TSTP Solution File: GRP386-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP386-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 167.95s 168.28s
% Output : Refutation 167.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP386-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 00:34:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 15.95/16.25 ============================== Prover9 ===============================
% 15.95/16.25 Prover9 (32) version 2009-11A, November 2009.
% 15.95/16.25 Process 11858 was started by sandbox2 on n029.cluster.edu,
% 15.95/16.25 Tue Jun 14 00:34:56 2022
% 15.95/16.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11705_n029.cluster.edu".
% 15.95/16.25 ============================== end of head ===========================
% 15.95/16.25
% 15.95/16.25 ============================== INPUT =================================
% 15.95/16.25
% 15.95/16.25 % Reading from file /tmp/Prover9_11705_n029.cluster.edu
% 15.95/16.25
% 15.95/16.25 set(prolog_style_variables).
% 15.95/16.25 set(auto2).
% 15.95/16.25 % set(auto2) -> set(auto).
% 15.95/16.25 % set(auto) -> set(auto_inference).
% 15.95/16.25 % set(auto) -> set(auto_setup).
% 15.95/16.25 % set(auto_setup) -> set(predicate_elim).
% 15.95/16.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 15.95/16.25 % set(auto) -> set(auto_limits).
% 15.95/16.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 15.95/16.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 15.95/16.25 % set(auto) -> set(auto_denials).
% 15.95/16.25 % set(auto) -> set(auto_process).
% 15.95/16.25 % set(auto2) -> assign(new_constants, 1).
% 15.95/16.25 % set(auto2) -> assign(fold_denial_max, 3).
% 15.95/16.25 % set(auto2) -> assign(max_weight, "200.000").
% 15.95/16.25 % set(auto2) -> assign(max_hours, 1).
% 15.95/16.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 15.95/16.25 % set(auto2) -> assign(max_seconds, 0).
% 15.95/16.25 % set(auto2) -> assign(max_minutes, 5).
% 15.95/16.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 15.95/16.25 % set(auto2) -> set(sort_initial_sos).
% 15.95/16.25 % set(auto2) -> assign(sos_limit, -1).
% 15.95/16.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 15.95/16.25 % set(auto2) -> assign(max_megs, 400).
% 15.95/16.25 % set(auto2) -> assign(stats, some).
% 15.95/16.25 % set(auto2) -> clear(echo_input).
% 15.95/16.25 % set(auto2) -> set(quiet).
% 15.95/16.25 % set(auto2) -> clear(print_initial_clauses).
% 15.95/16.25 % set(auto2) -> clear(print_given).
% 15.95/16.25 assign(lrs_ticks,-1).
% 15.95/16.25 assign(sos_limit,10000).
% 15.95/16.25 assign(order,kbo).
% 15.95/16.25 set(lex_order_vars).
% 15.95/16.25 clear(print_given).
% 15.95/16.25
% 15.95/16.25 % formulas(sos). % not echoed (54 formulas)
% 15.95/16.25
% 15.95/16.25 ============================== end of input ==========================
% 15.95/16.25
% 15.95/16.25 % From the command line: assign(max_seconds, 300).
% 15.95/16.25
% 15.95/16.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 15.95/16.25
% 15.95/16.25 % Formulas that are not ordinary clauses:
% 15.95/16.25
% 15.95/16.25 ============================== end of process non-clausal formulas ===
% 15.95/16.25
% 15.95/16.25 ============================== PROCESS INITIAL CLAUSES ===============
% 15.95/16.25
% 15.95/16.25 ============================== PREDICATE ELIMINATION =================
% 15.95/16.25
% 15.95/16.25 ============================== end predicate elimination =============
% 15.95/16.25
% 15.95/16.25 Auto_denials: (non-Horn, no changes).
% 15.95/16.25
% 15.95/16.25 Term ordering decisions:
% 15.95/16.25
% 15.95/16.25 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 15.95/16.25 Function symbol KB weights: sk_c10=1. sk_c9=1. sk_c7=1. sk_c8=1. sk_c1=1. sk_c5=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 15.95/16.25
% 15.95/16.25 ============================== end of process initial clauses ========
% 15.95/16.25
% 15.95/16.25 ============================== CLAUSES FOR SEARCH ====================
% 15.95/16.25
% 15.95/16.25 ============================== end of clauses for search =============
% 15.95/16.25
% 15.95/16.25 ============================== SEARCH ================================
% 15.95/16.25
% 15.95/16.25 % Starting search at 0.26 seconds.
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=1897, wt=80.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=570, wt=71.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=11130, wt=49.000
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=63.000, iters=7771
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=60.000, iters=6320
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=59.000, iters=6121
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=55.000, iters=3713
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=54.000, iters=3416
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=13818, wt=48.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=13821, wt=47.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=13829, wt=44.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=13832, wt=43.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=13844, wt=42.000
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=53.000, iters=3343
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=51.000, iters=3364
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=17994, wt=41.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=18087, wt=40.000
% 15.95/16.25
% 15.95/16.25 Low Water (keep): wt=50.000, iters=3391
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=18380, wt=39.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=18560, wt=38.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=18678, wt=37.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=19038, wt=36.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=19578, wt=34.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=20135, wt=33.000
% 15.95/16.25
% 15.95/16.25 Low Water (displace): id=20544, wt=32.000
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=20604, wt=31.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=49.000, iters=3364
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=20960, wt=17.000
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=20975, wt=15.000
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=21162, wt=14.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=48.000, iters=3372
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=23534, wt=13.000
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=23605, wt=12.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=47.000, iters=3333
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=46.000, iters=3340
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=29030, wt=11.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=45.000, iters=3333
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=36966, wt=10.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=44.000, iters=3335
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=43.000, iters=3339
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=42.000, iters=3364
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=41.000, iters=3352
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=40.000, iters=3454
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=39.000, iters=3354
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=38.000, iters=3355
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=63516, wt=9.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=37.000, iters=3377
% 167.95/168.28
% 167.95/168.28 Low Water (displace): id=63957, wt=8.000
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=36.000, iters=3333
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=35.000, iters=3335
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=34.000, iters=3387
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=33.000, iters=3390
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=30.000, iters=3349
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=27.000, iters=3531
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=15.000, iters=3335
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=14.000, iters=3620
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=13.000, iters=3333
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=12.000, iters=3344
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=11.000, iters=3803
% 167.95/168.28
% 167.95/168.28 Low Water (keep): wt=10.000, iters=3564
% 167.95/168.28
% 167.95/168.28 ============================== PROOF =================================
% 167.95/168.28 % SZS status Unsatisfiable
% 167.95/168.28 % SZS output start Refutation
% 167.95/168.28
% 167.95/168.28 % Proof 1 at 163.98 (+ 3.35) seconds.
% 167.95/168.28 % Length of proof is 128.
% 167.95/168.28 % Level of proof is 22.
% 167.95/168.28 % Maximum clause weight is 68.000.
% 167.95/168.28 % Given clauses 9086.
% 167.95/168.28
% 167.95/168.28 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 167.95/168.28 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 167.95/168.28 3 inverse(sk_c10) = sk_c9 | inverse(sk_c2) = sk_c10 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 167.95/168.28 4 inverse(sk_c10) = sk_c9 | inverse(sk_c3) = sk_c9 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 167.95/168.28 5 inverse(sk_c10) = sk_c9 | inverse(sk_c4) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 167.95/168.28 8 inverse(sk_c1) = sk_c10 | inverse(sk_c2) = sk_c10 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 167.95/168.28 9 inverse(sk_c1) = sk_c10 | inverse(sk_c3) = sk_c9 # label(prove_this_34) # label(negated_conjecture). [assumption].
% 167.95/168.28 13 inverse(sk_c10) = sk_c9 | multiply(sk_c2,sk_c10) = sk_c9 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 167.95/168.28 14 inverse(sk_c10) = sk_c9 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 167.95/168.28 15 inverse(sk_c10) = sk_c9 | multiply(sk_c4,sk_c7) = sk_c10 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 167.95/168.28 18 multiply(sk_c9,sk_c8) = sk_c10 | inverse(sk_c2) = sk_c10 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 167.95/168.28 23 multiply(sk_c10,sk_c8) = sk_c9 | inverse(sk_c2) = sk_c10 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 167.95/168.28 24 multiply(sk_c10,sk_c8) = sk_c9 | inverse(sk_c3) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 167.95/168.28 28 inverse(sk_c1) = sk_c10 | multiply(sk_c2,sk_c10) = sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 167.95/168.28 29 inverse(sk_c1) = sk_c10 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_33) # label(negated_conjecture). [assumption].
% 167.95/168.28 33 multiply(sk_c1,sk_c9) = sk_c10 | inverse(sk_c2) = sk_c10 # label(prove_this_42) # label(negated_conjecture). [assumption].
% 167.95/168.28 34 multiply(sk_c1,sk_c9) = sk_c10 | inverse(sk_c3) = sk_c9 # label(prove_this_44) # label(negated_conjecture). [assumption].
% 167.95/168.28 38 multiply(sk_c9,sk_c8) = sk_c10 | multiply(sk_c2,sk_c10) = sk_c9 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 167.95/168.28 43 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c2,sk_c10) = sk_c9 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 167.95/168.28 44 multiply(sk_c10,sk_c8) = sk_c9 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 167.95/168.28 48 multiply(sk_c1,sk_c9) = sk_c10 | multiply(sk_c2,sk_c10) = sk_c9 # label(prove_this_41) # label(negated_conjecture). [assumption].
% 167.95/168.28 53 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 167.95/168.28 54 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(B,sk_c10) != sk_c9 | inverse(B) != sk_c10 | multiply(C,sk_c9) != sk_c8 | inverse(C) != sk_c9 | multiply(D,E) != sk_c10 | inverse(D) != E | multiply(E,sk_c9) != sk_c10 | inverse(F) != V6 | inverse(V6) != E | multiply(F,E) != V6 # label(prove_this_51) # label(negated_conjecture). [assumption].
% 167.95/168.28 62 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(A,sk_c10) != sk_c9 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(C,D) != sk_c10 | inverse(C) != D | multiply(D,sk_c9) != sk_c10 | inverse(E) != F | inverse(F) != D | multiply(E,D) != F. [factor(54,d,g)].
% 167.95/168.28 117 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(A,sk_c10) != sk_c9 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(C,A) != sk_c10 | inverse(C) != A | inverse(D) != E | inverse(E) != A | multiply(D,A) != E. [factor(62,e,k)].
% 167.95/168.28 253 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(A,sk_c10) != sk_c9 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(C,A) != sk_c10 | inverse(C) != A | inverse(A) != A | multiply(C,A) != A. [factor(117,j,k)].
% 167.95/168.28 354 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | inverse(A) != sk_c10 | multiply(A,sk_c9) != sk_c10 | multiply(A,sk_c10) != sk_c9 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,A) != sk_c10 | inverse(A) != A | multiply(A,A) != A. [factor(253,j,k)].
% 167.95/168.28 376 inverse(sk_c10) = sk_c9 | multiply(sk_c10,sk_c2) = identity. [para(3(b,1),2(a,1,1))].
% 167.95/168.28 377 inverse(sk_c10) = sk_c9 | multiply(sk_c9,sk_c3) = identity. [para(4(b,1),2(a,1,1))].
% 167.95/168.28 378 inverse(sk_c10) = sk_c9 | multiply(sk_c7,sk_c4) = identity. [para(5(b,1),2(a,1,1))].
% 167.95/168.28 386 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),53(a,1,1)),rewrite([1(2)]),flip(a)].
% 167.95/168.28 388 inverse(sk_c10) = sk_c9 | multiply(A,multiply(sk_c2,sk_c10)) = multiply(A,sk_c9). [para(13(b,1),53(a,2,2)),rewrite([53(8)])].
% 167.95/168.28 392 inverse(sk_c10) = sk_c9 | multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c10). [para(15(b,1),53(a,2,2)),rewrite([53(8)])].
% 167.95/168.28 398 inverse(sk_c2) = sk_c10 | multiply(A,multiply(sk_c9,sk_c8)) = multiply(A,sk_c10). [para(18(a,1),53(a,2,2)),rewrite([53(8)])].
% 167.95/168.28 427 inverse(sk_c2) = sk_c10 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c10,A). [para(33(a,1),53(a,1,1)),flip(b)].
% 167.95/168.28 429 inverse(sk_c3) = sk_c9 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c10,A). [para(34(a,1),53(a,1,1)),flip(b)].
% 167.95/168.28 12208 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),386(a,1,2))].
% 167.95/168.28 12229 inverse(sk_c3) = sk_c9 | multiply(inverse(sk_c10),sk_c9) = sk_c8. [para(24(a,1),386(a,1,2))].
% 167.95/168.28 12371 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c10),identity) = sk_c2. [para(376(b,1),386(a,1,2))].
% 167.95/168.28 12372 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(386(a,1),386(a,1,2))].
% 167.95/168.28 12587 multiply(A,identity) = A. [back_rewrite(12208),rewrite([12372(4)])].
% 167.95/168.28 12694 inverse(sk_c10) = sk_c9 | inverse(sk_c10) = sk_c2. [back_rewrite(12371),rewrite([12587(8)])].
% 167.95/168.28 12843 inverse(identity) = identity. [para(12587(a,1),2(a,1))].
% 167.95/168.28 12885 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9. [para(12587(a,1),354(i,1)),rewrite([12843(16),1(20),1(23),12843(35),12587(39)]),flip(f),xx(j),xx(k),merge(f),merge(i)].
% 167.95/168.28 13396 inverse(sk_c10) = sk_c9 | multiply(sk_c2,sk_c10) = identity. [para(12694(b,1),2(a,1,1))].
% 167.95/168.28 13399 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = sk_c3. [para(377(b,1),386(a,1,2)),rewrite([12587(8)])].
% 167.95/168.28 13416 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,multiply(B,sk_c9)) != sk_c8 | inverse(multiply(A,B)) != sk_c9. [para(53(a,1),12885(f,1))].
% 167.95/168.28 13427 inverse(sk_c10) = sk_c9 | multiply(sk_c3,sk_c9) = identity. [para(13399(b,1),2(a,1,1))].
% 167.95/168.28 13430 inverse(sk_c10) = sk_c9 | inverse(sk_c7) = sk_c4. [para(378(b,1),386(a,1,2)),rewrite([12587(8)])].
% 167.95/168.28 13431 inverse(sk_c10) = sk_c9 | multiply(sk_c4,sk_c7) = identity. [para(13430(b,1),2(a,1,1))].
% 167.95/168.28 13448 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,multiply(B,multiply(C,sk_c9))) != sk_c8 | inverse(multiply(A,multiply(B,C))) != sk_c9. [para(53(a,1),13416(f,1,2))].
% 167.95/168.28 14164 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | sk_c8 != A | inverse(multiply(A,multiply(inverse(multiply(B,sk_c9)),B))) != sk_c9. [para(2(a,1),13448(f,1,2)),rewrite([12587(22)]),flip(f)].
% 167.95/168.28 14186 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,B) != sk_c8 | inverse(multiply(A,multiply(B,multiply(inverse(multiply(C,sk_c9)),C)))) != sk_c9. [para(53(a,1),14164(g,1,1)),flip(f)].
% 167.95/168.28 14281 multiply(A,inverse(A)) = identity. [para(12372(a,1),2(a,1))].
% 167.95/168.28 15019 multiply(A,multiply(inverse(A),B)) = B. [para(12372(a,1),386(a,1))].
% 167.95/168.28 15020 inverse(inverse(A)) = A. [para(12372(a,1),12587(a,1)),rewrite([12587(2)]),flip(a)].
% 167.95/168.28 15983 inverse(sk_c1) = sk_c10 | multiply(sk_c2,sk_c10) = identity. [para(8(b,1),14281(a,1,2))].
% 167.95/168.28 15984 inverse(sk_c1) = sk_c10 | multiply(sk_c3,sk_c9) = identity. [para(9(b,1),14281(a,1,2))].
% 167.95/168.28 15987 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(14281(a,1),53(a,1)),flip(a)].
% 167.95/168.28 16782 inverse(sk_c10) = sk_c9 | identity = sk_c9. [para(13396(b,1),13(b,1)),merge(b)].
% 167.95/168.28 16784 inverse(sk_c10) = sk_c9 | multiply(A,sk_c9) = A. [para(13396(b,1),388(b,1,2)),rewrite([12587(10)]),flip(c),merge(b)].
% 167.95/168.28 16910 inverse(sk_c10) = sk_c9 | identity = sk_c8. [para(13427(b,1),14(b,1)),merge(b)].
% 167.95/168.28 17041 inverse(sk_c10) = sk_c9 | identity = sk_c10. [para(13431(b,1),15(b,1)),merge(b)].
% 167.95/168.28 17043 inverse(sk_c10) = sk_c9 | multiply(A,sk_c10) = A. [para(13431(b,1),392(b,1,2)),rewrite([12587(10)]),flip(c),merge(b)].
% 167.95/168.28 17046 identity = sk_c10 | inverse(sk_c9) = sk_c10. [para(17041(a,1),15020(a,1,1))].
% 167.95/168.28 17243 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,multiply(B,C)) != sk_c8 | inverse(multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(D,sk_c9)),D))))) != sk_c9. [para(53(a,1),14186(g,1,1,2))].
% 167.95/168.28 17445 inverse(sk_c1) = sk_c10 | identity = sk_c9. [para(15983(b,1),28(b,1)),merge(b)].
% 167.95/168.28 17453 identity = sk_c9 | multiply(sk_c10,multiply(sk_c1,A)) = A. [para(17445(a,1),386(a,1,1))].
% 167.95/168.28 17454 identity = sk_c9 | inverse(sk_c10) = sk_c1. [para(17445(a,1),15020(a,1,1))].
% 167.95/168.28 17455 identity = sk_c9 | multiply(sk_c1,sk_c10) = identity. [para(17445(a,1),14281(a,1,2))].
% 167.95/168.28 17456 identity = sk_c9 | multiply(sk_c1,multiply(sk_c10,A)) = A. [para(17445(a,1),15019(a,1,2,1))].
% 167.95/168.28 17457 identity = sk_c9 | sk_c1 = sk_c9. [para(17454(b,1),16782(a,1)),merge(c)].
% 167.95/168.28 17520 sk_c1 = sk_c9 | inverse(sk_c9) = identity. [para(17457(a,1),12843(a,1,1))].
% 167.95/168.28 17548 sk_c1 = sk_c9 | identity = sk_c10. [para(17520(b,1),17046(b,1)),merge(c)].
% 167.95/168.28 17771 identity = sk_c9 | inverse(sk_c2) = sk_c10 | multiply(sk_c1,multiply(sk_c9,sk_c8)) = identity. [para(17455(b,1),398(b,2))].
% 167.95/168.28 18946 inverse(sk_c1) = sk_c10 | identity = sk_c8. [para(15984(b,1),29(b,1)),merge(b)].
% 167.95/168.28 18986 identity = sk_c8 | inverse(sk_c10) = sk_c1. [para(18946(a,1),15020(a,1,1))].
% 167.95/168.28 18993 identity = sk_c8 | sk_c1 = sk_c9. [para(18986(b,1),16910(a,1)),merge(c)].
% 167.95/168.28 19247 sk_c1 = sk_c9 | sk_c8 = sk_c10. [para(18993(a,1),17548(b,1)),merge(b)].
% 167.95/168.28 22441 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = identity. [para(16784(b,1),2(a,1))].
% 167.95/168.28 22997 inverse(sk_c10) = sk_c9 | multiply(sk_c9,A) = A. [para(22441(b,1),386(a,1,1)),rewrite([1(8)])].
% 167.95/168.28 25678 inverse(sk_c2) = sk_c10 | multiply(sk_c1,multiply(sk_c9,sk_c8)) = sk_c9. [para(23(a,1),427(b,2)),merge(b)].
% 167.95/168.28 25795 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(A,multiply(inverse(multiply(B,multiply(inverse(multiply(C,sk_c9)),C))),B)) != sk_c8 | inverse(A) != sk_c9. [para(2(a,1),17243(g,1,1,2)),rewrite([12587(32)])].
% 167.95/168.28 25891 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | inverse(multiply(sk_c8,multiply(inverse(multiply(A,sk_c9)),A))) != sk_c9. [resolve(25795,f,15019,a)].
% 167.95/168.28 25990 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | inverse(multiply(sk_c8,multiply(inverse(multiply(A,multiply(B,sk_c9))),multiply(A,B)))) != sk_c9. [para(53(a,1),25891(f,1,1,2,1,1))].
% 167.95/168.28 32688 inverse(sk_c10) = sk_c9 | multiply(inverse(sk_c9),A) = A. [para(22997(b,1),386(a,1,2))].
% 167.95/168.28 59862 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(15987(a,1),386(a,1,2)),rewrite([12587(3)]),flip(a)].
% 167.95/168.28 60769 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(59862(a,1),386(a,1,2)),flip(a)].
% 167.95/168.28 60817 inverse(sk_c10) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(sk_c9,inverse(sk_c8)) != sk_c9. [para(59862(a,1),25990(f,1,1,2,2)),rewrite([60769(23),53(26),15019(27),60769(25),15020(25),53(26),14281(25),12587(25),60769(25),15020(23)])].
% 167.95/168.28 75162 inverse(sk_c10) = sk_c9 | inverse(sk_c9) = sk_c10. [para(32688(b,1),17043(b,1)),flip(c),merge(b)].
% 167.95/168.28 75265 inverse(sk_c10) = sk_c9. [para(75162(b,1),15020(a,1,1)),merge(b)].
% 167.95/168.28 77956 multiply(sk_c9,sk_c8) != sk_c10 | multiply(sk_c10,sk_c8) != sk_c9 | identity != sk_c10 | sk_c9 != sk_c10 | multiply(sk_c9,inverse(sk_c8)) != sk_c9. [back_rewrite(60817),rewrite([75265(2)]),xx(a)].
% 167.95/168.28 79273 inverse(sk_c3) = sk_c9 | multiply(sk_c9,sk_c9) = sk_c8. [back_rewrite(12229),rewrite([75265(6)])].
% 167.95/168.28 83109 inverse(sk_c9) = sk_c10. [para(75265(a,1),15020(a,1,1))].
% 167.95/168.28 83110 multiply(sk_c10,sk_c9) = identity. [para(75265(a,1),14281(a,1,2))].
% 167.95/168.28 84281 inverse(sk_c3) = sk_c9 | multiply(sk_c1,sk_c8) = identity. [para(79273(b,1),429(b,1,2)),rewrite([83110(14)]),merge(b)].
% 167.95/168.28 85137 inverse(sk_c3) = sk_c9 | inverse(sk_c1) = sk_c8. [para(84281(b,1),386(a,1,2)),rewrite([12587(8)])].
% 167.95/168.28 85167 inverse(sk_c1) = sk_c8 | sk_c3 = sk_c10. [para(85137(a,1),15020(a,1,1)),rewrite([83109(6)]),flip(b)].
% 167.95/168.28 85179 sk_c8 = sk_c10 | sk_c3 = sk_c10. [para(19247(a,1),85167(a,1,1)),rewrite([83109(5)]),flip(b),merge(b)].
% 167.95/168.28 85201 sk_c8 = sk_c10 | multiply(sk_c10,sk_c8) = sk_c9 | identity = sk_c8. [para(85179(b,1),44(b,1,1)),rewrite([83110(11)])].
% 167.95/168.28 90729 inverse(sk_c2) = sk_c10 | identity = sk_c9. [para(25678(b,1),17771(c,1)),flip(d),merge(c),merge(d)].
% 167.95/168.28 90740 identity = sk_c9 | multiply(sk_c2,sk_c10) = identity. [para(90729(a,1),14281(a,1,2))].
% 167.95/168.28 90787 identity = sk_c9 | multiply(sk_c9,sk_c8) = sk_c10. [para(90740(b,1),38(b,1)),merge(c)].
% 167.95/168.28 90788 identity = sk_c9 | multiply(sk_c10,sk_c8) = sk_c9. [para(90740(b,1),43(b,1)),merge(c)].
% 167.95/168.28 90789 identity = sk_c9 | multiply(sk_c1,sk_c9) = sk_c10. [para(90740(b,1),48(b,1)),merge(c)].
% 167.95/168.28 90984 identity = sk_c9 | multiply(sk_c10,sk_c10) = sk_c8. [para(90787(b,1),386(a,1,2)),rewrite([83109(5)])].
% 167.95/168.28 90989 identity = sk_c9 | multiply(sk_c1,sk_c9) = sk_c8. [para(90788(b,1),17456(b,1,2)),merge(b)].
% 167.95/168.28 91038 identity = sk_c9 | multiply(sk_c10,sk_c10) = sk_c9. [para(90789(b,1),17453(b,1,2)),merge(b)].
% 167.95/168.28 91140 identity = sk_c9 | sk_c8 = sk_c10. [para(90989(b,1),90789(b,1)),merge(b)].
% 167.95/168.28 91143 sk_c8 = sk_c10 | identity = sk_c10. [para(91140(a,1),12843(a,1,1)),rewrite([83109(5)]),flip(b)].
% 167.95/168.28 91182 sk_c8 = sk_c10 | sk_c9 = sk_c10. [para(91143(b,1),91140(a,1)),flip(b),merge(c)].
% 167.95/168.28 91268 identity = sk_c9 | multiply(sk_c9,sk_c9) = sk_c10. [para(91038(b,1),386(a,1,2)),rewrite([75265(5)])].
% 167.95/168.28 91269 identity = sk_c9 | sk_c8 = sk_c9. [para(91038(b,1),90984(b,1)),flip(c),merge(b)].
% 167.95/168.28 91283 sk_c8 = sk_c9 | identity = sk_c10. [para(91269(a,1),12843(a,1,1)),rewrite([83109(5)]),flip(b)].
% 167.95/168.28 91294 sk_c8 = sk_c9 | sk_c9 = sk_c10. [para(91283(b,1),91269(a,1)),flip(b),merge(c)].
% 167.95/168.28 91296 sk_c9 = sk_c10. [para(91294(a,1),91182(a,1)),merge(b),merge(c)].
% 167.95/168.28 91310 identity = sk_c10 | multiply(sk_c10,sk_c10) = sk_c10. [back_rewrite(91268),rewrite([91296(2),91296(4),91296(5)])].
% 167.95/168.28 94125 sk_c8 = sk_c10 | multiply(sk_c10,sk_c8) = sk_c10 | identity = sk_c8. [back_rewrite(85201),rewrite([91296(7)])].
% 167.95/168.28 94655 multiply(sk_c10,sk_c10) = identity. [back_rewrite(83110),rewrite([91296(2)])].
% 167.95/168.28 94718 multiply(sk_c10,sk_c8) != sk_c10 | identity != sk_c10 | multiply(sk_c10,inverse(sk_c8)) != sk_c10. [back_rewrite(77956),rewrite([91296(1),91296(9),91296(14),91296(17),91296(21)]),xx(d),merge(b)].
% 167.95/168.28 94954 inverse(sk_c10) = sk_c10. [back_rewrite(75265),rewrite([91296(3)])].
% 167.95/168.28 98685 identity = sk_c10. [back_rewrite(91310),rewrite([94655(6)]),merge(b)].
% 167.95/168.28 98924 multiply(sk_c10,sk_c8) != sk_c10 | multiply(sk_c10,inverse(sk_c8)) != sk_c10. [back_rewrite(94718),rewrite([98685(6)]),xx(b)].
% 167.95/168.28 98946 sk_c8 = sk_c10 | multiply(sk_c10,sk_c8) = sk_c10. [back_rewrite(94125),rewrite([98685(9)]),flip(c),merge(c)].
% 167.95/168.28 99171 multiply(A,sk_c10) = A. [back_rewrite(12587),rewrite([98685(1)])].
% 167.95/168.28 99173 multiply(sk_c10,A) = A. [back_rewrite(1),rewrite([98685(1)])].
% 167.95/168.28 99352 sk_c8 = sk_c10. [back_rewrite(98946),rewrite([99173(6)]),merge(b)].
% 167.95/168.28 99361 $F. [back_rewrite(98924),rewrite([99352(2),99171(3),99352(5),94954(6),99171(6)]),xx(a),xx(b)].
% 167.95/168.28
% 167.95/168.28 % SZS output end Refutation
% 167.95/168.28 ============================== end of proof ==========================
% 167.95/168.28
% 167.95/168.28 ============================== STATISTICS ============================
% 167.95/168.28
% 167.95/168.28 Given=9086. Generated=6071385. Kept=99360. proofs=1.
% 167.95/168.28 Usable=293. Sos=4668. Demods=20. Limbo=188, Disabled=94265. Hints=0.
% 167.95/168.28 Megabytes=103.62.
% 167.95/168.28 User_CPU=163.98, System_CPU=3.35, Wall_clock=167.
% 167.95/168.28
% 167.95/168.28 ============================== end of statistics =====================
% 167.95/168.28
% 167.95/168.28 ============================== end of search =========================
% 167.95/168.28
% 167.95/168.28 THEOREM PROVED
% 167.95/168.28 % SZS status Unsatisfiable
% 167.95/168.28
% 167.95/168.28 Exiting with 1 proof.
% 167.95/168.28
% 167.95/168.28 Process 11858 exit (max_proofs) Tue Jun 14 00:37:43 2022
% 167.95/168.28 Prover9 interrupted
%------------------------------------------------------------------------------