TSTP Solution File: REL028-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL028-2 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 19:54:03 EDT 2022
% Result : Unsatisfiable 10.57s 10.89s
% Output : Refutation 10.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL028-2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n025.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 : Fri Jul 8 07:58:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.17/3.48 ============================== Prover9 ===============================
% 3.17/3.48 Prover9 (32) version 2009-11A, November 2009.
% 3.17/3.48 Process 23258 was started by sandbox2 on n025.cluster.edu,
% 3.17/3.48 Fri Jul 8 07:59:00 2022
% 3.17/3.48 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23103_n025.cluster.edu".
% 3.17/3.48 ============================== end of head ===========================
% 3.17/3.48
% 3.17/3.48 ============================== INPUT =================================
% 3.17/3.48
% 3.17/3.48 % Reading from file /tmp/Prover9_23103_n025.cluster.edu
% 3.17/3.48
% 3.17/3.48 set(prolog_style_variables).
% 3.17/3.48 set(auto2).
% 3.17/3.48 % set(auto2) -> set(auto).
% 3.17/3.48 % set(auto) -> set(auto_inference).
% 3.17/3.48 % set(auto) -> set(auto_setup).
% 3.17/3.48 % set(auto_setup) -> set(predicate_elim).
% 3.17/3.48 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.17/3.48 % set(auto) -> set(auto_limits).
% 3.17/3.48 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.17/3.48 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.17/3.48 % set(auto) -> set(auto_denials).
% 3.17/3.48 % set(auto) -> set(auto_process).
% 3.17/3.48 % set(auto2) -> assign(new_constants, 1).
% 3.17/3.48 % set(auto2) -> assign(fold_denial_max, 3).
% 3.17/3.48 % set(auto2) -> assign(max_weight, "200.000").
% 3.17/3.48 % set(auto2) -> assign(max_hours, 1).
% 3.17/3.48 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.17/3.48 % set(auto2) -> assign(max_seconds, 0).
% 3.17/3.48 % set(auto2) -> assign(max_minutes, 5).
% 3.17/3.48 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.17/3.48 % set(auto2) -> set(sort_initial_sos).
% 3.17/3.48 % set(auto2) -> assign(sos_limit, -1).
% 3.17/3.48 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.17/3.48 % set(auto2) -> assign(max_megs, 400).
% 3.17/3.48 % set(auto2) -> assign(stats, some).
% 3.17/3.48 % set(auto2) -> clear(echo_input).
% 3.17/3.48 % set(auto2) -> set(quiet).
% 3.17/3.48 % set(auto2) -> clear(print_initial_clauses).
% 3.17/3.48 % set(auto2) -> clear(print_given).
% 3.17/3.48 assign(lrs_ticks,-1).
% 3.17/3.48 assign(sos_limit,10000).
% 3.17/3.48 assign(order,kbo).
% 3.17/3.48 set(lex_order_vars).
% 3.17/3.48 clear(print_given).
% 3.17/3.48
% 3.17/3.48 % formulas(sos). % not echoed (19 formulas)
% 3.17/3.48
% 3.17/3.48 ============================== end of input ==========================
% 3.17/3.48
% 3.17/3.48 % From the command line: assign(max_seconds, 300).
% 3.17/3.48
% 3.17/3.48 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.17/3.48
% 3.17/3.48 % Formulas that are not ordinary clauses:
% 3.17/3.48
% 3.17/3.48 ============================== end of process non-clausal formulas ===
% 3.17/3.48
% 3.17/3.48 ============================== PROCESS INITIAL CLAUSES ===============
% 3.17/3.48
% 3.17/3.48 ============================== PREDICATE ELIMINATION =================
% 3.17/3.48
% 3.17/3.48 ============================== end predicate elimination =============
% 3.17/3.48
% 3.17/3.48 Auto_denials:
% 3.17/3.48 % copying label goals_19 to answer in negative clause
% 3.17/3.48
% 3.17/3.48 Term ordering decisions:
% 3.17/3.48 Function symbol KB weights: one=1. sk1=1. sk2=1. top=1. zero=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.17/3.48
% 3.17/3.48 ============================== end of process initial clauses ========
% 3.17/3.48
% 3.17/3.48 ============================== CLAUSES FOR SEARCH ====================
% 3.17/3.48
% 3.17/3.48 ============================== end of clauses for search =============
% 3.17/3.48
% 3.17/3.48 ============================== SEARCH ================================
% 3.17/3.48
% 3.17/3.48 % Starting search at 0.01 seconds.
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=125.000, iters=3337
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=104.000, iters=3386
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=71.000, iters=3381
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=70.000, iters=3345
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=67.000, iters=3351
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=66.000, iters=3348
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=65.000, iters=3346
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=63.000, iters=3364
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=62.000, iters=3447
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=61.000, iters=3403
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=60.000, iters=3385
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=59.000, iters=3375
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=58.000, iters=3485
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=57.000, iters=3420
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=56.000, iters=3463
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=55.000, iters=3398
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=54.000, iters=3380
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=53.000, iters=3353
% 3.17/3.48
% 3.17/3.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 47 (0.00 of 2.10 sec).
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=51.000, iters=3421
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=50.000, iters=3390
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=49.000, iters=3440
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=48.000, iters=3368
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=47.000, iters=3415
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=46.000, iters=3353
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=44.000, iters=3358
% 3.17/3.48
% 3.17/3.48 Low Water (keep): wt=43.000, iters=3390
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=42.000, iters=3413
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=36.000, iters=3376
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=35.000, iters=3397
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=33.000, iters=3366
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=31.000, iters=3367
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=5558, wt=171.000
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=5458, wt=166.000
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=4125, wt=157.000
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=12116, wt=15.000
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=29.000, iters=3337
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=12290, wt=14.000
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=12295, wt=13.000
% 10.57/10.89
% 10.57/10.89 Low Water (displace): id=12445, wt=12.000
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=28.000, iters=3423
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=27.000, iters=3351
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=26.000, iters=3359
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=25.000, iters=3348
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=24.000, iters=3336
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=23.000, iters=3370
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=22.000, iters=3336
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=21.000, iters=3381
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=20.000, iters=3381
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=19.000, iters=3350
% 10.57/10.89
% 10.57/10.89 Low Water (keep): wt=18.000, iters=3333
% 10.57/10.89
% 10.57/10.89 ============================== PROOF =================================
% 10.57/10.89 % SZS status Unsatisfiable
% 10.57/10.89 % SZS output start Refutation
% 10.57/10.89
% 10.57/10.89 % Proof 1 at 9.59 (+ 0.19) seconds: goals_19.
% 10.57/10.89 % Length of proof is 145.
% 10.57/10.89 % Level of proof is 34.
% 10.57/10.89 % Maximum clause weight is 48.000.
% 10.57/10.89 % Given clauses 1399.
% 10.57/10.89
% 10.57/10.89 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 10.57/10.89 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 10.57/10.89 3 join(sk1,one) = one # label(goals_17) # label(negated_conjecture). [assumption].
% 10.57/10.89 4 join(sk2,one) = one # label(goals_18) # label(negated_conjecture). [assumption].
% 10.57/10.89 5 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 10.57/10.89 6 join(A,complement(A)) = top. [copy(5),flip(a)].
% 10.57/10.89 7 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 10.57/10.89 8 meet(A,complement(A)) = zero. [copy(7),flip(a)].
% 10.57/10.89 9 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 10.57/10.89 10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 10.57/10.89 11 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 10.57/10.89 12 join(converse(A),converse(B)) = converse(join(A,B)). [copy(11),flip(a)].
% 10.57/10.89 13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 10.57/10.89 14 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(13),flip(a)].
% 10.57/10.89 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 10.57/10.89 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([9(4)])].
% 10.57/10.89 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 10.57/10.89 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 10.57/10.89 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 10.57/10.89 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 10.57/10.89 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 10.57/10.89 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([9(6)])].
% 10.57/10.89 23 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 10.57/10.89 24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(23),rewrite([9(6),9(8)]),flip(a),rewrite([9(6)])].
% 10.57/10.89 25 join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C) # label(modular_law_1_15) # label(axiom). [assumption].
% 10.57/10.89 26 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))). [copy(25),rewrite([10(2),9(4),10(8),10(13),9(15),10(20),10(25),9(27)])].
% 10.57/10.89 29 join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) # label(dedekind_law_14) # label(axiom). [assumption].
% 10.57/10.89 30 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))). [copy(29),rewrite([10(2),9(4),10(8),10(14),10(22),10(28)])].
% 10.57/10.89 31 composition(sk1,sk2) != meet(sk1,sk2) # label(goals_19) # label(negated_conjecture) # answer(goals_19). [assumption].
% 10.57/10.89 32 complement(join(complement(sk1),complement(sk2))) != composition(sk1,sk2) # answer(goals_19). [copy(31),rewrite([10(6)]),flip(a)].
% 10.57/10.89 33 join(one,sk2) = one. [back_rewrite(4),rewrite([9(3)])].
% 10.57/10.89 34 join(one,sk1) = one. [back_rewrite(3),rewrite([9(3)])].
% 10.57/10.89 35 complement(top) = zero. [back_rewrite(8),rewrite([10(2),6(4)])].
% 10.57/10.89 36 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),12(a,1,1)),rewrite([9(4)]),flip(a)].
% 10.57/10.89 37 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),14(a,1,1)),flip(a)].
% 10.57/10.89 38 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),14(a,1,2)),flip(a)].
% 10.57/10.89 39 join(A,join(B,complement(A))) = join(B,top). [para(6(a,1),16(a,2,2)),rewrite([9(2)])].
% 10.57/10.89 40 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 10.57/10.89 42 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(14(a,1),20(a,1,1)),rewrite([9(7)])].
% 10.57/10.89 46 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),22(a,1,2,2,1))].
% 10.57/10.89 51 join(zero,complement(join(complement(A),complement(A)))) = A. [para(6(a,1),24(a,1,1,1)),rewrite([35(2)])].
% 10.57/10.89 52 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(6(a,1),24(a,1,2,1)),rewrite([35(6),9(6)])].
% 10.57/10.89 55 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(24(a,1),24(a,1,2,1)),rewrite([9(10)])].
% 10.57/10.89 56 join(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A)))))))). [para(1(a,1),26(a,1,1,1,2,1))].
% 10.57/10.89 58 join(complement(join(complement(A),complement(composition(converse(B),C)))),complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A))))))))) = complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))). [para(2(a,1),26(a,1,2,1,2,1,2,1,2,1,1)),rewrite([2(23)])].
% 10.57/10.89 72 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A))))). [para(1(a,1),30(a,1,1,1,2,1))].
% 10.57/10.89 91 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(36(a,1),12(a,1,1)),rewrite([9(7),16(7,R),9(6)]),flip(a)].
% 10.57/10.89 92 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(36(a,1),12(a,1,2)),rewrite([16(4,R),9(3),12(3),91(7)]),flip(a)].
% 10.57/10.89 100 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(36(a,1),36(a,2,2)),rewrite([92(4),36(4),16(6,R),9(5)])].
% 10.57/10.89 101 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(91),rewrite([100(8),12(7)])].
% 10.57/10.89 108 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(37(a,1),12(a,1,1)),rewrite([9(7)]),flip(a)].
% 10.57/10.89 110 converse(composition(A,composition(converse(B),C))) = composition(converse(C),composition(B,converse(A))). [para(37(a,1),14(a,1,2)),rewrite([18(7)]),flip(a)].
% 10.57/10.89 116 composition(converse(one),A) = A. [para(1(a,1),38(a,1,1)),rewrite([2(2)]),flip(a)].
% 10.57/10.89 117 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(38(a,1),12(a,1,1)),rewrite([9(7)]),flip(a)].
% 10.57/10.89 125 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(24(a,1),39(a,1,2)),rewrite([9(4),39(4),9(3),9(8)]),flip(a)].
% 10.57/10.89 126 join(top,complement(complement(A))) = top. [para(26(a,1),39(a,1,2)),rewrite([6(22),9(8),125(8)]),flip(a)].
% 10.57/10.89 127 converse(one) = one. [para(116(a,1),1(a,1)),flip(a)].
% 10.57/10.89 131 join(complement(A),complement(composition(one,A))) = complement(A). [para(116(a,1),22(a,1,2))].
% 10.57/10.89 145 composition(one,A) = A. [para(116(a,1),40(a,2)),rewrite([127(2),40(4)])].
% 10.57/10.89 146 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A))))). [back_rewrite(72),rewrite([127(7),1(7),9(7),127(20),1(20),9(20)])].
% 10.57/10.89 151 join(complement(A),complement(A)) = complement(A). [back_rewrite(131),rewrite([145(3)])].
% 10.57/10.89 152 join(zero,complement(complement(A))) = A. [back_rewrite(51),rewrite([151(4)])].
% 10.57/10.89 153 converse(join(A,one)) = join(one,converse(A)). [para(127(a,1),12(a,1,1)),rewrite([9(5)]),flip(a)].
% 10.57/10.89 154 join(zero,complement(A)) = complement(A). [para(126(a,1),24(a,1,1,1)),rewrite([35(2),35(3),152(5)])].
% 10.57/10.89 157 complement(complement(A)) = A. [back_rewrite(152),rewrite([154(4)])].
% 10.57/10.89 167 complement(join(A,A)) = complement(A). [back_rewrite(52),rewrite([157(3),154(4)])].
% 10.57/10.89 169 join(A,top) = top. [back_rewrite(126),rewrite([157(3),9(2)])].
% 10.57/10.89 177 join(A,join(B,complement(A))) = top. [back_rewrite(39),rewrite([169(5)])].
% 10.57/10.89 185 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(157(a,1),24(a,1,1,1,2)),rewrite([157(5),9(4)])].
% 10.57/10.89 203 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(145(a,1),42(a,1,2)),rewrite([9(4),12(4)])].
% 10.57/10.89 208 join(A,A) = A. [para(167(a,1),24(a,1,1,1,2)),rewrite([167(6),24(8)]),flip(a)].
% 10.57/10.89 215 join(A,join(A,B)) = join(A,B). [para(208(a,1),16(a,1)),rewrite([9(3),16(4,R),9(3),16(3,R),208(2)]),flip(a)].
% 10.57/10.89 221 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(153(a,1),14(a,1,1))].
% 10.57/10.89 232 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(203),rewrite([221(8)]),flip(a)].
% 10.57/10.89 233 join(A,complement(join(B,complement(A)))) = A. [para(24(a,1),215(a,1,2)),rewrite([9(4),24(12)])].
% 10.57/10.89 238 join(complement(A),complement(join(A,B))) = complement(A). [para(157(a,1),233(a,1,2,1,2)),rewrite([9(2)])].
% 10.57/10.89 243 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(12(a,1),238(a,1,2,1))].
% 10.57/10.89 244 join(complement(composition(A,B)),complement(composition(join(A,C),B))) = complement(composition(A,B)). [para(20(a,1),238(a,1,2,1))].
% 10.57/10.89 256 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(157(a,1),46(a,1,2,2))].
% 10.57/10.89 305 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),256(a,1,2))].
% 10.57/10.89 309 converse(complement(one)) = complement(one). [para(305(a,1),12(a,2,1)),rewrite([2(7),9(6),305(6)]),flip(a)].
% 10.57/10.89 318 converse(top) = top. [para(309(a,1),153(a,2,2)),rewrite([9(4),6(4),6(6)])].
% 10.57/10.89 329 join(top,converse(A)) = top. [para(318(a,1),12(a,1,1)),rewrite([9(5),169(5),318(5)])].
% 10.57/10.89 336 join(top,composition(A,converse(B))) = top. [para(37(a,1),329(a,1,2))].
% 10.57/10.89 338 join(top,composition(A,B)) = top. [para(2(a,1),336(a,1,2,2))].
% 10.57/10.89 438 join(complement(A),complement(join(B,A))) = complement(A). [para(233(a,1),55(a,2)),rewrite([157(2),157(4),157(8),55(13)])].
% 10.57/10.89 588 join(complement(A),join(join(complement(A),complement(composition(converse(B),C))),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))) = join(complement(A),complement(composition(converse(B),C))). [para(58(a,1),238(a,1,2,1)),rewrite([157(7),157(17),16(16,R),9(15),157(23)])].
% 10.57/10.89 758 join(complement(one),complement(sk2)) = complement(sk2). [para(33(a,1),438(a,1,2,1)),rewrite([9(5)])].
% 10.57/10.89 759 join(complement(one),complement(sk1)) = complement(sk1). [para(34(a,1),438(a,1,2,1)),rewrite([9(5)])].
% 10.57/10.89 2263 join(one,join(sk2,converse(A))) = join(one,converse(A)). [para(33(a,1),100(a,1,1)),flip(a)].
% 10.57/10.89 2264 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(34(a,1),100(a,1,1)),flip(a)].
% 10.57/10.89 3295 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(42(a,1),117(a,1,1)),rewrite([12(3),14(4),2(4),2(4),2(6)]),flip(a)].
% 10.57/10.89 4331 join(A,join(one,converse(sk2))) = join(A,one). [para(2263(a,1),12(a,2,1)),rewrite([127(2),36(5),16(5,R),9(4),36(9),127(7)])].
% 10.57/10.89 4339 join(one,converse(sk2)) = one. [para(208(a,1),4331(a,2)),rewrite([215(6)])].
% 10.57/10.89 4340 join(A,composition(converse(sk2),A)) = A. [para(4339(a,1),20(a,2,1)),rewrite([145(2),145(6)])].
% 10.57/10.89 4342 join(complement(one),complement(converse(sk2))) = complement(converse(sk2)). [para(4339(a,1),438(a,1,2,1)),rewrite([9(6)])].
% 10.57/10.89 4349 join(complement(A),complement(composition(converse(sk2),A))) = complement(composition(converse(sk2),A)). [para(4340(a,1),438(a,1,2,1)),rewrite([9(6)])].
% 10.57/10.89 4353 join(A,composition(A,sk2)) = A. [para(4340(a,1),108(a,1,1)),rewrite([2(2),2(3),2(4),9(3)]),flip(a)].
% 10.57/10.89 4403 composition(converse(sk2),sk2) = converse(sk2). [para(4342(a,1),146(a,1,1,1)),rewrite([157(4),4342(8),157(6),2(9),1(9),758(9),157(7),4353(7),4342(8),157(6),2(9),1(9),758(9),157(7)]),flip(a)].
% 10.57/10.89 4480 converse(sk2) = sk2. [para(4403(a,1),14(a,2,1)),rewrite([2(5),4403(4),2(5)])].
% 10.57/10.89 4481 composition(sk2,composition(sk2,A)) = composition(sk2,A). [para(4403(a,1),18(a,1,1)),rewrite([4480(2),4480(4)]),flip(a)].
% 10.57/10.89 4491 composition(sk2,sk2) = sk2. [para(4403(a,1),38(a,1,1)),rewrite([4480(2),4480(2),4480(3)]),flip(a)].
% 10.57/10.89 4518 converse(composition(A,sk2)) = composition(sk2,converse(A)). [para(4403(a,1),110(a,1,1,2)),rewrite([4480(2),4480(5),4481(8)])].
% 10.57/10.89 4525 converse(join(A,sk2)) = join(sk2,converse(A)). [para(4403(a,1),117(a,1,1,2)),rewrite([4480(2),4480(5),4491(6)])].
% 10.57/10.89 4536 join(complement(A),complement(composition(sk2,A))) = complement(composition(sk2,A)). [back_rewrite(4349),rewrite([4480(3),4480(7)])].
% 10.57/10.89 4538 join(A,composition(sk2,A)) = A. [back_rewrite(4340),rewrite([4480(2)])].
% 10.57/10.89 4548 converse(composition(sk2,A)) = composition(converse(A),sk2). [para(4480(a,1),14(a,1,2)),flip(a)].
% 10.57/10.89 5054 join(one,join(sk1,sk2)) = one. [para(4480(a,1),2264(a,1,2,2)),rewrite([4480(8),33(8)])].
% 10.57/10.89 5056 join(one,converse(sk1)) = one. [para(5054(a,1),12(a,2,1)),rewrite([127(2),4525(5),2263(6),127(6)])].
% 10.57/10.89 5060 join(A,composition(converse(sk1),A)) = A. [para(5056(a,1),20(a,2,1)),rewrite([145(2),145(6)])].
% 10.57/10.89 5062 join(complement(one),complement(converse(sk1))) = complement(converse(sk1)). [para(5056(a,1),438(a,1,2,1)),rewrite([9(6)])].
% 10.57/10.89 5073 join(A,composition(A,sk1)) = A. [para(5060(a,1),108(a,1,1)),rewrite([2(2),2(3),2(4),9(3)]),flip(a)].
% 10.57/10.89 5131 join(complement(A),complement(composition(A,sk1))) = complement(composition(A,sk1)). [para(5073(a,1),438(a,1,2,1)),rewrite([9(5)])].
% 10.57/10.89 5237 composition(converse(sk1),sk1) = converse(sk1). [para(5062(a,1),146(a,1,1,1)),rewrite([157(4),5062(8),157(6),2(9),1(9),759(9),157(7),5073(7),5062(8),157(6),2(9),1(9),759(9),157(7)]),flip(a)].
% 10.57/10.89 5244 converse(sk1) = sk1. [para(5237(a,1),14(a,2,1)),rewrite([2(5),5237(4),2(5)])].
% 10.57/10.89 5245 composition(sk1,composition(sk1,A)) = composition(sk1,A). [para(5237(a,1),18(a,1,1)),rewrite([5244(2),5244(4)]),flip(a)].
% 10.57/10.89 5282 converse(composition(A,sk1)) = composition(sk1,converse(A)). [para(5237(a,1),110(a,1,1,2)),rewrite([5244(2),5244(5),5245(8)])].
% 10.57/10.89 9027 composition(A,join(B,one)) = join(A,composition(A,B)). [para(232(a,1),2(a,1,1)),rewrite([2(4)]),flip(a)].
% 10.57/10.89 10153 join(complement(converse(A)),converse(join(A,B))) = top. [para(243(a,1),177(a,1,2)),rewrite([9(5)])].
% 10.57/10.89 10216 join(A,join(B,converse(complement(converse(A))))) = top. [para(10153(a,1),12(a,2,1)),rewrite([2(6),16(5),9(4),16(5,R),9(4),318(7)])].
% 10.57/10.89 10317 join(A,converse(complement(converse(A)))) = top. [para(208(a,1),10216(a,1,2))].
% 10.57/10.89 10348 join(complement(converse(A)),converse(join(B,A))) = top. [para(10317(a,1),101(a,1,1,2)),rewrite([169(2),318(2)]),flip(a)].
% 10.57/10.89 10506 join(converse(A),complement(composition(sk2,converse(A)))) = top. [para(4353(a,1),10348(a,1,2,1)),rewrite([4518(3),9(6)])].
% 10.57/10.89 10507 join(converse(A),complement(composition(converse(A),sk2))) = top. [para(4538(a,1),10348(a,1,2,1)),rewrite([4548(3),9(6)])].
% 10.57/10.89 10645 join(A,converse(complement(composition(sk2,converse(A))))) = top. [para(10506(a,1),12(a,2,1)),rewrite([2(2),318(8)])].
% 10.57/10.89 10749 join(A,complement(composition(A,sk2))) = top. [para(2(a,1),10507(a,1,1)),rewrite([2(2)])].
% 10.57/10.89 10761 join(A,join(B,complement(composition(A,sk2)))) = top. [para(10749(a,1),16(a,2,2)),rewrite([9(4),169(7)])].
% 10.57/10.89 10990 join(one,converse(complement(composition(sk2,sk1)))) = top. [para(10645(a,1),2264(a,1,2)),rewrite([169(3),5244(5)]),flip(a)].
% 10.57/10.89 11000 join(one,complement(composition(sk2,sk1))) = top. [para(10990(a,1),12(a,2,1)),rewrite([127(2),2(7),318(8)])].
% 10.57/10.89 11008 complement(join(complement(one),complement(composition(sk2,sk1)))) = composition(sk2,sk1). [para(11000(a,1),24(a,1,1,1)),rewrite([35(2),154(10)])].
% 10.57/10.89 11009 join(complement(one),complement(composition(sk2,sk1))) = complement(composition(sk2,sk1)). [para(11000(a,1),55(a,1,2,1,1)),rewrite([11008(13),338(9),35(6),9(6),154(6)]),flip(a)].
% 10.57/10.89 11011 complement(join(one,composition(sk2,sk1))) = complement(one). [para(11000(a,1),185(a,1,2,1)),rewrite([9(5),35(8),9(8),154(8)])].
% 10.57/10.89 11123 join(one,composition(sk2,sk1)) = one. [para(11011(a,1),24(a,1,1,1,2)),rewrite([11011(11),24(10)]),flip(a)].
% 10.57/10.89 11124 join(one,composition(sk1,sk2)) = one. [para(11123(a,1),12(a,2,1)),rewrite([127(2),5282(5),4480(4),127(7)])].
% 10.57/10.89 11132 join(complement(one),complement(composition(sk1,sk2))) = complement(composition(sk1,sk2)). [para(11124(a,1),438(a,1,2,1)),rewrite([9(7)])].
% 10.57/10.89 11293 join(join(A,B),complement(composition(A,sk2))) = top. [para(244(a,1),10761(a,1,2))].
% 10.57/10.89 11503 join(join(A,B),complement(composition(B,sk2))) = top. [para(9(a,1),11293(a,1,1))].
% 10.57/10.89 11810 join(one,complement(composition(sk2,composition(sk1,sk2)))) = top. [para(11123(a,1),11503(a,1,1)),rewrite([18(6)])].
% 10.57/10.89 12068 complement(join(complement(one),complement(composition(sk2,composition(sk1,sk2))))) = composition(sk2,composition(sk1,sk2)). [para(11810(a,1),24(a,1,1,1)),rewrite([35(2),154(12)])].
% 10.57/10.89 12069 join(complement(one),complement(composition(sk2,composition(sk1,sk2)))) = complement(composition(sk2,composition(sk1,sk2))). [para(11810(a,1),55(a,1,2,1,1)),rewrite([12068(17),338(13),35(8),9(8),154(8)]),flip(a)].
% 10.57/10.89 25180 composition(sk2,composition(sk1,sk2)) = composition(sk2,sk1). [para(11009(a,1),56(a,1,1,1)),rewrite([157(5),5282(14),4480(13),1(15),11132(15),157(13),18(12),5245(11),12069(12),157(10),3295(9),9027(6,R),9(5),33(5),1(4),5282(14),4480(13),1(15),11132(15),157(13),18(12),5245(11),12069(12),157(10)]),flip(a)].
% 10.57/10.89 25193 join(complement(sk1),complement(sk2)) = complement(composition(sk2,sk1)). [para(11009(a,1),588(a,1,2,2,1,2,1)),rewrite([4480(6),1(7),4480(9),157(13),4481(12),9(12),16(12),9(11),4536(11),5131(9),4536(7),4480(8),1(9)]),flip(a)].
% 10.57/10.89 25200 composition(sk2,sk1) != composition(sk1,sk2) # answer(goals_19). [back_rewrite(32),rewrite([25193(5),157(5)])].
% 10.57/10.89 25201 composition(sk2,sk1) = composition(sk1,sk2). [para(25180(a,1),14(a,2,1)),rewrite([4518(4),5244(3),4480(5),18(5),25180(5),5282(7),4480(6)])].
% 10.57/10.89 25202 $F # answer(goals_19). [resolve(25201,a,25200,a)].
% 10.57/10.89
% 10.57/10.89 % SZS output end Refutation
% 10.57/10.89 ============================== end of proof ==========================
% 10.57/10.89
% 10.57/10.89 ============================== STATISTICS ============================
% 10.57/10.89
% 10.57/10.89 Given=1399. Generated=317794. Kept=25188. proofs=1.
% 10.57/10.89 Usable=982. Sos=9944. Demods=10629. Limbo=0, Disabled=14280. Hints=0.
% 10.57/10.89 Megabytes=30.19.
% 10.57/10.89 User_CPU=9.60, System_CPU=0.19, Wall_clock=10.
% 10.57/10.89
% 10.57/10.89 ============================== end of statistics =====================
% 10.57/10.89
% 10.57/10.89 ============================== end of search =========================
% 10.57/10.89
% 10.57/10.89 THEOREM PROVED
% 10.57/10.89 % SZS status Unsatisfiable
% 10.57/10.89
% 10.57/10.89 Exiting with 1 proof.
% 10.57/10.89
% 10.57/10.89 Process 23258 exit (max_proofs) Fri Jul 8 07:59:10 2022
% 10.57/10.89 Prover9 interrupted
%------------------------------------------------------------------------------