TSTP Solution File: GRP388-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP388-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:18:52 EDT 2022
% Result : Unsatisfiable 46.59s 46.95s
% Output : Refutation 46.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP388-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.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 04:35:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.05/5.34 ============================== Prover9 ===============================
% 5.05/5.34 Prover9 (32) version 2009-11A, November 2009.
% 5.05/5.34 Process 9688 was started by sandbox on n019.cluster.edu,
% 5.05/5.34 Tue Jun 14 04:35:55 2022
% 5.05/5.34 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9463_n019.cluster.edu".
% 5.05/5.34 ============================== end of head ===========================
% 5.05/5.34
% 5.05/5.34 ============================== INPUT =================================
% 5.05/5.34
% 5.05/5.34 % Reading from file /tmp/Prover9_9463_n019.cluster.edu
% 5.05/5.34
% 5.05/5.34 set(prolog_style_variables).
% 5.05/5.34 set(auto2).
% 5.05/5.34 % set(auto2) -> set(auto).
% 5.05/5.34 % set(auto) -> set(auto_inference).
% 5.05/5.34 % set(auto) -> set(auto_setup).
% 5.05/5.34 % set(auto_setup) -> set(predicate_elim).
% 5.05/5.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.05/5.34 % set(auto) -> set(auto_limits).
% 5.05/5.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.05/5.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.05/5.34 % set(auto) -> set(auto_denials).
% 5.05/5.34 % set(auto) -> set(auto_process).
% 5.05/5.34 % set(auto2) -> assign(new_constants, 1).
% 5.05/5.34 % set(auto2) -> assign(fold_denial_max, 3).
% 5.05/5.34 % set(auto2) -> assign(max_weight, "200.000").
% 5.05/5.34 % set(auto2) -> assign(max_hours, 1).
% 5.05/5.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.05/5.34 % set(auto2) -> assign(max_seconds, 0).
% 5.05/5.34 % set(auto2) -> assign(max_minutes, 5).
% 5.05/5.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.05/5.34 % set(auto2) -> set(sort_initial_sos).
% 5.05/5.34 % set(auto2) -> assign(sos_limit, -1).
% 5.05/5.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.05/5.34 % set(auto2) -> assign(max_megs, 400).
% 5.05/5.34 % set(auto2) -> assign(stats, some).
% 5.05/5.34 % set(auto2) -> clear(echo_input).
% 5.05/5.34 % set(auto2) -> set(quiet).
% 5.05/5.34 % set(auto2) -> clear(print_initial_clauses).
% 5.05/5.34 % set(auto2) -> clear(print_given).
% 5.05/5.34 assign(lrs_ticks,-1).
% 5.05/5.34 assign(sos_limit,10000).
% 5.05/5.34 assign(order,kbo).
% 5.05/5.34 set(lex_order_vars).
% 5.05/5.34 clear(print_given).
% 5.05/5.34
% 5.05/5.34 % formulas(sos). % not echoed (37 formulas)
% 5.05/5.34
% 5.05/5.34 ============================== end of input ==========================
% 5.05/5.34
% 5.05/5.34 % From the command line: assign(max_seconds, 300).
% 5.05/5.34
% 5.05/5.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.05/5.34
% 5.05/5.34 % Formulas that are not ordinary clauses:
% 5.05/5.34
% 5.05/5.34 ============================== end of process non-clausal formulas ===
% 5.05/5.34
% 5.05/5.34 ============================== PROCESS INITIAL CLAUSES ===============
% 5.05/5.34
% 5.05/5.34 ============================== PREDICATE ELIMINATION =================
% 5.05/5.34
% 5.05/5.34 ============================== end predicate elimination =============
% 5.05/5.34
% 5.05/5.34 Auto_denials: (non-Horn, no changes).
% 5.05/5.34
% 5.05/5.34 Term ordering decisions:
% 5.05/5.34
% 5.05/5.34 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 5.05/5.34 Function symbol KB weights: sk_c10=1. sk_c9=1. sk_c8=1. sk_c1=1. sk_c2=1. sk_c6=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 5.05/5.34
% 5.05/5.34 ============================== end of process initial clauses ========
% 5.05/5.34
% 5.05/5.34 ============================== CLAUSES FOR SEARCH ====================
% 5.05/5.34
% 5.05/5.34 ============================== end of clauses for search =============
% 5.05/5.34
% 5.05/5.34 ============================== SEARCH ================================
% 5.05/5.34
% 5.05/5.34 % Starting search at 0.02 seconds.
% 5.05/5.34
% 5.05/5.34 Low Water (keep): wt=44.000, iters=3431
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=42.000, iters=3387
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=41.000, iters=3340
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=40.000, iters=3398
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=38.000, iters=3394
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=35.000, iters=3406
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=34.000, iters=3368
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=33.000, iters=3337
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=32.000, iters=3359
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=31.000, iters=3375
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=30.000, iters=3335
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=29.000, iters=3369
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=28.000, iters=3349
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=27.000, iters=3370
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=26.000, iters=3360
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=25.000, iters=3443
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=24.000, iters=3354
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=23.000, iters=3367
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=22.000, iters=3344
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=21.000, iters=3390
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=20.000, iters=3333
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=19.000, iters=3340
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=18.000, iters=3334
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=17.000, iters=3352
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=16.000, iters=3341
% 5.05/5.35
% 5.05/5.35 Low Water (keep): wt=15.000, iters=3337
% 46.59/46.95
% 46.59/46.95 Low Water (keep): wt=14.000, iters=3348
% 46.59/46.95
% 46.59/46.95 Low Water (keep): wt=13.000, iters=3337
% 46.59/46.95
% 46.59/46.95 Low Water (displace): id=16851, wt=12.000
% 46.59/46.95
% 46.59/46.95 Low Water (displace): id=16883, wt=11.000
% 46.59/46.95
% 46.59/46.95 Low Water (keep): wt=12.000, iters=3334
% 46.59/46.95
% 46.59/46.95 ============================== PROOF =================================
% 46.59/46.95 % SZS status Unsatisfiable
% 46.59/46.95 % SZS output start Refutation
% 46.59/46.95
% 46.59/46.95 % Proof 1 at 44.58 (+ 1.35) seconds.
% 46.59/46.95 % Length of proof is 163.
% 46.59/46.95 % Level of proof is 26.
% 46.59/46.95 % Maximum clause weight is 60.000.
% 46.59/46.95 % Given clauses 4392.
% 46.59/46.95
% 46.59/46.95 1 inverse(sk_c10) = sk_c9 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 46.59/46.95 2 sk_c9 = inverse(sk_c10). [copy(1),flip(a)].
% 46.59/46.95 3 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 46.59/46.95 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 46.59/46.95 5 inverse(sk_c1) = sk_c10 | inverse(sk_c3) = sk_c10 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 46.59/46.95 6 inverse(sk_c1) = sk_c10 | inverse(sk_c5) = sk_c6 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 46.59/46.95 10 multiply(sk_c8,sk_c9) = sk_c10 | inverse(sk_c5) = sk_c6 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 46.59/46.95 11 multiply(sk_c8,inverse(sk_c10)) = sk_c10 | inverse(sk_c5) = sk_c6. [copy(10),rewrite([2(2)])].
% 46.59/46.95 12 multiply(sk_c8,sk_c9) = sk_c10 | inverse(sk_c7) = sk_c10 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 46.59/46.95 13 multiply(sk_c8,inverse(sk_c10)) = sk_c10 | inverse(sk_c7) = sk_c10. [copy(12),rewrite([2(2)])].
% 46.59/46.95 16 multiply(sk_c10,sk_c2) = sk_c9 | inverse(sk_c5) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 46.59/46.95 17 multiply(sk_c10,sk_c2) = inverse(sk_c10) | inverse(sk_c5) = sk_c6. [copy(16),rewrite([2(4)])].
% 46.59/46.95 18 multiply(sk_c10,sk_c2) = sk_c9 | inverse(sk_c7) = sk_c10 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 46.59/46.95 19 multiply(sk_c10,sk_c2) = inverse(sk_c10) | inverse(sk_c7) = sk_c10. [copy(18),rewrite([2(4)])].
% 46.59/46.95 21 multiply(sk_c1,sk_c10) = sk_c2 | inverse(sk_c5) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 46.59/46.95 22 multiply(sk_c1,sk_c10) = sk_c2 | inverse(sk_c7) = sk_c10 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 46.59/46.95 23 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c4) = sk_c9 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 46.59/46.95 24 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c4) = inverse(sk_c10). [copy(23),rewrite([2(8)])].
% 46.59/46.95 25 inverse(sk_c1) = sk_c10 | multiply(sk_c3,sk_c10) = sk_c4 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 46.59/46.95 26 inverse(sk_c1) = sk_c10 | multiply(sk_c5,sk_c6) = sk_c8 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 46.59/46.95 29 inverse(sk_c1) = sk_c10 | multiply(sk_c7,sk_c8) = sk_c10 # label(prove_this_33) # label(negated_conjecture). [assumption].
% 46.59/46.95 34 multiply(sk_c8,sk_c9) = sk_c10 | multiply(sk_c5,sk_c6) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 46.59/46.95 35 multiply(sk_c8,inverse(sk_c10)) = sk_c10 | multiply(sk_c5,sk_c6) = sk_c8. [copy(34),rewrite([2(2)])].
% 46.59/46.95 38 multiply(sk_c8,sk_c9) = sk_c10 | multiply(sk_c7,sk_c8) = sk_c10 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 46.59/46.95 39 multiply(sk_c8,inverse(sk_c10)) = sk_c10 | multiply(sk_c7,sk_c8) = sk_c10. [copy(38),rewrite([2(2)])].
% 46.59/46.95 44 multiply(sk_c10,sk_c2) = sk_c9 | multiply(sk_c5,sk_c6) = sk_c8 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 46.59/46.95 45 multiply(sk_c10,sk_c2) = inverse(sk_c10) | multiply(sk_c5,sk_c6) = sk_c8. [copy(44),rewrite([2(4)])].
% 46.59/46.95 53 multiply(sk_c1,sk_c10) = sk_c2 | multiply(sk_c5,sk_c6) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 46.59/46.95 57 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 46.59/46.95 58 inverse(sk_c10) != sk_c9 | multiply(sk_c8,sk_c9) != sk_c10 | multiply(sk_c10,A) != sk_c9 | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | multiply(sk_c10,C) != sk_c9 | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | multiply(E,F) != sk_c8 | inverse(E) != F | multiply(F,sk_c9) != sk_c8 | inverse(V6) != sk_c10 | multiply(V6,sk_c8) != sk_c10 # label(prove_this_34) # label(negated_conjecture). [assumption].
% 46.59/46.95 59 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | multiply(sk_c10,C) != inverse(sk_c10) | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | multiply(E,F) != sk_c8 | inverse(E) != F | multiply(F,inverse(sk_c10)) != sk_c8 | inverse(V6) != sk_c10 | multiply(V6,sk_c8) != sk_c10. [copy(58),rewrite([2(3),2(7),2(14),2(25),2(39)]),xx(a)].
% 46.59/46.95 61 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | multiply(C,D) != sk_c8 | inverse(C) != D | multiply(D,inverse(sk_c10)) != sk_c8 | inverse(E) != sk_c10 | multiply(E,sk_c8) != sk_c10. [factor(59,c,f),merge(e),merge(f)].
% 46.59/46.95 73 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c5) = identity. [para(6(b,1),4(a,1,1))].
% 46.59/46.95 75 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),57(a,1,1)),rewrite([3(2)]),flip(a)].
% 46.59/46.95 78 inverse(sk_c5) = sk_c6 | multiply(sk_c8,multiply(inverse(sk_c10),A)) = multiply(sk_c10,A). [para(11(a,1),57(a,1,1)),flip(b)].
% 46.59/46.95 80 inverse(sk_c7) = sk_c10 | multiply(sk_c8,multiply(inverse(sk_c10),A)) = multiply(sk_c10,A). [para(13(a,1),57(a,1,1)),flip(b)].
% 46.59/46.95 86 inverse(sk_c7) = sk_c10 | multiply(sk_c10,multiply(sk_c2,A)) = multiply(inverse(sk_c10),A). [para(19(a,1),57(a,1,1)),flip(b)].
% 46.59/46.95 87 inverse(sk_c7) = sk_c10 | multiply(A,multiply(sk_c10,sk_c2)) = multiply(A,inverse(sk_c10)). [para(19(a,1),57(a,2,2)),rewrite([57(8)])].
% 46.59/46.95 90 inverse(sk_c5) = sk_c6 | multiply(sk_c1,multiply(sk_c10,A)) = multiply(sk_c2,A). [para(21(a,1),57(a,1,1)),flip(b)].
% 46.59/46.95 92 inverse(sk_c7) = sk_c10 | multiply(sk_c1,multiply(sk_c10,A)) = multiply(sk_c2,A). [para(22(a,1),57(a,1,1)),flip(b)].
% 46.59/46.95 99 inverse(sk_c1) = sk_c10 | multiply(A,multiply(sk_c5,sk_c6)) = multiply(A,sk_c8). [para(26(b,1),57(a,2,2)),rewrite([57(8)])].
% 46.59/46.95 151 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,identity) != inverse(sk_c10) | inverse(inverse(sk_c10)) != sk_c10 | multiply(A,B) != sk_c8 | inverse(A) != B | multiply(B,inverse(sk_c10)) != sk_c8 | inverse(C) != sk_c10 | multiply(C,sk_c8) != sk_c10. [resolve(61,c,4,a)].
% 46.59/46.95 171 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | identity != A | inverse(inverse(sk_c10)) != sk_c10 | multiply(B,C) != sk_c8 | inverse(B) != C | multiply(C,inverse(sk_c10)) != sk_c8 | inverse(D) != sk_c10 | multiply(D,sk_c8) != sk_c10. [para(4(a,1),61(c,1))].
% 46.59/46.95 173 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | multiply(C,inverse(inverse(sk_c10))) != sk_c8 | inverse(inverse(sk_c10)) != inverse(C) | identity != sk_c8 | inverse(D) != sk_c10 | multiply(D,sk_c8) != sk_c10. [para(4(a,1),61(g,1)),flip(f)].
% 46.59/46.95 281 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,identity) != inverse(sk_c10) | inverse(inverse(sk_c10)) != sk_c10 | identity != sk_c8 | multiply(sk_c10,inverse(sk_c10)) != sk_c8 | inverse(A) != sk_c10 | multiply(A,sk_c8) != sk_c10. [factor(151,c,e),rewrite([4(21)])].
% 46.59/46.95 326 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | identity != A | inverse(inverse(sk_c10)) != sk_c10 | identity != sk_c8 | multiply(sk_c10,inverse(sk_c10)) != sk_c8 | inverse(B) != sk_c10 | multiply(B,sk_c8) != sk_c10. [factor(171,d,f),rewrite([4(22)])].
% 46.59/46.95 470 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8 | inverse(inverse(sk_c10)) != sk_c10 | multiply(sk_c10,inverse(sk_c10)) != sk_c8 | inverse(A) != sk_c10 | multiply(A,sk_c8) != sk_c10. [factor(326,c,e)].
% 46.59/46.95 554 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),75(a,1,2))].
% 46.59/46.95 567 inverse(sk_c1) = sk_c10 | multiply(inverse(sk_c3),sk_c4) = sk_c10. [para(25(b,1),75(a,1,2))].
% 46.59/46.95 590 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(75(a,1),75(a,1,2))].
% 46.59/46.95 593 multiply(A,identity) = A. [back_rewrite(554),rewrite([590(4)])].
% 46.59/46.95 604 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | inverse(inverse(sk_c10)) != sk_c10 | identity != sk_c8 | multiply(sk_c10,inverse(sk_c10)) != sk_c8 | inverse(A) != sk_c10 | multiply(A,sk_c8) != sk_c10. [back_rewrite(281),rewrite([593(9)]),flip(b)].
% 46.59/46.95 615 inverse(identity) = identity. [para(593(a,1),4(a,1))].
% 46.59/46.95 680 inverse(sk_c1) = sk_c10 | inverse(sk_c6) = sk_c5. [para(73(b,1),75(a,1,2)),rewrite([593(8)])].
% 46.59/46.95 685 inverse(sk_c1) = sk_c10 | multiply(sk_c5,sk_c6) = identity. [para(680(b,1),4(a,1,1))].
% 46.59/46.95 710 multiply(A,inverse(A)) = identity. [para(590(a,1),4(a,1))].
% 46.59/46.95 732 multiply(A,multiply(inverse(A),B)) = B. [para(590(a,1),75(a,1))].
% 46.59/46.95 733 inverse(inverse(A)) = A. [para(590(a,1),593(a,1)),rewrite([593(2)]),flip(a)].
% 46.59/46.95 788 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | identity != sk_c8 | inverse(A) != sk_c10 | multiply(A,sk_c8) != sk_c10. [back_rewrite(604),rewrite([733(13),710(20)]),xx(c),merge(d)].
% 46.59/46.95 830 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8 | inverse(A) != sk_c10 | multiply(A,sk_c8) != sk_c10. [back_rewrite(470),rewrite([733(18),710(22)]),xx(d),merge(d)].
% 46.59/46.95 1007 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | multiply(C,sk_c10) != sk_c8 | inverse(C) != sk_c10 | identity != sk_c8 | inverse(D) != sk_c10 | multiply(D,sk_c8) != sk_c10. [back_rewrite(173),rewrite([733(20),733(24)]),flip(f)].
% 46.59/46.95 1048 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(710(a,1),57(a,1)),flip(a)].
% 46.59/46.95 1157 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | identity != sk_c8 | inverse(multiply(A,B)) != sk_c10 | multiply(A,multiply(B,sk_c8)) != sk_c10. [para(57(a,1),788(e,1))].
% 46.59/46.95 1272 inverse(sk_c5) = sk_c6 | multiply(sk_c10,sk_c10) = sk_c8. [para(4(a,1),78(b,1,2)),rewrite([593(7)]),flip(b)].
% 46.59/46.95 1400 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8 | inverse(multiply(A,B)) != sk_c10 | multiply(A,multiply(B,sk_c8)) != sk_c10. [para(57(a,1),830(e,1))].
% 46.59/46.95 1416 inverse(sk_c1) = sk_c10 | identity = sk_c8. [para(685(b,1),26(b,1)),merge(b)].
% 46.59/46.95 1419 identity = sk_c8 | multiply(sk_c10,multiply(sk_c1,A)) = A. [para(1416(a,1),75(a,1,1))].
% 46.59/46.95 1420 identity = sk_c8 | inverse(sk_c10) = sk_c1. [para(1416(a,1),733(a,1,1))].
% 46.59/46.95 1421 identity = sk_c8 | multiply(sk_c1,sk_c10) = identity. [para(1416(a,1),710(a,1,2))].
% 46.59/46.95 1422 identity = sk_c8 | multiply(sk_c1,multiply(sk_c10,A)) = A. [para(1416(a,1),732(a,1,2,1))].
% 46.59/46.95 1512 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | identity != sk_c8 | inverse(multiply(A,inverse(sk_c8))) != sk_c10 | sk_c10 != A. [para(4(a,1),1157(e,1,2)),rewrite([593(21)]),flip(e)].
% 46.59/46.95 1520 identity = sk_c8 | identity = sk_c2 | inverse(sk_c7) = sk_c10. [para(1421(b,1),22(a,1))].
% 46.59/46.95 1522 identity = sk_c8 | multiply(A,multiply(sk_c1,sk_c10)) = A. [para(1421(b,1),57(a,2,2)),rewrite([57(7),593(9)])].
% 46.59/46.95 2071 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8 | inverse(multiply(A,inverse(sk_c8))) != sk_c10 | sk_c10 != A. [para(4(a,1),1400(e,1,2)),rewrite([593(23)]),flip(e)].
% 46.59/46.95 2216 inverse(sk_c7) = sk_c10 | multiply(sk_c8,sk_c2) = identity. [para(87(b,1),80(b,2)),rewrite([75(15),710(15)]),merge(b)].
% 46.59/46.95 2330 inverse(sk_c7) = sk_c10 | multiply(sk_c8,multiply(sk_c2,A)) = A. [para(2216(b,1),57(a,1,1)),rewrite([3(6)]),flip(b)].
% 46.59/46.95 2332 inverse(sk_c7) = sk_c10 | inverse(sk_c8) = sk_c2. [para(2216(b,1),75(a,1,2)),rewrite([593(8)])].
% 46.59/46.95 2334 inverse(sk_c8) = sk_c2 | multiply(sk_c10,sk_c7) = identity. [para(2332(a,1),4(a,1,1))].
% 46.59/46.95 2336 inverse(sk_c8) = sk_c2 | inverse(sk_c10) = sk_c7. [para(2332(a,1),733(a,1,1))].
% 46.59/46.95 2602 inverse(sk_c10) = sk_c7 | inverse(sk_c2) = sk_c8. [para(2336(a,1),733(a,1,1))].
% 46.59/46.95 2808 inverse(sk_c5) = sk_c6 | multiply(sk_c2,sk_c10) = multiply(sk_c1,sk_c8). [para(1272(b,1),90(b,1,2)),flip(c),merge(b)].
% 46.59/46.95 2938 inverse(sk_c1) = sk_c10 | multiply(sk_c10,sk_c4) = sk_c10. [para(5(b,1),567(b,1,1)),merge(b)].
% 46.59/46.95 2947 inverse(sk_c1) = sk_c10 | inverse(sk_c10) = sk_c10. [para(2938(b,1),24(b,1)),flip(c),merge(b)].
% 46.59/46.95 2958 inverse(sk_c10) = sk_c10 | inverse(sk_c10) = sk_c1. [para(2947(a,1),733(a,1,1))].
% 46.59/46.95 3211 inverse(sk_c7) = sk_c10 | multiply(sk_c2,inverse(sk_c10)) = sk_c1. [para(710(a,1),92(b,1,2)),rewrite([593(7)]),flip(b)].
% 46.59/46.95 3468 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(1048(a,1),75(a,1,2)),rewrite([593(3)]),flip(a)].
% 46.59/46.95 3645 inverse(sk_c5) = sk_c6 | multiply(sk_c2,sk_c10) = inverse(sk_c10). [para(17(a,1),3468(a,1,2,1)),rewrite([733(8)])].
% 46.59/46.95 3677 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(3468(a,1),75(a,1,2)),flip(a)].
% 46.59/46.95 4100 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8 | multiply(sk_c8,inverse(A)) != sk_c10 | sk_c10 != A. [back_rewrite(2071),rewrite([3677(19),733(18)])].
% 46.59/46.95 4162 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | identity != sk_c8 | multiply(sk_c8,inverse(A)) != sk_c10 | sk_c10 != A. [back_rewrite(1512),rewrite([3677(17),733(16)])].
% 46.59/46.95 4196 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10) | identity != sk_c8. [factor(4100,a,d),xx(d)].
% 46.59/46.95 4198 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != sk_c10 | identity != sk_c8. [factor(4162,a,d),xx(d)].
% 46.59/46.95 4600 inverse(sk_c8) = sk_c2 | identity = sk_c8 | sk_c7 = sk_c1. [para(2334(b,1),1422(b,1,2)),rewrite([593(10)]),flip(c)].
% 46.59/46.95 4809 identity = sk_c8 | identity = sk_c2 | inverse(sk_c10) = sk_c7. [para(1520(c,1),733(a,1,1))].
% 46.59/46.95 5295 inverse(sk_c1) = sk_c10 | multiply(A,sk_c8) = A. [para(685(b,1),99(b,1,2)),rewrite([593(10)]),flip(c),merge(b)].
% 46.59/46.95 5437 inverse(sk_c1) = sk_c10 | sk_c7 = sk_c10. [para(5295(b,1),29(b,1)),merge(b)].
% 46.59/46.95 5468 sk_c7 = sk_c10 | multiply(sk_c10,multiply(sk_c1,A)) = A. [para(5437(a,1),75(a,1,1))].
% 46.59/46.95 5470 sk_c7 = sk_c10 | multiply(sk_c1,sk_c10) = identity. [para(5437(a,1),710(a,1,2))].
% 46.59/46.95 7265 sk_c7 = sk_c10 | multiply(inverse(sk_c10),inverse(sk_c1)) = identity. [para(5470(b,1),3677(a,1,1)),rewrite([615(5)]),flip(b)].
% 46.59/46.95 8308 identity = sk_c8 | sk_c7 = sk_c1 | inverse(sk_c2) = sk_c8. [para(4600(a,1),733(a,1,1))].
% 46.59/46.95 8493 identity = sk_c8 | identity = sk_c2 | sk_c7 = sk_c1. [para(4809(c,1),1420(b,1)),merge(c)].
% 46.59/46.95 8511 identity = sk_c8 | sk_c7 = sk_c1 | inverse(sk_c2) = identity. [para(8493(b,1),615(a,1,1))].
% 46.59/46.95 11203 identity = sk_c8 | sk_c7 = sk_c1. [para(8511(c,1),8308(c,1)),merge(c),merge(d),merge(e)].
% 46.59/46.95 11204 sk_c7 = sk_c1 | multiply(sk_c8,A) = A. [para(11203(a,1),3(a,1,1))].
% 46.59/46.95 11207 sk_c7 = sk_c1 | inverse(sk_c8) = identity. [para(11203(a,1),615(a,1,1))].
% 46.59/46.95 11256 sk_c7 = sk_c1 | identity = sk_c2 | inverse(sk_c10) = sk_c7. [para(11207(b,1),2336(a,1))].
% 46.59/46.95 11260 sk_c7 = sk_c1 | inverse(sk_c8) = sk_c8. [para(11203(a,1),11207(b,2)),merge(b)].
% 46.59/46.95 11261 sk_c7 = sk_c1 | multiply(sk_c8,sk_c8) = identity. [para(11260(b,1),4(a,1,1))].
% 46.59/46.95 11306 sk_c7 = sk_c1 | inverse(sk_c10) != sk_c10 | identity != sk_c8. [para(11204(b,1),4198(a,1)),merge(c)].
% 46.59/46.95 11383 sk_c7 = sk_c1 | multiply(inverse(sk_c8),inverse(sk_c8)) = identity. [para(11261(b,1),3677(a,1,1)),rewrite([615(5)]),flip(b)].
% 46.59/46.95 12386 sk_c7 = sk_c1 | identity = sk_c2 | inverse(sk_c10) = sk_c10. [para(11256(c,1),2958(b,1)),merge(d)].
% 46.59/46.95 13666 sk_c7 = sk_c1 | identity = sk_c2 | identity != sk_c8. [resolve(12386,c,11306,b),merge(c)].
% 46.59/46.95 13673 sk_c7 = sk_c1 | identity = sk_c2. [resolve(13666,c,11203,a),merge(c)].
% 46.59/46.95 13713 sk_c7 = sk_c1 | inverse(sk_c8) = sk_c2. [para(13673(b,1),11207(b,2)),merge(b)].
% 46.59/46.95 13743 sk_c7 = sk_c1 | multiply(sk_c2,inverse(sk_c8)) = identity. [para(13713(b,1),11383(b,1,1)),merge(b)].
% 46.59/46.95 13861 sk_c7 = sk_c1 | inverse(sk_c7) = sk_c10 | multiply(inverse(sk_c10),inverse(sk_c8)) = sk_c10. [para(13743(b,1),86(b,1,2)),rewrite([593(10)]),flip(c)].
% 46.59/46.95 18673 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,sk_c10) != A | inverse(B) != sk_c10 | identity != sk_c8 | inverse(C) != sk_c10 | multiply(C,sk_c8) != sk_c10. [para(4(a,1),1007(e,1)),rewrite([733(23)]),xx(f),merge(f)].
% 46.59/46.95 18680 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(B,multiply(C,sk_c10)) != A | multiply(inverse(C),inverse(B)) != sk_c10 | identity != sk_c8 | inverse(D) != sk_c10 | multiply(D,sk_c8) != sk_c10. [para(57(a,1),18673(c,1)),rewrite([3677(17)])].
% 46.59/46.95 19191 inverse(sk_c7) = sk_c10 | multiply(sk_c8,sk_c1) = inverse(sk_c10). [para(3211(b,1),2330(b,1,2)),merge(b)].
% 46.59/46.95 19192 inverse(sk_c7) = sk_c10 | multiply(inverse(sk_c8),inverse(sk_c10)) = sk_c1. [para(19191(b,1),75(a,1,2))].
% 46.59/46.95 19852 inverse(sk_c5) = sk_c6 | multiply(sk_c1,sk_c8) = inverse(sk_c10). [para(2808(b,1),3645(b,1)),merge(b)].
% 46.59/46.95 19861 inverse(sk_c5) = sk_c6 | identity = sk_c8. [para(19852(b,1),1419(b,1,2)),rewrite([710(11)]),merge(c)].
% 46.59/46.95 19880 identity = sk_c8 | multiply(sk_c5,sk_c6) = identity. [para(19861(a,1),710(a,1,2))].
% 46.59/46.95 19892 identity = sk_c8 | multiply(sk_c8,inverse(sk_c10)) = sk_c10. [para(19880(b,1),35(b,1)),merge(c)].
% 46.59/46.95 19893 identity = sk_c8 | multiply(sk_c10,sk_c2) = inverse(sk_c10). [para(19880(b,1),45(b,1)),merge(c)].
% 46.59/46.95 19894 identity = sk_c8 | multiply(sk_c1,sk_c10) = sk_c2. [para(19880(b,1),53(b,1)),merge(c)].
% 46.59/46.95 19900 identity = sk_c8 | identity = sk_c2. [para(19894(b,1),1421(b,1)),flip(c),merge(b)].
% 46.59/46.95 19902 identity = sk_c8 | multiply(A,sk_c2) = A. [para(19894(b,1),1522(b,1,2)),merge(b)].
% 46.59/46.95 19910 identity = sk_c8 | inverse(sk_c2) = identity. [para(19900(b,1),615(a,1,1))].
% 46.59/46.95 19939 identity = sk_c8 | inverse(sk_c10) = sk_c7. [para(19910(b,1),2602(b,1)),merge(c)].
% 46.59/46.95 20059 identity = sk_c8 | multiply(inverse(sk_c8),sk_c10) = inverse(sk_c10). [para(19892(b,1),75(a,1,2))].
% 46.59/46.95 20092 identity = sk_c8 | inverse(sk_c10) = sk_c10. [para(19893(b,1),19902(b,1)),merge(b)].
% 46.59/46.95 20093 identity = sk_c8 | multiply(sk_c10,sk_c10) = identity. [para(20092(b,1),4(a,1,1))].
% 46.59/46.95 20101 identity = sk_c8 | sk_c7 = sk_c10. [para(20092(b,1),19939(b,1)),flip(c),merge(b)].
% 46.59/46.95 20256 sk_c7 = sk_c10 | multiply(sk_c8,A) = A. [para(20101(a,1),3(a,1,1))].
% 46.59/46.95 20257 sk_c7 = sk_c10 | multiply(A,sk_c8) = A. [para(20101(a,1),593(a,1,2))].
% 46.59/46.95 20462 sk_c7 = sk_c10 | multiply(sk_c8,inverse(sk_c10)) = sk_c10. [para(20257(b,1),39(b,1)),merge(c)].
% 46.59/46.95 21667 sk_c7 = sk_c10 | inverse(sk_c10) = sk_c10. [para(20462(b,1),20256(b,1)),flip(c),merge(b)].
% 46.59/46.95 21677 sk_c7 = sk_c10 | multiply(sk_c10,inverse(sk_c1)) = identity. [para(21667(b,1),7265(b,1,1)),merge(b)].
% 46.59/46.95 22151 sk_c7 = sk_c10 | multiply(sk_c1,inverse(sk_c10)) = identity. [para(21677(b,1),3677(a,1,1)),rewrite([615(5),733(7)]),flip(b)].
% 46.59/46.95 22351 sk_c7 = sk_c10 | multiply(sk_c1,inverse(sk_c10)) = sk_c8. [para(20101(a,1),22151(b,2)),merge(b)].
% 46.59/46.95 22420 sk_c7 = sk_c10 | multiply(sk_c10,sk_c8) = inverse(sk_c10). [para(22351(b,1),5468(b,1,2)),merge(b)].
% 46.59/46.95 22459 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | B != A | multiply(sk_c10,inverse(B)) != sk_c10 | identity != sk_c8 | inverse(C) != sk_c10 | multiply(C,sk_c8) != sk_c10. [para(4(a,1),18680(c,1,2)),rewrite([593(13),733(15)])].
% 46.59/46.95 22477 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | inverse(B) != A | multiply(sk_c10,B) != sk_c10 | identity != sk_c8 | inverse(C) != sk_c10 | multiply(C,sk_c8) != sk_c10. [para(733(a,1),22459(d,1,2))].
% 46.59/46.95 22484 sk_c7 = sk_c10 | multiply(inverse(sk_c8),inverse(sk_c10)) = sk_c10. [para(22420(b,1),3677(a,1,1)),rewrite([733(6)]),flip(b)].
% 46.59/46.95 22491 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(inverse(B),sk_c10) != A | sk_c10 != B | identity != sk_c8 | inverse(C) != sk_c10 | multiply(C,sk_c8) != sk_c10. [para(732(a,1),22477(d,1)),rewrite([3677(15),733(15)]),flip(d)].
% 46.59/46.95 22508 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(inverse(B),multiply(inverse(C),sk_c10)) != A | multiply(C,B) != sk_c10 | identity != sk_c8 | inverse(D) != sk_c10 | multiply(D,sk_c8) != sk_c10. [para(3677(a,1),22491(c,1,1)),rewrite([57(16)]),flip(d)].
% 46.59/46.95 22509 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,A) != inverse(sk_c10) | multiply(inverse(sk_c8),multiply(inverse(B),sk_c10)) != A | multiply(B,sk_c8) != sk_c10 | identity != sk_c8 | inverse(B) != sk_c10. [factor(22508,d,g)].
% 46.59/46.95 22511 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != A | multiply(inverse(sk_c8),multiply(inverse(B),sk_c10)) != multiply(inverse(sk_c10),A) | multiply(B,sk_c8) != sk_c10 | identity != sk_c8 | inverse(B) != sk_c10. [para(732(a,1),22509(b,1)),flip(b)].
% 46.59/46.95 22704 identity = sk_c8 | multiply(inverse(sk_c10),sk_c8) = sk_c10. [para(20059(b,1),3677(a,1,1)),rewrite([733(6),733(9)]),flip(b)].
% 46.59/46.95 22705 identity = sk_c8 | multiply(sk_c10,sk_c10) = sk_c8. [para(22704(b,1),75(a,1,2)),rewrite([733(6)])].
% 46.59/46.95 22711 identity = sk_c8. [para(22705(b,1),20093(b,1)),flip(c),merge(b),merge(c)].
% 46.59/46.95 22761 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | inverse(sk_c10) != A | multiply(inverse(sk_c8),multiply(inverse(B),sk_c10)) != multiply(inverse(sk_c10),A) | multiply(B,sk_c8) != sk_c10 | inverse(B) != sk_c10. [back_rewrite(22511),rewrite([22711(24)]),xx(e)].
% 46.59/46.95 24533 multiply(sk_c8,inverse(sk_c10)) != sk_c10 | multiply(sk_c10,sk_c8) != inverse(sk_c10). [back_rewrite(4196),rewrite([22711(13)]),xx(c)].
% 46.59/46.95 24581 inverse(sk_c8) = sk_c8. [back_rewrite(615),rewrite([22711(1),22711(3)])].
% 46.59/46.95 24582 multiply(A,sk_c8) = A. [back_rewrite(593),rewrite([22711(1)])].
% 46.59/46.95 24583 multiply(inverse(A),A) = sk_c8. [back_rewrite(4),rewrite([22711(3)])].
% 46.59/46.95 24584 multiply(sk_c8,A) = A. [back_rewrite(3),rewrite([22711(1)])].
% 46.59/46.95 24593 inverse(sk_c10) != sk_c10. [factor(22761,b,e),rewrite([24584(4),24581(10),24583(13),24582(11),24583(13),24582(14)]),xx(c),xx(d),merge(b)].
% 46.59/46.95 24596 sk_c7 = sk_c10. [back_rewrite(22484),rewrite([24581(5),24584(7)]),unit_del(b,24593)].
% 46.59/46.95 24604 inverse(sk_c10) = sk_c1. [back_rewrite(19192),rewrite([24596(1),24581(6),24584(8)]),unit_del(a,24593)].
% 46.59/46.95 24642 sk_c1 = sk_c10. [back_rewrite(13861),rewrite([24596(1),24596(4),24604(5),24604(8),24581(9),24582(9)]),flip(a),merge(b),merge(c)].
% 46.59/46.95 24684 $F. [back_rewrite(24533),rewrite([24604(3),24642(2),24584(3),24582(6),24604(6),24642(5)]),xx(a),xx(b)].
% 46.59/46.95
% 46.59/46.95 % SZS output end Refutation
% 46.59/46.95 ============================== end of proof ==========================
% 46.59/46.95
% 46.59/46.95 ============================== STATISTICS ============================
% 46.59/46.95
% 46.59/46.95 Given=4392. Generated=2582198. Kept=24661. proofs=1.
% 46.59/46.95 Usable=1067. Sos=4915. Demods=17. Limbo=102, Disabled=18614. Hints=0.
% 46.59/46.95 Megabytes=22.82.
% 46.59/46.95 User_CPU=44.58, System_CPU=1.35, Wall_clock=46.
% 46.59/46.95
% 46.59/46.95 ============================== end of statistics =====================
% 46.59/46.95
% 46.59/46.95 ============================== end of search =========================
% 46.59/46.95
% 46.59/46.95 THEOREM PROVED
% 46.59/46.95 % SZS status Unsatisfiable
% 46.59/46.95
% 46.59/46.95 Exiting with 1 proof.
% 46.59/46.95
% 46.59/46.95 Process 9688 exit (max_proofs) Tue Jun 14 04:36:41 2022
% 46.59/46.95 Prover9 interrupted
%------------------------------------------------------------------------------