TSTP Solution File: GRP343-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:18:42 EDT 2022
% Result : Unsatisfiable 10.58s 10.89s
% Output : Refutation 10.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP343-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.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 05:12:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.15/6.47 ============================== Prover9 ===============================
% 6.15/6.47 Prover9 (32) version 2009-11A, November 2009.
% 6.15/6.47 Process 10176 was started by sandbox on n025.cluster.edu,
% 6.15/6.47 Tue Jun 14 05:12:55 2022
% 6.15/6.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10022_n025.cluster.edu".
% 6.15/6.47 ============================== end of head ===========================
% 6.15/6.47
% 6.15/6.47 ============================== INPUT =================================
% 6.15/6.47
% 6.15/6.47 % Reading from file /tmp/Prover9_10022_n025.cluster.edu
% 6.15/6.47
% 6.15/6.47 set(prolog_style_variables).
% 6.15/6.47 set(auto2).
% 6.15/6.47 % set(auto2) -> set(auto).
% 6.15/6.47 % set(auto) -> set(auto_inference).
% 6.15/6.47 % set(auto) -> set(auto_setup).
% 6.15/6.47 % set(auto_setup) -> set(predicate_elim).
% 6.15/6.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.15/6.47 % set(auto) -> set(auto_limits).
% 6.15/6.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.15/6.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.15/6.47 % set(auto) -> set(auto_denials).
% 6.15/6.47 % set(auto) -> set(auto_process).
% 6.15/6.47 % set(auto2) -> assign(new_constants, 1).
% 6.15/6.47 % set(auto2) -> assign(fold_denial_max, 3).
% 6.15/6.47 % set(auto2) -> assign(max_weight, "200.000").
% 6.15/6.47 % set(auto2) -> assign(max_hours, 1).
% 6.15/6.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.15/6.47 % set(auto2) -> assign(max_seconds, 0).
% 6.15/6.47 % set(auto2) -> assign(max_minutes, 5).
% 6.15/6.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.15/6.47 % set(auto2) -> set(sort_initial_sos).
% 6.15/6.47 % set(auto2) -> assign(sos_limit, -1).
% 6.15/6.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.15/6.47 % set(auto2) -> assign(max_megs, 400).
% 6.15/6.47 % set(auto2) -> assign(stats, some).
% 6.15/6.47 % set(auto2) -> clear(echo_input).
% 6.15/6.47 % set(auto2) -> set(quiet).
% 6.15/6.47 % set(auto2) -> clear(print_initial_clauses).
% 6.15/6.47 % set(auto2) -> clear(print_given).
% 6.15/6.47 assign(lrs_ticks,-1).
% 6.15/6.47 assign(sos_limit,10000).
% 6.15/6.47 assign(order,kbo).
% 6.15/6.47 set(lex_order_vars).
% 6.15/6.47 clear(print_given).
% 6.15/6.47
% 6.15/6.47 % formulas(sos). % not echoed (37 formulas)
% 6.15/6.47
% 6.15/6.47 ============================== end of input ==========================
% 6.15/6.47
% 6.15/6.47 % From the command line: assign(max_seconds, 300).
% 6.15/6.47
% 6.15/6.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.15/6.47
% 6.15/6.47 % Formulas that are not ordinary clauses:
% 6.15/6.47
% 6.15/6.47 ============================== end of process non-clausal formulas ===
% 6.15/6.47
% 6.15/6.47 ============================== PROCESS INITIAL CLAUSES ===============
% 6.15/6.47
% 6.15/6.47 ============================== PREDICATE ELIMINATION =================
% 6.15/6.47
% 6.15/6.47 ============================== end predicate elimination =============
% 6.15/6.47
% 6.15/6.47 Auto_denials: (non-Horn, no changes).
% 6.15/6.47
% 6.15/6.47 Term ordering decisions:
% 6.15/6.47
% 6.15/6.47 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 6.15/6.47 Function symbol KB weights: sk_c8=1. sk_c9=1. sk_c1=1. sk_c2=1. sk_c7=1. sk_c5=1. sk_c3=1. sk_c4=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 6.15/6.47
% 6.15/6.47 ============================== end of process initial clauses ========
% 6.15/6.47
% 6.15/6.47 ============================== CLAUSES FOR SEARCH ====================
% 6.15/6.47
% 6.15/6.47 ============================== end of clauses for search =============
% 6.15/6.47
% 6.15/6.47 ============================== SEARCH ================================
% 6.15/6.47
% 6.15/6.47 % Starting search at 0.07 seconds.
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=52.000, iters=3737
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=51.000, iters=3544
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=50.000, iters=3409
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=49.000, iters=3487
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=48.000, iters=3359
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=47.000, iters=3344
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=46.000, iters=3333
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=45.000, iters=3373
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=44.000, iters=3367
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=43.000, iters=3364
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=42.000, iters=3605
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=41.000, iters=3623
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=40.000, iters=3371
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=39.000, iters=3387
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=38.000, iters=3341
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=37.000, iters=3343
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=36.000, iters=3341
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=35.000, iters=3396
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=34.000, iters=3334
% 6.15/6.47
% 6.15/6.47 Low Water (displace): id=13676, wt=16.000
% 6.15/6.47
% 6.15/6.47 Low Water (displace): id=13680, wt=15.000
% 6.15/6.47
% 6.15/6.47 Low Water (displace): id=13728, wt=14.000
% 6.15/6.47
% 6.15/6.47 Low Water (displace): id=13911, wt=11.000
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=33.000, iters=3386
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=32.000, iters=3376
% 6.15/6.47
% 6.15/6.47 Low Water (keep): wt=31.000, iters=3343
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=30.000, iters=3349
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=29.000, iters=3350
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=28.000, iters=3378
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=27.000, iters=3333
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=26.000, iters=3363
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=25.000, iters=3385
% 10.58/10.89
% 10.58/10.89 Low Water (keep): wt=24.000, iters=3337
% 10.58/10.89
% 10.58/10.89 ============================== PROOF =================================
% 10.58/10.89 % SZS status Unsatisfiable
% 10.58/10.89 % SZS output start Refutation
% 10.58/10.89
% 10.58/10.89 % Proof 1 at 9.70 (+ 0.14) seconds.
% 10.58/10.89 % Length of proof is 135.
% 10.58/10.89 % Level of proof is 23.
% 10.58/10.89 % Maximum clause weight is 58.000.
% 10.58/10.89 % Given clauses 1416.
% 10.58/10.89
% 10.58/10.89 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 10.58/10.89 2 multiply(sk_c8,sk_c9) = sk_c7 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 10.58/10.89 3 sk_c7 = multiply(sk_c8,sk_c9). [copy(2),flip(a)].
% 10.58/10.89 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 10.58/10.89 5 inverse(sk_c1) = sk_c9 | inverse(sk_c3) = sk_c9 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 10.58/10.89 6 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 10.58/10.89 9 inverse(sk_c2) = sk_c8 | inverse(sk_c3) = sk_c9 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 10.58/10.89 10 inverse(sk_c2) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 10.58/10.89 13 inverse(sk_c1) = sk_c9 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 10.58/10.89 14 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 10.58/10.89 15 inverse(sk_c1) = sk_c9 | multiply(sk_c9,multiply(sk_c8,sk_c9)) = sk_c8. [copy(14),rewrite([3(6)])].
% 10.58/10.89 16 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c8) = sk_c9 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 10.58/10.89 18 multiply(sk_c1,sk_c8) = sk_c9 | inverse(sk_c3) = sk_c9 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 10.58/10.89 22 inverse(sk_c2) = sk_c8 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 10.58/10.89 23 inverse(sk_c2) = sk_c8 | multiply(sk_c9,sk_c7) = sk_c8 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 10.58/10.89 24 inverse(sk_c2) = sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) = sk_c8. [copy(23),rewrite([3(6)])].
% 10.58/10.89 25 inverse(sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c9 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 10.58/10.89 27 multiply(sk_c2,sk_c7) = sk_c8 | inverse(sk_c3) = sk_c9 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 10.58/10.89 28 multiply(sk_c2,multiply(sk_c8,sk_c9)) = sk_c8 | inverse(sk_c3) = sk_c9. [copy(27),rewrite([3(2)])].
% 10.58/10.89 29 multiply(sk_c2,sk_c7) = sk_c8 | inverse(sk_c4) = sk_c8 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 10.58/10.89 30 multiply(sk_c2,multiply(sk_c8,sk_c9)) = sk_c8 | inverse(sk_c4) = sk_c8. [copy(29),rewrite([3(2)])].
% 10.58/10.89 35 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 10.58/10.89 40 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c3,sk_c9) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 10.58/10.89 41 multiply(sk_c2,multiply(sk_c8,sk_c9)) = sk_c8 | multiply(sk_c3,sk_c9) = sk_c8. [copy(40),rewrite([3(2)])].
% 10.58/10.89 44 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c9 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 10.58/10.89 45 multiply(sk_c2,multiply(sk_c8,sk_c9)) = sk_c8 | multiply(sk_c4,sk_c8) = sk_c9. [copy(44),rewrite([3(2)])].
% 10.58/10.89 48 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 10.58/10.89 49 multiply(sk_c8,sk_c9) != sk_c7 | inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(C,sk_c9) != sk_c8 | inverse(C) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | inverse(E) != F | inverse(F) != sk_c9 | multiply(E,sk_c9) != F # label(prove_this_34) # label(negated_conjecture). [assumption].
% 10.58/10.89 50 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(C,sk_c9) != sk_c8 | inverse(C) != sk_c9 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | inverse(E) != F | inverse(F) != sk_c9 | multiply(E,sk_c9) != F. [copy(49),rewrite([3(4),3(18),3(32)]),xx(a)].
% 10.58/10.89 51 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c9) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | inverse(D) != E | inverse(E) != sk_c9 | multiply(D,sk_c9) != E. [factor(50,a,f)].
% 10.58/10.89 65 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c9) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | inverse(A) != sk_c8 | inverse(C) != D | inverse(D) != sk_c9 | multiply(C,sk_c9) != D. [factor(51,b,g)].
% 10.58/10.89 236 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),48(a,1,1)),rewrite([1(2)]),flip(a)].
% 10.58/10.89 237 inverse(sk_c1) = sk_c9 | multiply(sk_c3,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(13(b,1),48(a,1,1)),flip(b)].
% 10.58/10.89 238 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c3,sk_c9)) = multiply(A,sk_c8). [para(13(b,1),48(a,2,2)),rewrite([48(8)])].
% 10.58/10.89 239 inverse(sk_c1) = sk_c9 | multiply(sk_c9,multiply(sk_c8,multiply(sk_c9,A))) = multiply(sk_c8,A). [para(15(b,1),48(a,1,1)),rewrite([48(11)]),flip(b)].
% 10.58/10.89 242 inverse(sk_c1) = sk_c9 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c9). [para(16(b,1),48(a,2,2)),rewrite([48(8)])].
% 10.58/10.89 245 inverse(sk_c3) = sk_c9 | multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c9,A). [para(18(a,1),48(a,1,1)),flip(b)].
% 10.58/10.89 254 inverse(sk_c2) = sk_c8 | multiply(A,multiply(sk_c3,sk_c9)) = multiply(A,sk_c8). [para(22(b,1),48(a,2,2)),rewrite([48(8)])].
% 10.58/10.89 258 inverse(sk_c2) = sk_c8 | multiply(A,multiply(sk_c4,sk_c8)) = multiply(A,sk_c9). [para(25(b,1),48(a,2,2)),rewrite([48(8)])].
% 10.58/10.89 269 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c3,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(35(b,1),48(a,1,1)),flip(b)].
% 10.58/10.89 323 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(C,sk_c9) != sk_c8 | inverse(C) != sk_c9 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(D,sk_c8) != sk_c9 | inverse(D) != sk_c8 | inverse(inverse(sk_c9)) != identity | inverse(identity) != sk_c9. [resolve(50,l,4,a)].
% 10.58/10.89 716 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(B,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c9) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | inverse(inverse(sk_c9)) != identity | inverse(identity) != sk_c9. [factor(323,a,f)].
% 10.58/10.89 2001 inverse(identity) != sk_c9 | sk_c9 != sk_c8 | inverse(A) != sk_c8 | multiply(A,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | inverse(inverse(sk_c9)) != identity. [factor(716,a,j),rewrite([1(7),1(19)]),flip(b),merge(e)].
% 10.58/10.89 3795 inverse(identity) != sk_c9 | sk_c9 != sk_c8 | inverse(A) != sk_c8 | multiply(A,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c8) != sk_c9 | inverse(inverse(sk_c9)) != identity. [factor(2001,c,g)].
% 10.58/10.89 6173 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),236(a,1,2))].
% 10.58/10.89 6219 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | inverse(inverse(sk_c8)) != sk_c8 | sk_c9 != sk_c8 | multiply(A,sk_c9) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | inverse(A) != sk_c8 | inverse(B) != C | inverse(C) != sk_c9 | multiply(B,sk_c9) != C. [para(236(a,1),65(d,1))].
% 10.58/10.89 6259 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(236(a,1),236(a,1,2))].
% 10.58/10.89 6260 multiply(A,identity) = A. [back_rewrite(6173),rewrite([6259(4)])].
% 10.58/10.89 6263 inverse(identity) = identity. [para(6260(a,1),4(a,1))].
% 10.58/10.89 6370 identity != sk_c9 | sk_c9 != sk_c8 | inverse(A) != sk_c8 | multiply(A,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c8) != sk_c9 | inverse(inverse(sk_c9)) != identity. [back_rewrite(3795),rewrite([6263(2)])].
% 10.58/10.89 6894 multiply(A,inverse(A)) = identity. [para(6259(a,1),4(a,1))].
% 10.58/10.89 7277 multiply(A,multiply(inverse(A),B)) = B. [para(6259(a,1),236(a,1))].
% 10.58/10.89 7278 inverse(inverse(A)) = A. [para(6259(a,1),6260(a,1)),rewrite([6260(2)]),flip(a)].
% 10.58/10.89 7313 identity != sk_c9 | sk_c9 != sk_c8 | inverse(A) != sk_c8 | multiply(A,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | multiply(A,sk_c8) != sk_c9. [back_rewrite(6370),rewrite([7278(29)]),flip(g),merge(g)].
% 10.58/10.89 7353 inverse(A) != sk_c9 | multiply(A,sk_c8) != sk_c9 | sk_c9 != sk_c8 | multiply(A,sk_c9) != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8 | inverse(A) != sk_c8 | inverse(B) != C | inverse(C) != sk_c9 | multiply(B,sk_c9) != C. [back_rewrite(6219),rewrite([7278(10)]),xx(c)].
% 10.58/10.89 7691 inverse(sk_c1) = sk_c9 | multiply(sk_c3,sk_c9) = identity. [para(5(b,1),6894(a,1,2))].
% 10.58/10.89 7692 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c8) = identity. [para(6(b,1),6894(a,1,2))].
% 10.58/10.89 7694 inverse(sk_c2) = sk_c8 | multiply(sk_c3,sk_c9) = identity. [para(9(b,1),6894(a,1,2))].
% 10.58/10.89 7695 inverse(sk_c2) = sk_c8 | multiply(sk_c4,sk_c8) = identity. [para(10(b,1),6894(a,1,2))].
% 10.58/10.89 7697 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(6894(a,1),48(a,1)),flip(a)].
% 10.58/10.89 7704 inverse(sk_c1) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = sk_c3. [para(6894(a,1),237(b,1,2)),rewrite([6260(7)]),flip(b)].
% 10.58/10.89 7921 identity != sk_c9 | sk_c9 != sk_c8 | multiply(sk_c9,multiply(sk_c8,sk_c9)) != sk_c8. [para(236(a,1),7313(d,1)),rewrite([7278(9),4(23)]),xx(c),merge(c),merge(e)].
% 10.58/10.89 7985 identity != sk_c9 | sk_c9 != sk_c8 | inverse(sk_c1) = sk_c9. [resolve(7921,c,15,b)].
% 10.58/10.89 8176 inverse(sk_c3) = sk_c9 | multiply(sk_c1,multiply(sk_c8,inverse(sk_c9))) = identity. [para(6894(a,1),245(b,2))].
% 10.58/10.89 8233 inverse(sk_c1) = sk_c9 | multiply(A,sk_c8) = A. [para(7691(b,1),238(b,1,2)),rewrite([6260(10)]),flip(c),merge(b)].
% 10.58/10.89 8357 inverse(sk_c1) = sk_c9 | multiply(A,sk_c9) = A. [para(7692(b,1),242(b,1,2)),rewrite([6260(10)]),flip(c),merge(b)].
% 10.58/10.89 9118 inverse(sk_c2) = sk_c8 | multiply(A,sk_c8) = A. [para(7694(b,1),254(b,1,2)),rewrite([6260(10)]),flip(c),merge(b)].
% 10.58/10.89 9612 inverse(sk_c2) = sk_c8 | multiply(A,sk_c9) = A. [para(7695(b,1),258(b,1,2)),rewrite([6260(10)]),flip(c),merge(b)].
% 10.58/10.89 9752 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c8) = sk_c8. [para(8357(b,1),15(b,1,2)),merge(b)].
% 10.58/10.89 9787 inverse(sk_c1) = sk_c9 | identity = sk_c3. [para(8357(b,1),7691(b,1)),flip(c),merge(b)].
% 10.58/10.89 9942 identity = sk_c3 | inverse(sk_c9) = sk_c1. [para(9787(a,1),7278(a,1,1))].
% 10.58/10.89 9943 identity = sk_c3 | multiply(sk_c1,sk_c9) = identity. [para(9787(a,1),6894(a,1,2))].
% 10.58/10.89 11425 inverse(sk_c2) = sk_c8 | sk_c3 = sk_c8. [para(9612(b,1),22(b,1)),merge(b)].
% 10.58/10.89 11426 inverse(sk_c2) = sk_c8 | multiply(sk_c9,sk_c8) = sk_c8. [para(9612(b,1),24(b,1,2)),merge(b)].
% 10.58/10.89 11438 inverse(sk_c2) = sk_c8 | identity = sk_c3. [para(9612(b,1),7694(b,1)),flip(c),merge(b)].
% 10.58/10.89 11476 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c2. [para(11425(a,1),7278(a,1,1))].
% 10.58/10.89 11548 identity = sk_c3 | inverse(sk_c8) = sk_c2. [para(11438(a,1),7278(a,1,1))].
% 10.58/10.89 11581 multiply(sk_c1,sk_c8) = sk_c9 | multiply(sk_c3,multiply(sk_c9,inverse(sk_c8))) = identity. [para(6894(a,1),269(b,2))].
% 10.58/10.89 12246 inverse(sk_c1) = sk_c9 | multiply(inverse(sk_c9),sk_c8) = sk_c8. [para(9752(b,1),236(a,1,2))].
% 10.58/10.89 12967 inverse(sk_c2) = sk_c8 | multiply(inverse(sk_c9),sk_c8) = sk_c8. [para(11426(b,1),236(a,1,2))].
% 10.58/10.89 12972 inverse(sk_c2) = sk_c8 | sk_c9 = sk_c8. [para(11426(b,1),9118(b,1)),flip(c),merge(b)].
% 10.58/10.89 12977 sk_c9 = sk_c8 | multiply(sk_c2,multiply(sk_c8,A)) = A. [para(12972(a,1),7277(a,1,2,1))].
% 10.58/10.89 14095 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(7697(a,1),236(a,1,2)),rewrite([6260(3)]),flip(a)].
% 10.58/10.89 14200 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(14095(a,1),236(a,1,2)),flip(a)].
% 10.58/10.89 15571 inverse(sk_c1) = sk_c9 | multiply(sk_c9,sk_c8) = sk_c3. [para(7704(b,1),239(b,2)),rewrite([6894(14),6260(12)]),merge(b)].
% 10.58/10.89 15582 inverse(sk_c1) = sk_c9 | sk_c3 = sk_c9. [para(15571(b,1),8233(b,1)),merge(b)].
% 10.58/10.89 15587 sk_c3 = sk_c9 | inverse(sk_c9) = sk_c1. [para(15582(a,1),7278(a,1,1))].
% 10.58/10.89 19423 inverse(sk_c2) = sk_c8 | inverse(sk_c9) = sk_c8. [para(12967(b,1),9118(b,1)),flip(c),merge(b)].
% 10.58/10.89 19428 inverse(sk_c9) = sk_c8 | inverse(sk_c8) = sk_c2. [para(19423(a,1),7278(a,1,1))].
% 10.58/10.89 19431 inverse(sk_c8) = sk_c2 | multiply(sk_c8,sk_c9) = identity. [para(19428(a,1),4(a,1,1))].
% 10.58/10.89 19563 inverse(sk_c8) = sk_c2 | identity != sk_c9 | sk_c9 != sk_c8. [para(19431(b,1),7921(c,1,2)),rewrite([6260(13)]),merge(d)].
% 10.58/10.89 19720 sk_c9 = sk_c8 | inverse(sk_c3) = sk_c9. [para(12977(b,1),28(a,1)),merge(b)].
% 10.58/10.89 19721 sk_c9 = sk_c8 | inverse(sk_c4) = sk_c8. [para(12977(b,1),30(a,1)),merge(b)].
% 10.58/10.89 19724 sk_c9 = sk_c8 | multiply(sk_c3,sk_c9) = sk_c8. [para(12977(b,1),41(a,1)),merge(b)].
% 10.58/10.89 19726 sk_c9 = sk_c8 | multiply(sk_c4,sk_c8) = sk_c9. [para(12977(b,1),45(a,1)),merge(b)].
% 10.58/10.89 19738 sk_c9 = sk_c8 | multiply(sk_c3,sk_c9) = identity. [para(19720(b,1),6894(a,1,2))].
% 10.58/10.89 19744 sk_c9 = sk_c8 | multiply(sk_c4,sk_c8) = identity. [para(19721(b,1),6894(a,1,2))].
% 10.58/10.89 19874 sk_c9 = sk_c8 | identity = sk_c8. [para(19738(b,1),19724(b,1)),merge(b)].
% 10.58/10.89 20057 sk_c9 = sk_c8 | identity = sk_c9. [para(19744(b,1),19726(b,1)),merge(b)].
% 10.58/10.89 20084 sk_c9 = sk_c8. [para(20057(b,1),19874(b,1)),merge(b),merge(c)].
% 10.58/10.89 20149 inverse(sk_c8) = sk_c2 | identity != sk_c8. [back_rewrite(19563),rewrite([20084(6),20084(8)]),xx(c)].
% 10.58/10.89 20761 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c1. [back_rewrite(15587),rewrite([20084(2),20084(4)])].
% 10.58/10.89 21485 inverse(sk_c1) = sk_c8 | identity = sk_c8. [back_rewrite(12246),rewrite([20084(3),20084(5),4(8)])].
% 10.58/10.89 21622 multiply(sk_c1,sk_c8) = sk_c8 | identity = sk_c3. [back_rewrite(11581),rewrite([20084(4),20084(7),6894(10),6260(8)]),flip(b)].
% 10.58/10.89 21870 identity = sk_c3 | multiply(sk_c1,sk_c8) = identity. [back_rewrite(9943),rewrite([20084(5)])].
% 10.58/10.89 21871 identity = sk_c3 | inverse(sk_c8) = sk_c1. [back_rewrite(9942),rewrite([20084(4)])].
% 10.58/10.89 22202 inverse(sk_c3) = sk_c8 | identity = sk_c1. [back_rewrite(8176),rewrite([20084(3),20084(7),6894(9),6260(7)]),flip(b)].
% 10.58/10.89 22246 identity != sk_c8 | inverse(sk_c1) = sk_c8. [back_rewrite(7985),rewrite([20084(2),20084(4),20084(9)]),xx(b)].
% 10.58/10.89 22385 inverse(A) != sk_c8 | multiply(A,sk_c8) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | inverse(B) != C | inverse(C) != sk_c8 | multiply(B,sk_c8) != C. [back_rewrite(7353),rewrite([20084(2),20084(6),20084(8),20084(11),20084(15),20084(17),20084(28),20084(30)]),xx(c),merge(c),merge(e)].
% 10.58/10.89 22630 sk_c3 = sk_c8 | sk_c2 = sk_c1. [para(20761(b,1),11476(b,1)),flip(c),merge(b)].
% 10.58/10.89 22801 identity = sk_c3 | sk_c2 = sk_c1. [para(21871(b,1),11548(b,1)),flip(c),merge(b)].
% 10.58/10.89 22830 sk_c2 = sk_c1 | identity = sk_c8. [para(22630(a,1),22801(a,2)),merge(c)].
% 10.58/10.89 22832 sk_c2 = sk_c1 | inverse(sk_c8) = sk_c2. [resolve(22830,b,20149,b)].
% 10.58/10.89 22943 inverse(A) != sk_c8 | multiply(A,sk_c8) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | identity != B | inverse(B) != sk_c8 | sk_c8 != B. [para(1(a,1),22385(f,1)),rewrite([6263(16)])].
% 10.58/10.89 23032 multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c8)) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | identity != C | inverse(C) != sk_c8 | sk_c8 != C. [para(48(a,1),22943(b,1)),rewrite([14200(2)])].
% 10.58/10.89 24115 inverse(sk_c1) = sk_c8 | sk_c2 = sk_c1. [resolve(22246,a,22830,b)].
% 10.58/10.89 24873 sk_c2 = sk_c1 | inverse(sk_c8) = sk_c1. [para(24115(a,1),7278(a,1,1))].
% 10.58/10.89 25288 multiply(sk_c8,inverse(A)) != sk_c8 | sk_c8 != A | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | identity != B | inverse(B) != sk_c8 | sk_c8 != B. [para(4(a,1),23032(b,1,2)),rewrite([7278(3),6260(7)]),flip(b)].
% 10.58/10.89 25299 multiply(sk_c8,A) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | identity != B | inverse(B) != sk_c8 | sk_c8 != B. [para(7278(a,1),25288(a,1,2)),flip(b)].
% 10.58/10.89 25306 multiply(sk_c8,A) != sk_c8 | inverse(A) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | identity != A | sk_c8 != A. [factor(25299,b,e)].
% 10.58/10.89 25352 sk_c8 != A | multiply(inverse(A),sk_c8) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | multiply(inverse(sk_c8),A) != identity | multiply(inverse(sk_c8),A) != sk_c8. [para(7277(a,1),25306(a,1)),rewrite([14200(6),7278(6)]),flip(a),flip(d),flip(e)].
% 10.58/10.89 25383 sk_c2 = sk_c1. [para(24873(b,1),22832(b,1)),flip(c),merge(b),merge(c)].
% 10.58/10.89 26896 inverse(sk_c8) = sk_c1 | identity != sk_c8. [back_rewrite(20149),rewrite([25383(3)])].
% 10.58/10.89 27405 inverse(A) != sk_c8 | multiply(A,sk_c8) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | multiply(inverse(sk_c8),inverse(A)) != identity | multiply(inverse(sk_c8),inverse(A)) != sk_c8. [para(7278(a,1),25352(b,1,1)),flip(a)].
% 10.58/10.89 27417 multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c8)) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | multiply(inverse(sk_c8),multiply(inverse(A),inverse(B))) != identity | multiply(inverse(sk_c8),multiply(inverse(A),inverse(B))) != sk_c8. [para(48(a,1),27405(b,1)),rewrite([14200(2),14200(21),14200(29)])].
% 10.58/10.89 28300 identity = sk_c3 | identity = sk_c8. [para(21870(b,1),21622(a,1)),merge(c)].
% 10.58/10.89 28319 identity = sk_c8 | inverse(sk_c3) = identity. [para(28300(a,1),6263(a,1,1))].
% 10.58/10.89 28336 identity = sk_c8 | identity = sk_c1. [para(28319(b,1),22202(a,1)),merge(b)].
% 10.58/10.89 28377 identity = sk_c8 | inverse(sk_c1) = identity. [para(28336(b,1),6263(a,1,1))].
% 10.58/10.89 28483 identity = sk_c8. [para(28377(b,1),21485(a,1)),merge(b),merge(c)].
% 10.58/10.89 28671 multiply(inverse(A),inverse(B)) != sk_c8 | multiply(B,multiply(A,sk_c8)) != sk_c8 | multiply(sk_c8,multiply(sk_c8,sk_c8)) != sk_c8 | multiply(inverse(sk_c8),multiply(inverse(A),inverse(B))) != sk_c8. [back_rewrite(27417),rewrite([28483(24)]),merge(e)].
% 10.58/10.89 28756 inverse(sk_c8) = sk_c1. [back_rewrite(26896),rewrite([28483(5)]),xx(b)].
% 10.58/10.89 29263 sk_c1 = sk_c8. [back_rewrite(6263),rewrite([28483(1),28756(2),28483(2)])].
% 10.58/10.89 29264 multiply(A,sk_c8) = A. [back_rewrite(6260),rewrite([28483(1)])].
% 10.58/10.89 29270 $F. [factor(28671,b,c),rewrite([28756(2),29263(1),28756(3),29263(2),29264(3),29264(7),29264(6),28756(8),29263(7),28756(9),29263(8),28756(10),29263(9),29264(10),29264(9)]),xx(a),xx(b),xx(c)].
% 10.58/10.89
% 10.58/10.89 % SZS output end Refutation
% 10.58/10.89 ============================== end of proof ==========================
% 10.58/10.89
% 10.58/10.89 ============================== STATISTICS ============================
% 10.58/10.89
% 10.58/10.89 Given=1416. Generated=191772. Kept=29256. proofs=1.
% 10.58/10.89 Usable=150. Sos=2073. Demods=20. Limbo=599, Disabled=26471. Hints=0.
% 10.58/10.89 Megabytes=29.84.
% 10.58/10.89 User_CPU=9.70, System_CPU=0.14, Wall_clock=10.
% 10.58/10.89
% 10.58/10.89 ============================== end of statistics =====================
% 10.58/10.89
% 10.58/10.89 ============================== end of search =========================
% 10.58/10.89
% 10.58/10.89 THEOREM PROVED
% 10.58/10.89 % SZS status Unsatisfiable
% 10.58/10.89
% 10.58/10.89 Exiting with 1 proof.
% 10.58/10.89
% 10.58/10.89 Process 10176 exit (max_proofs) Tue Jun 14 05:13:05 2022
% 10.58/10.89 Prover9 interrupted
%------------------------------------------------------------------------------