717 identity = sk_c8 | sk_c3 = sk_c7. [para(33713(a,1),1135(a,1,1)),rewrite([27194(5)]),flip(b)].
% 30.18/30.47 33727 sk_c3 = sk_c7 | inverse(sk_c3) = sk_c8. [resolve(33717,a,33484,b)].
% 30.18/30.47 33930 sk_c3 = sk_c7. [para(33727(b,1),1135(a,1,1)),rewrite([27194(5)]),flip(b),merge(b)].
% 30.18/30.47 33999 multiply(sk_c7,sk_c7) = sk_c8. [back_rewrite(32433),rewrite([33930(1)]),merge(b)].
% 30.18/30.47 34151 sk_c7 != sk_c8. [back_rewrite(31731),rewrite([33999(3),33999(6),33999(10),31506(9)]),flip(a),xx(b),xx(c)].
% 30.18/30.47 34202 identity != sk_c8. [back_rewrite(30646),rewrite([33999(6)]),xx(b)].
% 30.18/30.47 34392 multiply(sk_c1,sk_c2) = sk_c6. [back_unit_del(32979),unit_del(a,34202),unit_del(b,34151)].
% 30.18/30.47 34395 multiply(A,sk_c6) = A. [back_unit_del(32976),rewrite([34392(6)]),unit_del(a,34151)].
% 30.18/30.47 34396 $F. [back_unit_del(32975),rewrite([34395(9)]),flip(c),merge(c),unit_del(a,34151),unit_del(b,34202)].
% 30.18/30.47
% 30.18/30.47 % SZS output end Refutation
% 30.18/30.47 ============================== end of proof ==========================
% 30.18/30.47
% 30.18/30.47 ============================== STATISTICS ============================
% 30.18/30.47
% 30.18/30.47 Given=4196. Generated=1573777. Kept=34395. proofs=1.
% 30.18/30.47 Usable=91. Sos=1935. Demods=23. Limbo=245, Disabled=32158. Hints=0.
% 30.18/30.47 Megabytes=26.64.
% 30.18/30.47 User_CPU=28.67, System_CPU=0.80, Wall_clock=29.
% 30.18/30.47
% 30.18/30.47 ============================== end of statistics =====================
% 30.18/30.47
% 30.18/30.47 ============================== end of search =========================
% 30.18/30.47
% 30.18/30.47 THEOREM PROVED
% 30.18/30.47 % SZS status Unsatisfiable
% 30.18/30.47
% 30.18/30.47 Exiting with 1 proof.
% 30.18/30.47
% 30.18/30.47 Process 5772 exit (max_proofs) Mon Jun 13 05:08:50 2022
% 30.18/30.47 Prover9 interrupted
%------------------------------------------------------------------------------