TSTP Solution File: GRP387-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP387-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 19.26s 19.59s
% Output : Refutation 19.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP387-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n006.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 08:01:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 19.26/19.59 ============================== Prover9 ===============================
% 19.26/19.59 Prover9 (32) version 2009-11A, November 2009.
% 19.26/19.59 Process 14029 was started by sandbox2 on n006.cluster.edu,
% 19.26/19.59 Tue Jun 14 08:01:42 2022
% 19.26/19.59 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13876_n006.cluster.edu".
% 19.26/19.59 ============================== end of head ===========================
% 19.26/19.59
% 19.26/19.59 ============================== INPUT =================================
% 19.26/19.59
% 19.26/19.59 % Reading from file /tmp/Prover9_13876_n006.cluster.edu
% 19.26/19.59
% 19.26/19.59 set(prolog_style_variables).
% 19.26/19.59 set(auto2).
% 19.26/19.59 % set(auto2) -> set(auto).
% 19.26/19.59 % set(auto) -> set(auto_inference).
% 19.26/19.59 % set(auto) -> set(auto_setup).
% 19.26/19.59 % set(auto_setup) -> set(predicate_elim).
% 19.26/19.59 % set(auto_setup) -> assign(eq_defs, unfold).
% 19.26/19.59 % set(auto) -> set(auto_limits).
% 19.26/19.59 % set(auto_limits) -> assign(max_weight, "100.000").
% 19.26/19.59 % set(auto_limits) -> assign(sos_limit, 20000).
% 19.26/19.59 % set(auto) -> set(auto_denials).
% 19.26/19.59 % set(auto) -> set(auto_process).
% 19.26/19.59 % set(auto2) -> assign(new_constants, 1).
% 19.26/19.59 % set(auto2) -> assign(fold_denial_max, 3).
% 19.26/19.59 % set(auto2) -> assign(max_weight, "200.000").
% 19.26/19.59 % set(auto2) -> assign(max_hours, 1).
% 19.26/19.59 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 19.26/19.59 % set(auto2) -> assign(max_seconds, 0).
% 19.26/19.59 % set(auto2) -> assign(max_minutes, 5).
% 19.26/19.59 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 19.26/19.59 % set(auto2) -> set(sort_initial_sos).
% 19.26/19.59 % set(auto2) -> assign(sos_limit, -1).
% 19.26/19.59 % set(auto2) -> assign(lrs_ticks, 3000).
% 19.26/19.59 % set(auto2) -> assign(max_megs, 400).
% 19.26/19.59 % set(auto2) -> assign(stats, some).
% 19.26/19.59 % set(auto2) -> clear(echo_input).
% 19.26/19.59 % set(auto2) -> set(quiet).
% 19.26/19.59 % set(auto2) -> clear(print_initial_clauses).
% 19.26/19.59 % set(auto2) -> clear(print_given).
% 19.26/19.59 assign(lrs_ticks,-1).
% 19.26/19.59 assign(sos_limit,10000).
% 19.26/19.59 assign(order,kbo).
% 19.26/19.59 set(lex_order_vars).
% 19.26/19.59 clear(print_given).
% 19.26/19.59
% 19.26/19.59 % formulas(sos). % not echoed (34 formulas)
% 19.26/19.59
% 19.26/19.59 ============================== end of input ==========================
% 19.26/19.59
% 19.26/19.59 % From the command line: assign(max_seconds, 300).
% 19.26/19.59
% 19.26/19.59 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 19.26/19.59
% 19.26/19.59 % Formulas that are not ordinary clauses:
% 19.26/19.59
% 19.26/19.59 ============================== end of process non-clausal formulas ===
% 19.26/19.59
% 19.26/19.59 ============================== PROCESS INITIAL CLAUSES ===============
% 19.26/19.59
% 19.26/19.59 ============================== PREDICATE ELIMINATION =================
% 19.26/19.59
% 19.26/19.59 ============================== end predicate elimination =============
% 19.26/19.59
% 19.26/19.59 Auto_denials: (non-Horn, no changes).
% 19.26/19.59
% 19.26/19.59 Term ordering decisions:
% 19.26/19.59
% 19.26/19.59 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 19.26/19.59 Function symbol KB weights: sk_c7=1. sk_c6=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 19.26/19.59
% 19.26/19.59 ============================== end of process initial clauses ========
% 19.26/19.59
% 19.26/19.59 ============================== CLAUSES FOR SEARCH ====================
% 19.26/19.59
% 19.26/19.59 ============================== end of clauses for search =============
% 19.26/19.59
% 19.26/19.59 ============================== SEARCH ================================
% 19.26/19.59
% 19.26/19.59 % Starting search at 0.01 seconds.
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=45.000, iters=3412
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=44.000, iters=3353
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=43.000, iters=3335
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=42.000, iters=3333
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=41.000, iters=3443
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=40.000, iters=3371
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=39.000, iters=3343
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=38.000, iters=3380
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=37.000, iters=3334
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=36.000, iters=3497
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=35.000, iters=3349
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=34.000, iters=3341
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=33.000, iters=3588
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=19.000, iters=3345
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=16.000, iters=3432
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=15.000, iters=3582
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=14.000, iters=3421
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=13.000, iters=3334
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=12.000, iters=3375
% 19.26/19.59
% 19.26/19.59 Low Water (keep): wt=11.000, iters=3333
% 19.26/19.59
% 19.26/19.59 ============================== PROOF =================================
% 19.26/19.59 % SZS status Unsatisfiable
% 19.26/19.59 % SZS output start Refutation
% 19.26/19.59
% 19.26/19.59 % Proof 1 at 18.11 (+ 0.46) seconds.
% 19.26/19.59 % Length of proof is 122.
% 19.26/19.59 % Level of proof is 28.
% 19.26/19.59 % Maximum clause weight is 50.000.
% 19.26/19.59 % Given clauses 3915.
% 19.26/19.59
% 19.26/19.59 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 19.26/19.59 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 19.26/19.59 3 inverse(sk_c7) = sk_c6 | inverse(sk_c2) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 19.26/19.59 4 inverse(sk_c7) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 19.26/19.59 5 inverse(sk_c7) = sk_c6 | inverse(sk_c4) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 19.26/19.59 6 inverse(sk_c1) = sk_c7 | inverse(sk_c2) = sk_c7 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 19.26/19.59 7 inverse(sk_c1) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 19.26/19.59 9 inverse(sk_c7) = sk_c6 | multiply(sk_c2,sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 19.26/19.59 10 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c5 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 19.26/19.59 11 inverse(sk_c7) = sk_c6 | multiply(sk_c4,sk_c7) = sk_c5 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 19.26/19.59 12 multiply(sk_c6,sk_c5) = sk_c7 | inverse(sk_c2) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 19.26/19.59 15 multiply(sk_c7,sk_c5) = sk_c6 | inverse(sk_c2) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 19.26/19.59 16 multiply(sk_c7,sk_c5) = sk_c6 | inverse(sk_c3) = sk_c6 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 19.26/19.59 18 inverse(sk_c1) = sk_c7 | multiply(sk_c2,sk_c7) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 19.26/19.59 21 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c2) = sk_c7 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 19.26/19.59 22 multiply(sk_c1,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c6 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 19.26/19.59 24 multiply(sk_c6,sk_c5) = sk_c7 | multiply(sk_c2,sk_c7) = sk_c6 # label(prove_this_7) # label(negated_conjecture). [assumption].
% 19.26/19.59 27 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c2,sk_c7) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 19.26/19.59 28 multiply(sk_c7,sk_c5) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c5 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 19.26/19.59 30 multiply(sk_c1,sk_c6) = sk_c7 | multiply(sk_c2,sk_c7) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 19.26/19.59 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 19.26/19.59 34 inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(B,sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(C,sk_c6) != sk_c5 | inverse(C) != sk_c6 | inverse(D) != sk_c5 | multiply(D,sk_c7) != sk_c5 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 19.26/19.59 36 inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(A,sk_c7) != sk_c6 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | inverse(C) != sk_c5 | multiply(C,sk_c7) != sk_c5. [factor(34,d,g)].
% 19.26/19.59 38 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c2) = identity. [para(3(b,1),2(a,1,1))].
% 19.26/19.59 39 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c3) = identity. [para(4(b,1),2(a,1,1))].
% 19.26/19.59 40 inverse(sk_c7) = sk_c6 | multiply(sk_c5,sk_c4) = identity. [para(5(b,1),2(a,1,1))].
% 19.26/19.59 42 inverse(sk_c1) = sk_c7 | multiply(sk_c6,sk_c3) = identity. [para(7(b,1),2(a,1,1))].
% 19.26/19.59 44 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 19.26/19.59 45 inverse(sk_c7) = sk_c6 | multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(9(b,1),33(a,1,1)),flip(b)].
% 19.26/19.59 46 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c6). [para(9(b,1),33(a,2,2)),rewrite([33(8)])].
% 19.26/19.59 47 inverse(sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c5,A). [para(10(b,1),33(a,1,1)),flip(b)].
% 19.26/19.59 48 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c5). [para(10(b,1),33(a,2,2)),rewrite([33(8)])].
% 19.26/19.59 52 inverse(sk_c2) = sk_c7 | multiply(A,multiply(sk_c6,sk_c5)) = multiply(A,sk_c7). [para(12(a,1),33(a,2,2)),rewrite([33(8)])].
% 19.26/19.59 60 inverse(sk_c3) = sk_c6 | multiply(A,multiply(sk_c7,sk_c5)) = multiply(A,sk_c6). [para(16(a,1),33(a,2,2)),rewrite([33(8)])].
% 19.26/19.59 69 inverse(sk_c2) = sk_c7 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(21(a,1),33(a,1,1)),flip(b)].
% 19.26/19.59 71 inverse(sk_c3) = sk_c6 | multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c7,A). [para(22(a,1),33(a,1,1)),flip(b)].
% 19.26/19.59 241 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),44(a,1,2))].
% 19.26/19.59 247 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c2),sk_c6) = sk_c7. [para(9(b,1),44(a,1,2))].
% 19.26/19.59 249 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c4),sk_c5) = sk_c7. [para(11(b,1),44(a,1,2))].
% 19.26/19.59 271 multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C. [para(33(a,1),44(a,1,2))].
% 19.26/19.59 272 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c7),identity) = sk_c2. [para(38(b,1),44(a,1,2))].
% 19.26/19.59 273 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(44(a,1),44(a,1,2))].
% 19.26/19.59 274 multiply(A,identity) = A. [back_rewrite(241),rewrite([273(4)])].
% 19.26/19.59 275 inverse(sk_c7) = sk_c6 | inverse(sk_c7) = sk_c2. [back_rewrite(272),rewrite([274(8)])].
% 19.26/19.59 277 inverse(identity) = identity. [para(274(a,1),2(a,1))].
% 19.26/19.59 320 inverse(sk_c7) = sk_c6 | multiply(sk_c2,sk_c7) = identity. [para(275(b,1),2(a,1,1))].
% 19.26/19.59 323 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c3. [para(39(b,1),44(a,1,2)),rewrite([274(8)])].
% 19.26/19.59 335 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = identity. [para(323(b,1),2(a,1,1))].
% 19.26/19.59 344 inverse(sk_c1) = sk_c7 | inverse(sk_c6) = sk_c3. [para(42(b,1),44(a,1,2)),rewrite([274(8)])].
% 19.26/19.59 365 inverse(sk_c6) = sk_c3 | multiply(sk_c7,sk_c1) = identity. [para(344(a,1),2(a,1,1))].
% 19.26/19.59 402 multiply(A,inverse(A)) = identity. [para(273(a,1),2(a,1))].
% 19.26/19.59 421 multiply(A,multiply(inverse(A),B)) = B. [para(273(a,1),44(a,1))].
% 19.26/19.59 422 inverse(inverse(A)) = A. [para(273(a,1),274(a,1)),rewrite([274(2)]),flip(a)].
% 19.26/19.59 451 inverse(sk_c1) = sk_c7 | multiply(sk_c2,sk_c7) = identity. [para(6(b,1),402(a,1,2))].
% 19.26/19.59 500 inverse(sk_c7) = sk_c6 | multiply(sk_c3,multiply(sk_c6,sk_c4)) = identity. [para(40(b,1),47(b,2)),merge(b)].
% 19.26/19.59 549 inverse(sk_c7) = sk_c6 | multiply(A,sk_c6) = A. [para(320(b,1),46(b,1,2)),rewrite([274(10)]),flip(c),merge(b)].
% 19.26/19.59 597 inverse(sk_c7) = sk_c6 | multiply(A,multiply(sk_c3,sk_c6)) = A. [para(335(b,1),33(a,2,2)),rewrite([33(8),274(10)])].
% 19.26/19.59 599 inverse(sk_c7) = sk_c6 | multiply(A,sk_c5) = A. [para(335(b,1),48(b,1,2)),rewrite([274(10)]),flip(c),merge(b)].
% 19.26/19.59 714 inverse(sk_c6) = sk_c3 | multiply(A,multiply(sk_c7,sk_c1)) = A. [para(365(b,1),33(a,2,2)),rewrite([33(8),274(10)])].
% 19.26/19.59 786 inverse(sk_c1) = sk_c7 | identity = sk_c6. [para(451(b,1),18(b,1)),merge(b)].
% 19.26/19.59 804 identity = sk_c6 | multiply(sk_c7,multiply(sk_c1,A)) = A. [para(786(a,1),44(a,1,1))].
% 19.26/19.59 806 identity = sk_c6 | multiply(sk_c1,sk_c7) = identity. [para(786(a,1),402(a,1,2))].
% 19.26/19.59 807 identity = sk_c6 | multiply(sk_c1,multiply(sk_c7,A)) = A. [para(786(a,1),421(a,1,2,1))].
% 19.26/19.59 1006 identity = sk_c6 | inverse(sk_c2) = sk_c7 | multiply(sk_c1,multiply(sk_c6,sk_c5)) = identity. [para(806(b,1),52(b,2))].
% 19.26/19.59 2443 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = identity. [para(549(b,1),2(a,1))].
% 19.26/19.59 2728 inverse(sk_c7) = sk_c6 | multiply(sk_c6,A) = A. [para(2443(b,1),44(a,1,1)),rewrite([1(8)])].
% 19.26/19.59 4338 inverse(sk_c7) = sk_c6 | multiply(inverse(sk_c6),A) = A. [para(2728(b,1),44(a,1,2))].
% 19.26/19.59 4415 inverse(sk_c2) = sk_c7 | multiply(sk_c1,multiply(sk_c6,sk_c5)) = sk_c6. [para(15(a,1),69(b,2)),merge(b)].
% 19.26/19.59 4853 inverse(sk_c3) = sk_c6 | multiply(sk_c1,multiply(sk_c6,multiply(sk_c7,sk_c5))) = multiply(sk_c7,sk_c6). [para(60(b,1),71(b,2)),merge(b)].
% 19.26/19.59 9250 inverse(sk_c7) = sk_c6 | inverse(sk_c4) = sk_c7. [para(249(b,1),599(b,1)),flip(c),merge(b)].
% 19.26/19.59 9257 inverse(sk_c7) = sk_c6 | multiply(sk_c7,sk_c4) = identity. [para(9250(b,1),2(a,1,1))].
% 19.26/19.59 10304 inverse(sk_c7) = sk_c6 | multiply(sk_c6,sk_c4) = sk_c2. [para(9257(b,1),45(b,1,2)),rewrite([274(11)]),flip(c),merge(b)].
% 19.26/19.59 12369 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(402(a,1),271(a,1,2,2)),rewrite([274(4)])].
% 19.26/19.59 13155 inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(A,sk_c7) != sk_c6 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | multiply(sk_c7,C) != sk_c5 | inverse(C) != sk_c5. [para(12369(a,1),36(j,1)),rewrite([422(36)])].
% 19.26/19.59 13158 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(44(a,1),12369(a,1,1,1)),flip(a)].
% 19.26/19.59 15805 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c2) = identity. [para(10304(b,1),500(b,1,2)),merge(b)].
% 19.26/19.59 16000 inverse(sk_c7) = sk_c6 | inverse(sk_c3) = sk_c2. [para(15805(b,1),44(a,1,2)),rewrite([274(8)])].
% 19.26/19.59 16005 inverse(sk_c7) = sk_c6 | inverse(sk_c2) = sk_c3. [para(16000(b,1),422(a,1,1))].
% 19.26/19.59 16008 inverse(sk_c7) = sk_c6 | multiply(sk_c3,sk_c6) = sk_c7. [para(16005(b,1),247(b,1,1)),merge(b)].
% 19.26/19.59 16221 inverse(sk_c7) = sk_c6 | multiply(A,sk_c7) = A. [para(16008(b,1),597(b,1,2)),merge(b)].
% 19.26/19.59 16760 inverse(sk_c7) = sk_c6 | inverse(sk_c6) = sk_c7. [para(4338(b,1),16221(b,1)),flip(c),merge(b)].
% 19.26/19.59 16777 inverse(sk_c7) = sk_c6. [para(16760(b,1),422(a,1,1)),merge(b)].
% 19.26/19.59 18007 multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(A,sk_c7) != sk_c6 | multiply(B,sk_c6) != sk_c5 | inverse(B) != sk_c6 | multiply(sk_c7,C) != sk_c5 | inverse(C) != sk_c5. [back_rewrite(13155),rewrite([16777(2)]),xx(a)].
% 19.26/19.59 18900 inverse(sk_c6) = sk_c3 | multiply(inverse(sk_c1),sk_c6) = identity. [para(714(b,1),2(a,1)),rewrite([13158(8),16777(8)])].
% 19.26/19.59 18903 multiply(sk_c6,multiply(sk_c7,A)) = A. [para(16777(a,1),44(a,1,1))].
% 19.26/19.59 18904 inverse(sk_c6) = sk_c7. [para(16777(a,1),422(a,1,1))].
% 19.26/19.59 18905 multiply(sk_c7,sk_c6) = identity. [para(16777(a,1),402(a,1,2))].
% 19.26/19.59 18925 inverse(sk_c3) = sk_c6 | multiply(sk_c1,sk_c5) = identity. [back_rewrite(4853),rewrite([18903(10),18905(10)])].
% 19.26/19.59 18931 sk_c3 = sk_c7 | multiply(inverse(sk_c1),sk_c6) = identity. [back_rewrite(18900),rewrite([18904(2)]),flip(a)].
% 19.26/19.59 19777 inverse(sk_c3) = sk_c6 | inverse(sk_c1) = sk_c5. [para(18925(b,1),44(a,1,2)),rewrite([274(8)])].
% 19.26/19.59 19785 inverse(sk_c1) = sk_c5 | sk_c3 = sk_c7. [para(19777(a,1),422(a,1,1)),rewrite([18904(6)]),flip(b)].
% 19.26/19.59 20616 sk_c3 = sk_c7 | multiply(sk_c5,sk_c6) = identity. [para(19785(a,1),18931(b,1,1)),merge(b)].
% 19.26/19.59 23508 inverse(sk_c2) = sk_c7 | identity = sk_c6. [para(4415(b,1),1006(c,1)),flip(d),merge(c),merge(d)].
% 19.26/19.59 23524 identity = sk_c6 | multiply(sk_c2,sk_c7) = identity. [para(23508(a,1),402(a,1,2))].
% 19.26/19.59 23576 identity = sk_c6 | multiply(sk_c6,sk_c5) = sk_c7. [para(23524(b,1),24(b,1)),merge(c)].
% 19.26/19.59 23577 identity = sk_c6 | multiply(sk_c7,sk_c5) = sk_c6. [para(23524(b,1),27(b,1)),merge(c)].
% 19.26/19.59 23578 identity = sk_c6 | multiply(sk_c1,sk_c6) = sk_c7. [para(23524(b,1),30(b,1)),merge(c)].
% 19.26/19.59 23738 identity = sk_c6 | multiply(sk_c7,sk_c7) = sk_c5. [para(23576(b,1),44(a,1,2)),rewrite([18904(5)])].
% 19.26/19.59 23742 identity = sk_c6 | multiply(sk_c1,sk_c6) = sk_c5. [para(23577(b,1),807(b,1,2)),merge(b)].
% 19.26/19.59 23745 identity = sk_c6 | multiply(sk_c7,sk_c7) = sk_c6. [para(23578(b,1),804(b,1,2)),merge(b)].
% 19.26/19.59 23865 identity = sk_c6 | sk_c5 = sk_c7. [para(23742(b,1),23578(b,1)),merge(b)].
% 19.26/19.59 23873 sk_c5 = sk_c7 | identity = sk_c7. [para(23865(a,1),277(a,1,1)),rewrite([18904(5)]),flip(b)].
% 19.26/19.59 23896 sk_c5 = sk_c7 | sk_c6 = sk_c7. [para(23873(b,1),23865(a,1)),flip(b),merge(c)].
% 19.26/19.59 23908 identity = sk_c6 | multiply(sk_c6,sk_c6) = sk_c7. [para(23745(b,1),44(a,1,2)),rewrite([16777(5)])].
% 19.26/19.59 23911 identity = sk_c6 | sk_c5 = sk_c6. [para(23745(b,1),23738(b,1)),flip(c),merge(b)].
% 19.26/19.59 23918 sk_c5 = sk_c6 | identity = sk_c7. [para(23911(a,1),277(a,1,1)),rewrite([18904(5)]),flip(b)].
% 19.26/19.59 23933 sk_c5 = sk_c6 | sk_c6 = sk_c7. [para(23918(b,1),23911(a,1)),flip(b),merge(c)].
% 19.26/19.59 23945 sk_c6 = sk_c7. [para(23933(a,1),23896(a,1)),merge(b),merge(c)].
% 19.26/19.59 23952 identity = sk_c7 | multiply(sk_c7,sk_c7) = sk_c7. [back_rewrite(23908),rewrite([23945(2),23945(4),23945(5)])].
% 19.26/19.59 25940 sk_c3 = sk_c7 | multiply(sk_c5,sk_c7) = identity. [back_rewrite(20616),rewrite([23945(5)])].
% 19.26/19.59 26957 multiply(sk_c7,sk_c7) = identity. [back_rewrite(18905),rewrite([23945(2)])].
% 19.26/19.59 27191 multiply(sk_c7,sk_c5) != sk_c7 | inverse(A) != sk_c7 | multiply(A,sk_c7) != sk_c7 | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(sk_c7,C) != sk_c5 | inverse(C) != sk_c5. [back_rewrite(18007),rewrite([23945(1),23945(9),23945(14),23945(20),23945(22),23945(27)]),merge(b),merge(e)].
% 19.26/19.59 27511 inverse(sk_c7) = sk_c7. [back_rewrite(16777),rewrite([23945(3)])].
% 19.26/19.59 28947 multiply(sk_c7,sk_c5) = sk_c7 | multiply(sk_c3,sk_c7) = sk_c5. [back_rewrite(28),rewrite([23945(4),23945(7)])].
% 19.26/19.59 29020 identity = sk_c7. [back_rewrite(23952),rewrite([26957(6)]),merge(b)].
% 19.26/19.59 29053 multiply(sk_c7,sk_c5) != sk_c7 | inverse(A) != sk_c7 | multiply(A,sk_c7) != sk_c7 | multiply(A,sk_c7) != sk_c5 | multiply(sk_c7,B) != sk_c5 | inverse(B) != sk_c5. [factor(27191,b,e)].
% 19.26/19.59 29200 sk_c3 = sk_c7 | multiply(sk_c5,sk_c7) = sk_c7. [back_rewrite(25940),rewrite([29020(7)])].
% 19.26/19.59 29365 multiply(A,sk_c7) = A. [back_rewrite(274),rewrite([29020(1)])].
% 19.26/19.59 29367 multiply(sk_c7,A) = A. [back_rewrite(1),rewrite([29020(1)])].
% 19.26/19.59 29371 sk_c5 != sk_c7. [factor(29053,d,e),rewrite([29367(3),27511(5),29365(9),29365(12),27511(14)]),flip(d),flip(e),xx(b),xx(c),merge(b),merge(c)].
% 19.26/19.59 29377 sk_c3 = sk_c7. [back_rewrite(29200),rewrite([29365(6)]),unit_del(b,29371)].
% 19.26/19.59 29379 $F. [back_rewrite(28947),rewrite([29367(3),29377(4),29365(6)]),flip(b),merge(b),unit_del(a,29371)].
% 19.26/19.59
% 19.26/19.59 % SZS output end Refutation
% 19.26/19.59 ============================== end of proof ==========================
% 19.26/19.59
% 19.26/19.59 ============================== STATISTICS ============================
% 19.26/19.59
% 19.26/19.59 Given=3915. Generated=857142. Kept=29378. proofs=1.
% 19.26/19.59 Usable=156. Sos=3537. Demods=18. Limbo=14, Disabled=25705. Hints=0.
% 19.26/19.59 Megabytes=23.41.
% 19.26/19.59 User_CPU=18.11, System_CPU=0.46, Wall_clock=19.
% 19.26/19.59
% 19.26/19.59 ============================== end of statistics =====================
% 19.26/19.59
% 19.26/19.59 ============================== end of search =========================
% 19.26/19.59
% 19.26/19.59 THEOREM PROVED
% 19.26/19.59 % SZS status Unsatisfiable
% 19.26/19.59
% 19.26/19.59 Exiting with 1 proof.
% 19.26/19.59
% 19.26/19.59 Process 14029 exit (max_proofs) Tue Jun 14 08:02:01 2022
% 19.26/19.59 Prover9 interrupted
%------------------------------------------------------------------------------