TSTP Solution File: GRP287-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP287-1 : 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 11:18:29 EDT 2022
% Result : Unsatisfiable 186.06s 186.37s
% Output : Refutation 186.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP287-1 : TPTP v8.1.0. Released v2.5.0.
% 0.14/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 13:47:39 EDT 2022
% 0.21/0.36 % CPUTime :
% 186.06/186.37 ============================== Prover9 ===============================
% 186.06/186.37 Prover9 (32) version 2009-11A, November 2009.
% 186.06/186.37 Process 29716 was started by sandbox on n019.cluster.edu,
% 186.06/186.37 Tue Jun 14 13:47:40 2022
% 186.06/186.37 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29563_n019.cluster.edu".
% 186.06/186.37 ============================== end of head ===========================
% 186.06/186.37
% 186.06/186.37 ============================== INPUT =================================
% 186.06/186.37
% 186.06/186.37 % Reading from file /tmp/Prover9_29563_n019.cluster.edu
% 186.06/186.37
% 186.06/186.37 set(prolog_style_variables).
% 186.06/186.37 set(auto2).
% 186.06/186.37 % set(auto2) -> set(auto).
% 186.06/186.37 % set(auto) -> set(auto_inference).
% 186.06/186.37 % set(auto) -> set(auto_setup).
% 186.06/186.37 % set(auto_setup) -> set(predicate_elim).
% 186.06/186.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 186.06/186.37 % set(auto) -> set(auto_limits).
% 186.06/186.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 186.06/186.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 186.06/186.37 % set(auto) -> set(auto_denials).
% 186.06/186.37 % set(auto) -> set(auto_process).
% 186.06/186.37 % set(auto2) -> assign(new_constants, 1).
% 186.06/186.37 % set(auto2) -> assign(fold_denial_max, 3).
% 186.06/186.37 % set(auto2) -> assign(max_weight, "200.000").
% 186.06/186.37 % set(auto2) -> assign(max_hours, 1).
% 186.06/186.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 186.06/186.37 % set(auto2) -> assign(max_seconds, 0).
% 186.06/186.37 % set(auto2) -> assign(max_minutes, 5).
% 186.06/186.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 186.06/186.37 % set(auto2) -> set(sort_initial_sos).
% 186.06/186.37 % set(auto2) -> assign(sos_limit, -1).
% 186.06/186.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 186.06/186.37 % set(auto2) -> assign(max_megs, 400).
% 186.06/186.37 % set(auto2) -> assign(stats, some).
% 186.06/186.37 % set(auto2) -> clear(echo_input).
% 186.06/186.37 % set(auto2) -> set(quiet).
% 186.06/186.37 % set(auto2) -> clear(print_initial_clauses).
% 186.06/186.37 % set(auto2) -> clear(print_given).
% 186.06/186.37 assign(lrs_ticks,-1).
% 186.06/186.37 assign(sos_limit,10000).
% 186.06/186.37 assign(order,kbo).
% 186.06/186.37 set(lex_order_vars).
% 186.06/186.37 clear(print_given).
% 186.06/186.37
% 186.06/186.37 % formulas(sos). % not echoed (29 formulas)
% 186.06/186.37
% 186.06/186.37 ============================== end of input ==========================
% 186.06/186.37
% 186.06/186.37 % From the command line: assign(max_seconds, 300).
% 186.06/186.37
% 186.06/186.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 186.06/186.37
% 186.06/186.37 % Formulas that are not ordinary clauses:
% 186.06/186.37
% 186.06/186.37 ============================== end of process non-clausal formulas ===
% 186.06/186.37
% 186.06/186.37 ============================== PROCESS INITIAL CLAUSES ===============
% 186.06/186.37
% 186.06/186.37 ============================== PREDICATE ELIMINATION =================
% 186.06/186.37
% 186.06/186.37 ============================== end predicate elimination =============
% 186.06/186.37
% 186.06/186.37 Auto_denials: (non-Horn, no changes).
% 186.06/186.37
% 186.06/186.37 Term ordering decisions:
% 186.06/186.37
% 186.06/186.37 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 186.06/186.37 Function symbol KB weights: sk_c6=1. sk_c7=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 186.06/186.37
% 186.06/186.37 ============================== end of process initial clauses ========
% 186.06/186.37
% 186.06/186.37 ============================== CLAUSES FOR SEARCH ====================
% 186.06/186.37
% 186.06/186.37 ============================== end of clauses for search =============
% 186.06/186.37
% 186.06/186.37 ============================== SEARCH ================================
% 186.06/186.37
% 186.06/186.37 % Starting search at 0.02 seconds.
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=40.000, iters=3456
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=38.000, iters=3406
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=37.000, iters=3350
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=36.000, iters=3417
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=35.000, iters=3351
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=34.000, iters=3334
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=33.000, iters=3497
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=32.000, iters=3359
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=31.000, iters=3354
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=30.000, iters=3348
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=29.000, iters=3481
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=28.000, iters=3475
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=26.000, iters=3367
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=25.000, iters=3342
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=24.000, iters=3458
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=17.000, iters=3344
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=16.000, iters=3335
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=15.000, iters=3354
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=14.000, iters=3336
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=13.000, iters=3334
% 186.06/186.37
% 186.06/186.37 Low Water (displace): id=4242, wt=48.000
% 186.06/186.37
% 186.06/186.37 Low Water (displace): id=18154, wt=12.000
% 186.06/186.37
% 186.06/186.37 Low Water (displace): id=18901, wt=11.000
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=12.000, iters=3335
% 186.06/186.37
% 186.06/186.37 Low Water (keep): wt=11.000, iters=3348
% 186.06/186.37
% 186.06/186.37 Low Water (displace): id=33795, wt=10.000
% 186.06/186.37
% 186.06/186.37 ============================== PROOF =================================
% 186.06/186.37 % SZS status Unsatisfiable
% 186.06/186.37 % SZS output start Refutation
% 186.06/186.37
% 186.06/186.37 % Proof 1 at 180.72 (+ 4.59) seconds.
% 186.06/186.37 % Length of proof is 160.
% 186.06/186.37 % Level of proof is 33.
% 186.06/186.37 % Maximum clause weight is 52.000.
% 186.06/186.37 % Given clauses 8667.
% 186.06/186.37
% 186.06/186.37 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 186.06/186.37 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 186.06/186.37 3 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 186.06/186.37 4 inverse(sk_c1) = sk_c7 | inverse(sk_c4) = sk_c6 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 186.06/186.37 5 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 186.06/186.37 6 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 186.06/186.37 7 multiply(sk_c7,sk_c6) = sk_c5 | inverse(sk_c3) = sk_c6 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 186.06/186.37 9 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 186.06/186.37 10 multiply(sk_c1,sk_c7) = sk_c6 | inverse(sk_c4) = sk_c6 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 186.06/186.37 11 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 186.06/186.37 12 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 186.06/186.37 13 inverse(sk_c1) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 186.06/186.37 14 multiply(sk_c2,sk_c6) = sk_c5 | inverse(sk_c3) = sk_c6 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 186.06/186.37 16 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 186.06/186.37 17 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 186.06/186.37 18 inverse(sk_c2) = sk_c6 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 186.06/186.37 19 multiply(sk_c7,sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 186.06/186.37 22 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 186.06/186.37 23 multiply(sk_c1,sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 186.06/186.37 25 multiply(sk_c2,sk_c6) = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 186.06/186.37 26 multiply(sk_c2,sk_c6) = sk_c5 | multiply(sk_c3,sk_c6) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 186.06/186.37 27 multiply(sk_c2,sk_c6) = sk_c5 | multiply(sk_c4,sk_c5) = sk_c6 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 186.06/186.37 28 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 186.06/186.37 29 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6 | inverse(D) != sk_c6 | multiply(D,sk_c5) != sk_c6 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 186.06/186.37 39 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 186.06/186.37 40 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 186.06/186.37 41 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 186.06/186.37 42 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c4) = identity. [para(6(b,1),2(a,1,1))].
% 186.06/186.37 43 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),28(a,1,1)),rewrite([1(2)]),flip(a)].
% 186.06/186.37 49 inverse(sk_c3) = sk_c6 | multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6). [para(9(a,1),28(a,2,2)),rewrite([28(8)])].
% 186.06/186.37 53 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5). [para(11(b,1),28(a,2,2)),rewrite([28(8)])].
% 186.06/186.37 55 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(12(b,1),28(a,2,2)),rewrite([28(8)])].
% 186.06/186.37 56 inverse(sk_c1) = sk_c7 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(13(b,1),28(a,1,1)),flip(b)].
% 186.06/186.37 58 inverse(sk_c3) = sk_c6 | multiply(sk_c2,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(14(a,1),28(a,1,1)),flip(b)].
% 186.06/186.37 65 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7). [para(17(b,1),28(a,2,2)),rewrite([28(8)])].
% 186.06/186.37 66 inverse(sk_c2) = sk_c6 | multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A). [para(18(b,1),28(a,1,1)),flip(b)].
% 186.06/186.37 69 multiply(sk_c6,sk_c7) = sk_c5 | multiply(A,multiply(sk_c7,sk_c6)) = multiply(A,sk_c5). [para(19(a,1),28(a,2,2)),rewrite([28(9)])].
% 186.06/186.37 106 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c7 | inverse(inverse(sk_c6)) != sk_c6 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(2(a,1),29(g,1))].
% 186.06/186.37 331 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c6,sk_c3)) = multiply(A,identity). [para(39(b,1),28(a,2,2)),rewrite([28(8)])].
% 186.06/186.37 346 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),43(a,1,2))].
% 186.06/186.37 356 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(13(b,1),43(a,1,2))].
% 186.06/186.37 359 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(16(b,1),43(a,1,2))].
% 186.06/186.37 360 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c6. [para(17(b,1),43(a,1,2))].
% 186.06/186.37 361 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c4),sk_c6) = sk_c5. [para(18(b,1),43(a,1,2))].
% 186.06/186.37 373 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(43(a,1),43(a,1,2))].
% 186.06/186.37 374 multiply(A,identity) = A. [back_rewrite(346),rewrite([373(4)])].
% 186.06/186.37 376 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c6,sk_c3)) = A. [back_rewrite(331),rewrite([374(10)])].
% 186.06/186.37 377 inverse(identity) = identity. [para(374(a,1),2(a,1))].
% 186.06/186.37 409 inverse(sk_c1) = sk_c7 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(40(b,1),28(a,2,2)),rewrite([28(8),374(10)])].
% 186.06/186.37 413 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c6,sk_c3)) = A. [para(41(b,1),28(a,2,2)),rewrite([28(8),374(10)])].
% 186.06/186.37 414 inverse(sk_c2) = sk_c6 | inverse(sk_c6) = sk_c3. [para(41(b,1),43(a,1,2)),rewrite([374(8)])].
% 186.06/186.37 417 inverse(sk_c2) = sk_c6 | multiply(A,multiply(sk_c6,sk_c4)) = A. [para(42(b,1),28(a,2,2)),rewrite([28(8),374(10)])].
% 186.06/186.37 439 multiply(A,inverse(A)) = identity. [para(373(a,1),2(a,1))].
% 186.06/186.37 440 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),A) = multiply(sk_c3,A). [para(3(b,1),373(a,1,1,1))].
% 186.06/186.37 442 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c6),A) = multiply(sk_c3,A). [para(5(b,1),373(a,1,1,1))].
% 186.06/186.37 469 multiply(A,multiply(inverse(A),B)) = B. [para(373(a,1),43(a,1))].
% 186.06/186.37 470 inverse(inverse(A)) = A. [para(373(a,1),374(a,1)),rewrite([374(2)]),flip(a)].
% 186.06/186.37 473 inverse(sk_c6) = sk_c3 | multiply(inverse(sk_c6),A) = multiply(sk_c2,A). [para(414(a,1),373(a,1,1,1))].
% 186.06/186.37 499 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | identity != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [back_rewrite(106),rewrite([470(30)]),xx(h)].
% 186.06/186.37 506 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c6) = identity. [para(3(b,1),439(a,1,2))].
% 186.06/186.37 508 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(5(b,1),439(a,1,2))].
% 186.06/186.37 510 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(439(a,1),28(a,1)),flip(a)].
% 186.06/186.37 654 inverse(sk_c1) = sk_c7 | identity = sk_c7. [para(506(b,1),12(b,1)),merge(b)].
% 186.06/186.37 657 inverse(sk_c3) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c1,sk_c7)) = identity. [para(2(a,1),49(b,2))].
% 186.06/186.37 689 identity = sk_c7 | multiply(sk_c1,sk_c7) = identity. [para(654(a,1),439(a,1,2))].
% 186.06/186.37 751 inverse(sk_c2) = sk_c6 | identity = sk_c7. [para(508(b,1),17(b,1)),merge(b)].
% 186.06/186.37 756 identity = sk_c7 | multiply(sk_c2,sk_c6) = identity. [para(751(a,1),439(a,1,2))].
% 186.06/186.37 1318 inverse(sk_c1) = sk_c7 | multiply(A,sk_c7) = A. [para(506(b,1),55(b,1,2)),rewrite([374(10)]),flip(c),merge(b)].
% 186.06/186.37 1813 inverse(sk_c3) = sk_c6 | multiply(inverse(sk_c2),multiply(sk_c5,A)) = multiply(sk_c6,A). [para(58(b,1),43(a,1,2))].
% 186.06/186.37 2010 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c6) = sk_c5. [para(4(b,1),356(b,1,1)),merge(b)].
% 186.06/186.37 2042 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c6),sk_c5) = sk_c6. [para(2010(b,1),43(a,1,2))].
% 186.06/186.37 2438 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c7) = sk_c6. [para(5(b,1),360(b,1,1)),merge(b)].
% 186.06/186.37 2464 inverse(sk_c2) = sk_c6 | sk_c5 = sk_c6. [para(2438(b,1),16(b,1)),flip(c),merge(b)].
% 186.06/186.37 2574 sk_c5 = sk_c6 | inverse(sk_c6) = sk_c2. [para(2464(a,1),470(a,1,1))].
% 186.06/186.37 2769 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(510(a,1),43(a,1,2)),rewrite([374(3)]),flip(a)].
% 186.06/186.37 2806 inverse(sk_c3) = sk_c6 | multiply(sk_c6,inverse(sk_c5)) = inverse(sk_c7). [para(7(a,1),2769(a,1,2,1))].
% 186.06/186.37 2826 multiply(sk_c2,sk_c6) = sk_c5 | multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4). [para(27(b,1),2769(a,1,2,1))].
% 186.06/186.37 2830 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(2769(a,1),43(a,1,2)),flip(a)].
% 186.06/186.37 3761 inverse(sk_c2) = sk_c6 | multiply(A,sk_c7) = A. [para(508(b,1),65(b,1,2)),rewrite([374(10)]),flip(c),merge(b)].
% 186.06/186.37 4483 multiply(sk_c6,sk_c7) = sk_c5 | multiply(inverse(sk_c5),multiply(sk_c7,sk_c6)) = identity. [para(2(a,1),69(b,2))].
% 186.06/186.37 11534 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | multiply(A,sk_c6) != sk_c5 | inverse(A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [para(1(a,1),499(b,1)),rewrite([377(10)]),merge(g)].
% 186.06/186.37 11539 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | multiply(A,multiply(B,sk_c6)) != sk_c5 | multiply(inverse(B),inverse(A)) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6. [para(28(a,1),11534(d,1)),rewrite([2830(18)])].
% 186.06/186.37 11568 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | sk_c5 != A | multiply(sk_c6,inverse(A)) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c6 | multiply(B,sk_c5) != sk_c6. [para(2(a,1),11539(d,1,2)),rewrite([374(13),470(16)]),flip(d)].
% 186.06/186.37 11571 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | sk_c5 != A | multiply(sk_c6,inverse(A)) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(B),inverse(C)) != sk_c6 | multiply(C,multiply(B,sk_c5)) != sk_c6. [para(28(a,1),11568(h,1)),rewrite([2830(25)])].
% 186.06/186.37 11803 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | sk_c5 != A | multiply(sk_c6,inverse(A)) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(2(a,1),11571(h,1,2)),rewrite([470(26),374(30)]),flip(h)].
% 186.06/186.37 11806 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c5,inverse(B)) != sk_c6 | sk_c6 != B. [para(470(a,1),11803(e,1,2)),flip(d)].
% 186.06/186.37 11811 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c5,B) != sk_c6 | inverse(B) != sk_c6. [para(470(a,1),11806(g,1,2)),flip(h)].
% 186.06/186.37 11830 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | sk_c6 != B | multiply(inverse(B),sk_c5) != sk_c6. [para(469(a,1),11811(g,1)),rewrite([2830(29),470(29)]),flip(g)].
% 186.06/186.37 11867 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(B,C) != sk_c6 | multiply(inverse(C),multiply(inverse(B),sk_c5)) != sk_c6. [para(2830(a,1),11830(h,1,1)),rewrite([28(31)]),flip(g)].
% 186.06/186.37 12414 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(B,inverse(C)) != sk_c6 | multiply(C,multiply(inverse(B),sk_c5)) != sk_c6. [para(470(a,1),11867(h,1,1))].
% 186.06/186.37 13248 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(B,multiply(inverse(C),inverse(D))) != sk_c6 | multiply(D,multiply(C,multiply(inverse(B),sk_c5))) != sk_c6. [para(28(a,1),12414(h,1)),rewrite([2830(25)])].
% 186.06/186.37 14777 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c7. [para(440(b,1),53(b,2)),rewrite([43(14)]),flip(c),merge(b)].
% 186.06/186.37 14781 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = sk_c6. [para(440(b,1),2042(b,1)),merge(b)].
% 186.06/186.37 14827 inverse(sk_c2) = sk_c6 | multiply(sk_c3,sk_c5) = sk_c7. [para(442(b,1),359(b,1)),merge(b)].
% 186.06/186.37 15555 inverse(sk_c1) = sk_c7 | multiply(inverse(sk_c3),sk_c7) = sk_c5. [para(14777(b,1),43(a,1,2))].
% 186.06/186.37 15594 inverse(sk_c2) = sk_c6 | multiply(inverse(sk_c3),sk_c7) = sk_c5. [para(14827(b,1),43(a,1,2))].
% 186.06/186.37 17051 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c5. [para(15555(b,1),1318(b,1)),flip(c),merge(b)].
% 186.06/186.37 17068 inverse(sk_c1) = sk_c7 | multiply(sk_c5,sk_c3) = identity. [para(17051(b,1),2(a,1,1))].
% 186.06/186.37 17071 inverse(sk_c1) = sk_c7 | multiply(sk_c3,sk_c5) = identity. [para(17051(b,1),439(a,1,2))].
% 186.06/186.37 17116 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = sk_c4. [para(17068(b,1),56(b,1,2)),rewrite([374(11)]),flip(c),merge(b)].
% 186.06/186.37 17122 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(17071(b,1),14781(b,1)),merge(b)].
% 186.06/186.37 17126 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(17122(a,1),439(a,1,2))].
% 186.06/186.37 17176 identity = sk_c6 | inverse(sk_c4) = sk_c6. [para(17126(b,1),10(a,1)),merge(b)].
% 186.06/186.37 17177 identity = sk_c6 | multiply(sk_c6,sk_c7) = sk_c5. [para(17126(b,1),22(a,1)),merge(b)].
% 186.06/186.37 17219 identity = sk_c6 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(17177(b,1),43(a,1,2))].
% 186.06/186.37 17326 inverse(sk_c1) = sk_c7 | multiply(A,sk_c4) = A. [para(17116(b,1),376(b,1,2)),merge(b)].
% 186.06/186.37 17432 identity = sk_c6 | multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7). [para(17219(b,1),2830(a,1,1)),rewrite([470(10)]),flip(b)].
% 186.06/186.37 17479 inverse(sk_c1) = sk_c7 | multiply(A,sk_c6) = A. [para(17326(b,1),409(b,1,2)),merge(b)].
% 186.06/186.37 17622 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = identity. [para(17479(b,1),2(a,1))].
% 186.06/186.37 17673 inverse(sk_c6) = identity | multiply(sk_c1,sk_c7) = identity. [para(17622(a,1),439(a,1,2))].
% 186.06/186.37 18044 inverse(sk_c6) = identity | inverse(sk_c3) = sk_c6. [para(17673(b,1),657(b,1,2)),rewrite([374(12)]),merge(c)].
% 186.06/186.37 18048 inverse(sk_c6) = identity | inverse(sk_c6) = sk_c3. [para(18044(b,1),470(a,1,1))].
% 186.06/186.37 18069 inverse(sk_c6) = sk_c3 | multiply(sk_c2,A) = A. [para(18048(a,1),473(b,1,1)),rewrite([1(10)]),flip(c),merge(b)].
% 186.06/186.37 18303 inverse(sk_c6) = sk_c3 | inverse(sk_c2) = identity. [para(18069(b,1),439(a,1))].
% 186.06/186.37 18739 inverse(sk_c2) = sk_c6 | inverse(sk_c3) = sk_c5. [para(15594(b,1),3761(b,1)),flip(c),merge(b)].
% 186.06/186.37 18764 inverse(sk_c2) = sk_c6 | multiply(sk_c5,sk_c3) = identity. [para(18739(b,1),2(a,1,1))].
% 186.06/186.37 18805 inverse(sk_c2) = sk_c6 | multiply(sk_c6,sk_c3) = sk_c4. [para(18764(b,1),66(b,1,2)),rewrite([374(11)]),flip(c),merge(b)].
% 186.06/186.37 19390 inverse(sk_c2) = sk_c6 | multiply(A,sk_c4) = A. [para(18805(b,1),413(b,1,2)),merge(b)].
% 186.06/186.37 19872 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = identity. [para(19390(b,1),2(a,1))].
% 186.06/186.37 19900 inverse(sk_c2) = sk_c6 | multiply(A,sk_c6) = A. [para(19390(b,1),417(b,1,2)),merge(b)].
% 186.06/186.37 20231 inverse(sk_c2) = sk_c6 | inverse(sk_c4) = sk_c5. [para(19900(b,1),361(b,1)),merge(b)].
% 186.06/186.37 20282 inverse(sk_c2) = sk_c6 | identity = sk_c5. [para(20231(b,1),19872(b,1)),flip(c),merge(b)].
% 186.06/186.37 20290 identity = sk_c5 | inverse(sk_c6) = sk_c2. [para(20282(a,1),470(a,1,1))].
% 186.06/186.37 20291 identity = sk_c5 | multiply(sk_c2,sk_c6) = identity. [para(20282(a,1),439(a,1,2))].
% 186.06/186.37 20746 identity = sk_c5 | multiply(sk_c6,sk_c7) = sk_c5. [para(20291(b,1),25(a,1)),merge(b)].
% 186.06/186.37 21009 identity = sk_c5 | multiply(inverse(sk_c6),sk_c5) = sk_c7. [para(20746(b,1),43(a,1,2))].
% 186.06/186.37 21572 identity = sk_c5 | multiply(sk_c2,sk_c5) = sk_c7. [para(20290(b,1),21009(b,1,1)),merge(b)].
% 186.06/186.37 21586 identity = sk_c5 | multiply(inverse(sk_c2),sk_c7) = sk_c5. [para(21572(b,1),43(a,1,2))].
% 186.06/186.37 24861 identity = sk_c6 | multiply(sk_c5,inverse(sk_c7)) = sk_c6. [para(17432(b,1),43(a,1,2)),rewrite([470(6)])].
% 186.06/186.37 29200 multiply(sk_c7,sk_c6) != sk_c5 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c5 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(B,multiply(inverse(C),multiply(inverse(D),inverse(E)))) != sk_c6 | multiply(E,multiply(D,multiply(C,multiply(inverse(B),sk_c5)))) != sk_c6. [para(28(a,1),13248(h,1,2)),rewrite([2830(25),28(28)])].
% 186.06/186.37 32745 inverse(sk_c3) = sk_c6 | inverse(sk_c2) = inverse(sk_c7). [para(2806(b,1),1813(b,2)),rewrite([439(14),374(12)]),merge(b)].
% 186.06/186.37 32758 inverse(sk_c2) = inverse(sk_c7) | inverse(sk_c6) = sk_c3. [para(32745(a,1),470(a,1,1))].
% 186.06/186.37 32764 inverse(sk_c6) = sk_c3 | inverse(sk_c7) = identity. [para(32758(a,1),18303(b,1)),merge(b)].
% 186.06/186.37 32983 inverse(sk_c6) = sk_c3 | identity = sk_c7. [para(32764(b,1),2(a,1,1)),rewrite([1(7)]),flip(b)].
% 186.06/186.37 32986 identity = sk_c7 | multiply(sk_c3,sk_c6) = identity. [para(32983(a,1),2(a,1,1))].
% 186.06/186.37 33232 identity = sk_c7 | multiply(sk_c1,sk_c7) = sk_c6. [para(32986(b,1),23(b,1)),merge(c)].
% 186.06/186.37 33233 identity = sk_c7 | multiply(sk_c2,sk_c6) = sk_c5. [para(32986(b,1),26(b,1)),merge(c)].
% 186.06/186.37 33383 identity = sk_c7 | identity = sk_c6. [para(33232(b,1),689(b,1)),flip(c),merge(b)].
% 186.06/186.37 33403 identity = sk_c6 | inverse(sk_c7) = identity. [para(33383(a,1),377(a,1,1))].
% 186.06/186.37 33439 identity = sk_c6 | sk_c5 = sk_c6. [para(33403(b,1),24861(b,1,2)),rewrite([374(9)]),merge(b)].
% 186.06/186.37 33478 sk_c5 = sk_c6 | inverse(sk_c6) = identity. [para(33439(a,1),377(a,1,1))].
% 186.06/186.37 33618 sk_c5 = sk_c6 | identity = sk_c2. [para(33478(b,1),2574(b,1)),merge(b)].
% 186.06/186.37 33688 multiply(sk_c5,inverse(sk_c6)) = inverse(sk_c4) | identity = sk_c5. [para(2826(a,1),20291(b,1)),flip(c),merge(c)].
% 186.06/186.37 33988 identity = sk_c7 | identity = sk_c5. [para(33233(b,1),756(b,1)),flip(c),merge(b)].
% 186.06/186.37 34002 identity = sk_c7 | sk_c5 = sk_c6. [para(33988(b,1),33439(a,1)),merge(c)].
% 186.06/186.37 34031 sk_c5 = sk_c6 | sk_c2 = sk_c7. [para(34002(a,1),33618(b,1)),flip(c),merge(b)].
% 186.06/186.37 34071 sk_c5 = sk_c6 | identity = sk_c5. [para(34031(b,1),21586(b,1,1,1)),rewrite([2(10)]),merge(c)].
% 186.06/186.37 34127 sk_c5 = sk_c6. [para(34071(b,1),33439(a,1)),merge(b),merge(c)].
% 186.06/186.37 34198 inverse(sk_c4) = identity | identity = sk_c6. [back_rewrite(33688),rewrite([34127(1),439(4),34127(6)]),flip(a)].
% 186.06/186.37 34889 multiply(sk_c7,sk_c6) != sk_c6 | sk_c7 != sk_c6 | identity != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c6,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | multiply(B,multiply(inverse(C),multiply(inverse(D),inverse(E)))) != sk_c6 | multiply(E,multiply(D,multiply(C,multiply(inverse(B),sk_c6)))) != sk_c6. [back_rewrite(29200),rewrite([34127(4),34127(13),34127(22),34127(33)])].
% 186.06/186.37 37397 multiply(sk_c6,sk_c7) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c7,sk_c6)) = identity. [back_rewrite(4483),rewrite([34127(4),34127(6)])].
% 186.06/186.37 38493 multiply(sk_c7,sk_c6) != sk_c6 | sk_c7 != sk_c6 | identity != sk_c7 | multiply(inverse(sk_c6),multiply(A,multiply(inverse(B),inverse(C)))) != sk_c6 | multiply(sk_c6,multiply(C,multiply(B,multiply(inverse(A),sk_c6)))) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | multiply(A,multiply(inverse(B),multiply(inverse(C),inverse(sk_c6)))) != sk_c6. [factor(34889,e,h),rewrite([2830(17),2830(16),2830(15),470(15),28(16),28(18),28(17)])].
% 186.06/186.37 38663 identity = sk_c6. [para(34198(a,1),17176(b,1)),merge(b),merge(c)].
% 186.06/186.37 38743 multiply(sk_c7,sk_c6) != sk_c6 | sk_c7 != sk_c6 | multiply(inverse(sk_c6),multiply(A,multiply(inverse(B),inverse(C)))) != sk_c6 | multiply(sk_c6,multiply(C,multiply(B,multiply(inverse(A),sk_c6)))) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c6 | multiply(A,multiply(inverse(B),multiply(inverse(C),inverse(sk_c6)))) != sk_c6. [back_rewrite(38493),rewrite([38663(9)]),flip(c),merge(c)].
% 186.06/186.37 38779 multiply(sk_c6,sk_c7) = sk_c6 | multiply(inverse(sk_c6),multiply(sk_c7,sk_c6)) = sk_c6. [back_rewrite(37397),rewrite([38663(12)])].
% 186.06/186.37 39240 inverse(sk_c6) = sk_c6. [back_rewrite(377),rewrite([38663(1),38663(3)])].
% 186.06/186.37 39241 multiply(A,sk_c6) = A. [back_rewrite(374),rewrite([38663(1)])].
% 186.06/186.37 39243 multiply(sk_c6,A) = A. [back_rewrite(1),rewrite([38663(1)])].
% 186.06/186.37 39245 sk_c7 != sk_c6. [factor(38743,c,f),rewrite([39241(3),39240(8),39240(9),39240(10),39240(11),39241(11),39241(10),39241(9),39240(14),39240(14),39241(15),39241(14),39241(13),39241(12),39243(15)]),xx(c),xx(d),merge(b),merge(c)].
% 186.06/186.37 39264 $F. [back_rewrite(38779),rewrite([39243(3),39240(5),39241(7),39243(6)]),merge(b),unit_del(a,39245)].
% 186.06/186.37
% 186.06/186.37 % SZS output end Refutation
% 186.06/186.37 ============================== end of proof ==========================
% 186.06/186.37
% 186.06/186.37 ============================== STATISTICS ============================
% 186.06/186.37
% 186.06/186.37 Given=8667. Generated=8944545. Kept=39263. proofs=1.
% 186.06/186.37 Usable=1361. Sos=3162. Demods=23. Limbo=24, Disabled=34745. Hints=0.
% 186.06/186.37 Megabytes=34.34.
% 186.06/186.37 User_CPU=180.72, System_CPU=4.59, Wall_clock=185.
% 186.06/186.37
% 186.06/186.37 ============================== end of statistics =====================
% 186.06/186.37
% 186.06/186.37 ============================== end of search =========================
% 186.06/186.37
% 186.06/186.37 THEOREM PROVED
% 186.06/186.37 % SZS status Unsatisfiable
% 186.06/186.37
% 186.06/186.37 Exiting with 1 proof.
% 186.06/186.37
% 186.06/186.37 Process 29716 exit (max_proofs) Tue Jun 14 13:50:45 2022
% 186.06/186.37 Prover9 interrupted
%------------------------------------------------------------------------------