TSTP Solution File: REL026-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL026-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 19:53:57 EDT 2022
% Result : Unsatisfiable 11.82s 12.09s
% Output : Refutation 11.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL026-2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.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 : Fri Jul 8 14:38:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.22/3.48 ============================== Prover9 ===============================
% 3.22/3.48 Prover9 (32) version 2009-11A, November 2009.
% 3.22/3.48 Process 26638 was started by sandbox2 on n027.cluster.edu,
% 3.22/3.48 Fri Jul 8 14:38:46 2022
% 3.22/3.48 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26485_n027.cluster.edu".
% 3.22/3.48 ============================== end of head ===========================
% 3.22/3.48
% 3.22/3.48 ============================== INPUT =================================
% 3.22/3.48
% 3.22/3.48 % Reading from file /tmp/Prover9_26485_n027.cluster.edu
% 3.22/3.48
% 3.22/3.48 set(prolog_style_variables).
% 3.22/3.48 set(auto2).
% 3.22/3.48 % set(auto2) -> set(auto).
% 3.22/3.48 % set(auto) -> set(auto_inference).
% 3.22/3.48 % set(auto) -> set(auto_setup).
% 3.22/3.48 % set(auto_setup) -> set(predicate_elim).
% 3.22/3.48 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.22/3.48 % set(auto) -> set(auto_limits).
% 3.22/3.48 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.22/3.48 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.22/3.48 % set(auto) -> set(auto_denials).
% 3.22/3.48 % set(auto) -> set(auto_process).
% 3.22/3.48 % set(auto2) -> assign(new_constants, 1).
% 3.22/3.48 % set(auto2) -> assign(fold_denial_max, 3).
% 3.22/3.48 % set(auto2) -> assign(max_weight, "200.000").
% 3.22/3.48 % set(auto2) -> assign(max_hours, 1).
% 3.22/3.48 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.22/3.48 % set(auto2) -> assign(max_seconds, 0).
% 3.22/3.48 % set(auto2) -> assign(max_minutes, 5).
% 3.22/3.48 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.22/3.48 % set(auto2) -> set(sort_initial_sos).
% 3.22/3.48 % set(auto2) -> assign(sos_limit, -1).
% 3.22/3.48 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.22/3.48 % set(auto2) -> assign(max_megs, 400).
% 3.22/3.48 % set(auto2) -> assign(stats, some).
% 3.22/3.48 % set(auto2) -> clear(echo_input).
% 3.22/3.48 % set(auto2) -> set(quiet).
% 3.22/3.48 % set(auto2) -> clear(print_initial_clauses).
% 3.22/3.48 % set(auto2) -> clear(print_given).
% 3.22/3.48 assign(lrs_ticks,-1).
% 3.22/3.48 assign(sos_limit,10000).
% 3.22/3.48 assign(order,kbo).
% 3.22/3.48 set(lex_order_vars).
% 3.22/3.48 clear(print_given).
% 3.22/3.48
% 3.22/3.48 % formulas(sos). % not echoed (15 formulas)
% 3.22/3.48
% 3.22/3.48 ============================== end of input ==========================
% 3.22/3.48
% 3.22/3.48 % From the command line: assign(max_seconds, 300).
% 3.22/3.48
% 3.22/3.48 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.22/3.48
% 3.22/3.48 % Formulas that are not ordinary clauses:
% 3.22/3.48
% 3.22/3.48 ============================== end of process non-clausal formulas ===
% 3.22/3.48
% 3.22/3.48 ============================== PROCESS INITIAL CLAUSES ===============
% 3.22/3.48
% 3.22/3.48 ============================== PREDICATE ELIMINATION =================
% 3.22/3.48
% 3.22/3.48 ============================== end predicate elimination =============
% 3.22/3.48
% 3.22/3.48 Auto_denials:
% 3.22/3.48 % copying label goals_15 to answer in negative clause
% 3.22/3.48
% 3.22/3.48 Term ordering decisions:
% 3.22/3.48 Function symbol KB weights: one=1. sk1=1. top=1. zero=1. sk2=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 3.22/3.48
% 3.22/3.48 ============================== end of process initial clauses ========
% 3.22/3.48
% 3.22/3.48 ============================== CLAUSES FOR SEARCH ====================
% 3.22/3.48
% 3.22/3.48 ============================== end of clauses for search =============
% 3.22/3.48
% 3.22/3.48 ============================== SEARCH ================================
% 3.22/3.48
% 3.22/3.48 % Starting search at 0.01 seconds.
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=36.000, iters=3348
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=35.000, iters=3366
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=33.000, iters=3455
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=32.000, iters=3376
% 3.22/3.48
% 3.22/3.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.10 sec).
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=31.000, iters=3370
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=30.000, iters=3366
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=29.000, iters=3343
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=27.000, iters=3376
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=26.000, iters=3379
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=25.000, iters=3350
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=24.000, iters=3349
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=23.000, iters=3351
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=22.000, iters=3385
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=21.000, iters=3339
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=20.000, iters=3348
% 3.22/3.48
% 3.22/3.48 Low Water (keep): wt=19.000, iters=3354
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=3373, wt=46.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7275, wt=45.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7472, wt=44.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7127, wt=43.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7446, wt=42.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7447, wt=41.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=6899, wt=40.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7486, wt=39.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=7488, wt=38.000
% 3.22/3.48
% 3.22/3.48 Low Water (displace): id=13489, wt=15.000
% 11.82/12.09
% 11.82/12.09 Low Water (displace): id=13587, wt=14.000
% 11.82/12.09
% 11.82/12.09 Low Water (displace): id=13647, wt=13.000
% 11.82/12.09
% 11.82/12.09 Low Water (keep): wt=18.000, iters=3347
% 11.82/12.09
% 11.82/12.09 Low Water (keep): wt=17.000, iters=3333
% 11.82/12.09
% 11.82/12.09 Low Water (displace): id=17797, wt=12.000
% 11.82/12.09
% 11.82/12.09 Low Water (keep): wt=16.000, iters=3338
% 11.82/12.09
% 11.82/12.09 ============================== PROOF =================================
% 11.82/12.09 % SZS status Unsatisfiable
% 11.82/12.09 % SZS output start Refutation
% 11.82/12.09
% 11.82/12.09 % Proof 1 at 10.77 (+ 0.35) seconds: goals_15.
% 11.82/12.09 % Length of proof is 149.
% 11.82/12.09 % Level of proof is 36.
% 11.82/12.09 % Maximum clause weight is 37.000.
% 11.82/12.09 % Given clauses 1798.
% 11.82/12.09
% 11.82/12.09 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 11.82/12.09 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 11.82/12.09 3 join(sk1,one) = one # label(goals_14) # label(negated_conjecture). [assumption].
% 11.82/12.09 4 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 11.82/12.09 5 join(A,complement(A)) = top. [copy(4),flip(a)].
% 11.82/12.09 6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 11.82/12.09 7 meet(A,complement(A)) = zero. [copy(6),flip(a)].
% 11.82/12.09 8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 11.82/12.09 9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 11.82/12.09 10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 11.82/12.09 11 join(converse(A),converse(B)) = converse(join(A,B)). [copy(10),flip(a)].
% 11.82/12.09 12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 11.82/12.09 13 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(12),flip(a)].
% 11.82/12.09 14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 11.82/12.09 15 join(A,join(B,C)) = join(C,join(A,B)). [copy(14),rewrite([8(4)])].
% 11.82/12.09 16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 11.82/12.09 17 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(16),flip(a)].
% 11.82/12.09 18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 11.82/12.09 19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(18),flip(a)].
% 11.82/12.09 20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 11.82/12.09 21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(20),rewrite([8(6)])].
% 11.82/12.09 22 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 11.82/12.09 23 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(22),rewrite([8(6),8(8)]),flip(a),rewrite([8(6)])].
% 11.82/12.09 24 join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) | join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2) # label(goals_15) # label(negated_conjecture) # answer(goals_15). [assumption].
% 11.82/12.09 25 join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != complement(join(complement(sk2),complement(composition(sk1,top)))) | join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != composition(sk1,sk2) # answer(goals_15). [copy(24),rewrite([9(8),8(10),9(17),8(19),9(26),8(28),8(33)])].
% 11.82/12.09 26 join(one,sk1) = one. [back_rewrite(3),rewrite([8(3)])].
% 11.82/12.09 27 complement(top) = zero. [back_rewrite(7),rewrite([9(2),5(4)])].
% 11.82/12.09 28 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 11.82/12.09 29 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),13(a,1,1)),flip(a)].
% 11.82/12.09 30 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),13(a,1,2)),flip(a)].
% 11.82/12.09 31 join(A,join(B,complement(A))) = join(B,top). [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 11.82/12.09 32 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),17(a,1,1)),flip(a)].
% 11.82/12.09 34 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(13(a,1),19(a,1,1)),rewrite([8(7)])].
% 11.82/12.09 36 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(17(a,1),19(a,1,1)),rewrite([8(6)])].
% 11.82/12.09 38 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),21(a,1,2,2,1))].
% 11.82/12.09 41 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(13(a,1),21(a,1,2,2,1)),rewrite([2(4)])].
% 11.82/12.09 43 join(zero,complement(join(complement(A),complement(A)))) = A. [para(5(a,1),23(a,1,1,1)),rewrite([27(2)])].
% 11.82/12.09 47 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(23(a,1),23(a,1,2,1)),rewrite([8(10)])].
% 11.82/12.09 49 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(27(a,1),21(a,1,1)),rewrite([27(9)])].
% 11.82/12.09 51 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(27(a,1),23(a,1,2,1,1))].
% 11.82/12.09 52 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(28(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 11.82/12.09 53 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(28(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),52(7)]),flip(a)].
% 11.82/12.09 57 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(28(a,1),28(a,2,2)),rewrite([53(4),28(4),15(6,R),8(5)])].
% 11.82/12.09 58 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(52),rewrite([57(8),11(7)])].
% 11.82/12.09 60 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(29(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 11.82/12.09 64 composition(converse(one),A) = A. [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 11.82/12.09 70 converse(one) = one. [para(64(a,1),1(a,1)),flip(a)].
% 11.82/12.09 72 composition(join(A,one),B) = join(B,composition(A,B)). [para(64(a,1),19(a,1,1)),rewrite([70(4),8(4)]),flip(a)].
% 11.82/12.09 74 join(complement(A),complement(composition(one,A))) = complement(A). [para(64(a,1),21(a,1,2))].
% 11.82/12.09 75 composition(one,A) = A. [para(64(a,1),32(a,2)),rewrite([70(2),32(4)])].
% 11.82/12.09 76 join(complement(A),complement(A)) = complement(A). [back_rewrite(74),rewrite([75(3)])].
% 11.82/12.09 77 join(zero,complement(complement(A))) = A. [back_rewrite(43),rewrite([76(4)])].
% 11.82/12.09 78 converse(join(A,one)) = join(one,converse(A)). [para(70(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 11.82/12.09 82 join(top,complement(A)) = top. [para(76(a,1),31(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 11.82/12.09 83 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(51),rewrite([82(3),27(2)])].
% 11.82/12.09 84 join(top,top) = join(A,top). [para(82(a,1),31(a,1,2)),flip(a)].
% 11.82/12.09 89 join(A,top) = join(B,top). [para(84(a,1),31(a,2)),rewrite([82(3)])].
% 11.82/12.09 90 join(A,top) = c_0. [new_symbol(89)].
% 11.82/12.09 93 join(A,join(B,complement(A))) = c_0. [back_rewrite(31),rewrite([90(5)])].
% 11.82/12.09 99 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(75(a,1),34(a,1,2)),rewrite([8(4),11(4)])].
% 11.82/12.09 104 c_0 = top. [para(77(a,1),93(a,1,2)),rewrite([8(2),5(2)]),flip(a)].
% 11.82/12.09 105 join(A,join(B,complement(A))) = top. [back_rewrite(93),rewrite([104(4)])].
% 11.82/12.09 107 join(A,top) = top. [back_rewrite(90),rewrite([104(3)])].
% 11.82/12.09 118 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(78(a,1),13(a,1,1))].
% 11.82/12.09 125 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(99),rewrite([118(8)]),flip(a)].
% 11.82/12.09 128 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(75(a,1),36(a,1,2)),rewrite([8(3)]),flip(a)].
% 11.82/12.09 132 join(zero,complement(A)) = complement(A). [para(77(a,1),83(a,1,2,1))].
% 11.82/12.09 133 complement(complement(A)) = A. [back_rewrite(83),rewrite([132(4),132(4)])].
% 11.82/12.09 134 join(A,zero) = A. [back_rewrite(77),rewrite([133(3),8(2)])].
% 11.82/12.09 139 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(133(a,1),23(a,1,1,1,2)),rewrite([133(5),8(4)])].
% 11.82/12.09 141 join(A,A) = A. [para(133(a,1),76(a,1,1)),rewrite([133(2),133(3)])].
% 11.82/12.09 145 join(A,join(A,B)) = join(A,B). [para(141(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),141(2)]),flip(a)].
% 11.82/12.09 146 join(A,complement(join(B,complement(A)))) = A. [para(23(a,1),145(a,1,2)),rewrite([8(4),23(12)])].
% 11.82/12.09 148 join(A,join(B,complement(join(C,complement(A))))) = join(A,B). [para(146(a,1),15(a,2,2)),rewrite([8(4),8(6)])].
% 11.82/12.09 151 join(complement(A),complement(join(A,B))) = complement(A). [para(133(a,1),146(a,1,2,1,2)),rewrite([8(2)])].
% 11.82/12.09 159 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(133(a,1),38(a,1,2,2))].
% 11.82/12.09 162 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)). [para(11(a,1),151(a,1,2,1))].
% 11.82/12.09 173 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(49(a,1),11(a,2,1)),rewrite([30(8)])].
% 11.82/12.09 186 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(72(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 11.82/12.09 213 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),159(a,1,2))].
% 11.82/12.09 217 converse(complement(one)) = complement(one). [para(213(a,1),11(a,2,1)),rewrite([2(7),8(6),213(6)]),flip(a)].
% 11.82/12.09 218 converse(join(A,complement(one))) = join(complement(one),converse(A)). [para(217(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 11.82/12.09 222 converse(top) = top. [para(217(a,1),78(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 11.82/12.09 226 join(top,converse(A)) = top. [para(222(a,1),11(a,1,1)),rewrite([8(5),107(5),222(5)])].
% 11.82/12.09 227 converse(composition(A,top)) = composition(top,converse(A)). [para(222(a,1),13(a,1,1)),flip(a)].
% 11.82/12.09 235 join(top,composition(A,converse(B))) = top. [para(29(a,1),226(a,1,2))].
% 11.82/12.09 237 join(top,composition(A,B)) = top. [para(2(a,1),235(a,1,2,2))].
% 11.82/12.09 248 converse(composition(A,composition(B,top))) = composition(top,converse(composition(A,B))). [para(227(a,1),13(a,1,1)),rewrite([17(5),13(4)]),flip(a)].
% 11.82/12.09 253 composition(top,join(one,converse(A))) = top. [para(78(a,1),227(a,2,2)),rewrite([72(4),237(4),222(2)]),flip(a)].
% 11.82/12.09 258 composition(top,join(A,one)) = top. [para(2(a,1),253(a,1,2,2)),rewrite([8(3)])].
% 11.82/12.09 282 join(zero,composition(A,zero)) = zero. [para(258(a,1),41(a,1,2,2,1,1)),rewrite([222(2),27(2),222(5),27(5),72(5),145(6),222(6),27(6)])].
% 11.82/12.09 291 join(complement(A),complement(join(B,A))) = complement(A). [para(146(a,1),47(a,2)),rewrite([133(2),133(4),133(8),47(13)])].
% 11.82/12.09 292 join(A,complement(join(complement(A),complement(B)))) = A. [para(47(a,1),151(a,1,2,1)),rewrite([133(2),8(3),133(7)])].
% 11.82/12.09 297 join(A,composition(B,zero)) = A. [para(282(a,1),15(a,1,2)),rewrite([134(2),134(4),8(3)]),flip(a)].
% 11.82/12.09 301 composition(join(A,B),zero) = composition(A,zero). [para(297(a,1),19(a,1)),flip(a)].
% 11.82/12.09 303 composition(A,zero) = zero. [para(297(a,1),72(a,2)),rewrite([301(4)])].
% 11.82/12.09 305 composition(converse(zero),A) = converse(zero). [para(303(a,1),30(a,1,1)),flip(a)].
% 11.82/12.09 314 composition(join(A,composition(B,converse(zero))),C) = join(composition(B,converse(zero)),composition(A,C)). [para(305(a,1),36(a,1,1,2)),flip(a)].
% 11.82/12.09 318 converse(zero) = zero. [para(305(a,1),303(a,1))].
% 11.82/12.09 321 join(zero,composition(A,B)) = composition(A,B). [back_rewrite(314),rewrite([318(2),303(2),134(2),318(3),303(3)]),flip(a)].
% 11.82/12.09 324 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(173),rewrite([318(2),321(7),318(7)])].
% 11.82/12.09 348 join(zero,converse(A)) = converse(A). [para(318(a,1),11(a,1,1)),rewrite([8(5),134(5)])].
% 11.82/12.09 417 converse(composition(A,join(B,complement(composition(converse(A),top))))) = converse(composition(A,B)). [para(324(a,1),34(a,1,2)),rewrite([8(4),348(4),8(9),11(9),13(10)]),flip(a)].
% 11.82/12.09 453 join(one,join(sk1,converse(A))) = join(one,converse(A)). [para(26(a,1),57(a,1,1)),flip(a)].
% 11.82/12.09 549 join(complement(one),complement(sk1)) = complement(sk1). [para(26(a,1),291(a,1,2,1)),rewrite([8(5)])].
% 11.82/12.09 1348 join(A,join(one,converse(sk1))) = join(A,one). [para(453(a,1),11(a,2,1)),rewrite([70(2),28(5),15(5,R),8(4),28(9),70(7)])].
% 11.82/12.09 1376 join(one,converse(sk1)) = one. [para(141(a,1),1348(a,2)),rewrite([145(6)])].
% 11.82/12.09 1377 join(A,composition(converse(sk1),A)) = A. [para(1376(a,1),19(a,2,1)),rewrite([75(2),75(6)])].
% 11.82/12.09 1384 join(A,composition(A,sk1)) = A. [para(1377(a,1),60(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 11.82/12.09 1388 join(A,join(B,composition(A,sk1))) = join(A,B). [para(1384(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 11.82/12.09 1453 composition(A,join(B,one)) = join(A,composition(A,B)). [para(125(a,1),2(a,1,1)),rewrite([2(4)]),flip(a)].
% 11.82/12.09 1766 join(A,composition(sk1,A)) = A. [para(1384(a,1),128(a,1,1)),rewrite([75(2),75(4)]),flip(a)].
% 11.82/12.09 1784 join(A,join(B,composition(sk1,A))) = join(A,B). [para(1766(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 11.82/12.09 2092 join(A,complement(join(A,B))) = join(A,complement(B)). [para(139(a,1),148(a,1,2)),flip(a)].
% 11.82/12.09 2380 join(A,composition(join(A,B),sk1)) = join(A,composition(B,sk1)). [para(19(a,1),1388(a,1,2)),rewrite([8(1)])].
% 11.82/12.09 2565 join(complement(converse(A)),converse(join(A,B))) = top. [para(162(a,1),105(a,1,2)),rewrite([8(5)])].
% 11.82/12.09 2607 join(A,join(B,converse(complement(converse(A))))) = top. [para(2565(a,1),11(a,2,1)),rewrite([2(6),15(5),8(4),15(5,R),8(4),222(7)])].
% 11.82/12.09 2699 join(A,converse(complement(converse(A)))) = top. [para(141(a,1),2607(a,1,2))].
% 11.82/12.09 2772 join(complement(converse(A)),converse(join(B,A))) = top. [para(2699(a,1),58(a,1,1,2)),rewrite([107(2),222(2)]),flip(a)].
% 11.82/12.09 2829 join(converse(A),complement(composition(converse(A),sk1))) = top. [para(1377(a,1),2772(a,1,2,1)),rewrite([30(4),8(6)])].
% 11.82/12.09 2916 join(A,converse(complement(composition(converse(A),sk1)))) = top. [para(2829(a,1),11(a,2,1)),rewrite([2(2),222(8)])].
% 11.82/12.09 3038 join(complement(composition(converse(A),sk1)),converse(join(B,A))) = top. [para(2916(a,1),58(a,1,1,2)),rewrite([107(2),222(2)]),flip(a)].
% 11.82/12.09 3831 join(A,composition(complement(one),A)) = composition(top,A). [para(38(a,1),186(a,2,2,1)),rewrite([8(7),15(8,R),8(7),38(7),5(4)]),flip(a)].
% 11.82/12.09 3975 join(A,composition(A,complement(one))) = composition(A,top). [para(3831(a,1),60(a,1,1)),rewrite([29(4),222(2),217(5),2(7),8(6)]),flip(a)].
% 11.82/12.09 3979 join(complement(one),composition(top,sk1)) = join(sk1,complement(one)). [para(3831(a,1),1388(a,1,2)),rewrite([8(10)])].
% 11.82/12.09 4368 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)). [para(3975(a,1),1784(a,1,2)),rewrite([8(10)])].
% 11.82/12.09 5238 complement(join(complement(A),complement(join(B,complement(A))))) = complement(join(complement(A),complement(B))). [para(2092(a,1),9(a,2,1)),rewrite([8(2),9(3)])].
% 11.82/12.09 5252 join(complement(A),complement(join(B,complement(A)))) = join(complement(A),complement(B)). [para(2092(a,1),47(a,2)),rewrite([8(2),8(5),146(7),8(6),5238(9),292(8),8(5)])].
% 11.82/12.09 5339 join(A,complement(converse(complement(converse(A))))) = A. [para(2699(a,1),2092(a,1,2,1)),rewrite([27(2),134(2)]),flip(a)].
% 11.82/12.09 5414 join(converse(A),complement(converse(complement(A)))) = converse(A). [para(2(a,1),5339(a,1,2,1,1,1))].
% 11.82/12.09 5417 join(A,converse(complement(converse(complement(A))))) = converse(complement(converse(complement(A)))). [para(5339(a,1),23(a,1,2,1)),rewrite([133(9),8(8),2092(8),133(6)])].
% 11.82/12.09 5682 converse(complement(converse(complement(A)))) = A. [para(5414(a,1),11(a,2,1)),rewrite([2(2),5417(5),2(6)])].
% 11.82/12.09 5710 complement(converse(complement(A))) = converse(A). [para(5682(a,1),2(a,1,1)),flip(a)].
% 11.82/12.09 5764 converse(complement(A)) = complement(converse(A)). [para(5710(a,1),133(a,1,1)),flip(a)].
% 11.82/12.09 6155 join(complement(converse(A)),converse(B)) = converse(join(B,complement(A))). [para(5764(a,1),11(a,1,1)),rewrite([8(6)])].
% 11.82/12.09 7729 join(complement(one),complement(composition(top,sk1))) = complement(sk1). [para(3979(a,1),2092(a,1,2,1)),rewrite([5252(8),549(5)]),flip(a)].
% 11.82/12.09 13283 join(join(complement(one),converse(sk1)),complement(composition(top,composition(converse(sk1),sk1)))) = top. [para(4368(a,1),3038(a,1,2,1)),rewrite([227(4),17(6),218(12),8(13)])].
% 11.82/12.09 14158 composition(top,composition(A,converse(A))) = composition(top,converse(A)). [para(5(a,1),417(a,1,1,2)),rewrite([227(3),248(8),29(7)]),flip(a)].
% 11.82/12.09 14171 composition(top,composition(converse(A),A)) = composition(top,A). [para(2(a,1),14158(a,1,2,2)),rewrite([2(7)])].
% 11.82/12.10 14210 join(complement(sk1),converse(sk1)) = top. [back_rewrite(13283),rewrite([14171(11),8(10),15(10),8(9),7729(9),8(5)])].
% 11.82/12.10 14266 join(sk1,complement(converse(sk1))) = top. [para(14210(a,1),11(a,2,1)),rewrite([5764(3),2(6),8(5),222(7)])].
% 11.82/12.10 14272 join(complement(sk1),complement(converse(sk1))) = complement(sk1). [para(14210(a,1),2092(a,1,2,1)),rewrite([27(4),8(4),132(4)]),flip(a)].
% 11.82/12.10 14277 converse(sk1) = sk1. [para(14266(a,1),23(a,1,1,1)),rewrite([27(2),14272(7),133(4),8(3),134(3)]),flip(a)].
% 11.82/12.10 14353 converse(composition(A,sk1)) = composition(sk1,converse(A)). [para(14277(a,1),13(a,1,1)),flip(a)].
% 11.82/12.10 16871 converse(join(converse(A),complement(B))) = join(A,complement(converse(B))). [para(2(a,1),6155(a,1,2)),rewrite([8(3)]),flip(a)].
% 11.82/12.10 24043 join(A,composition(complement(A),sk1)) = join(A,composition(top,sk1)). [para(5(a,1),2380(a,1,2,1)),flip(a)].
% 11.82/12.10 24140 join(A,complement(composition(top,sk1))) = complement(composition(complement(A),sk1)). [para(24043(a,1),139(a,1,1,1)),rewrite([8(10),1453(10,R),8(9),26(9),1(8),133(7),8(6),2092(6)])].
% 11.82/12.10 24262 join(A,complement(composition(sk1,top))) = complement(composition(sk1,complement(A))). [para(24140(a,1),16871(a,1,1)),rewrite([5764(6),14353(5),5764(4),2(3),14353(8),222(7)]),flip(a)].
% 11.82/12.10 24288 $F # answer(goals_15). [back_rewrite(25),rewrite([24262(10),133(7),133(8),141(7),24262(10),133(7),133(8),24262(17),133(14),133(15),141(14)]),xx(a),xx(b)].
% 11.82/12.10
% 11.82/12.10 % SZS output end Refutation
% 11.82/12.10 ============================== end of proof ==========================
% 11.82/12.10
% 11.82/12.10 ============================== STATISTICS ============================
% 11.82/12.10
% 11.82/12.10 Given=1798. Generated=564906. Kept=24277. proofs=1.
% 11.82/12.10 Usable=1289. Sos=9938. Demods=10902. Limbo=26, Disabled=13039. Hints=0.
% 11.82/12.10 Megabytes=20.84.
% 11.82/12.10 User_CPU=10.77, System_CPU=0.35, Wall_clock=11.
% 11.82/12.10
% 11.82/12.10 ============================== end of statistics =====================
% 11.82/12.10
% 11.82/12.10 ============================== end of search =========================
% 11.82/12.10
% 11.82/12.10 THEOREM PROVED
% 11.82/12.10 % SZS status Unsatisfiable
% 11.82/12.10
% 11.82/12.10 Exiting with 1 proof.
% 11.82/12.10
% 11.82/12.10 Process 26638 exit (max_proofs) Fri Jul 8 14:38:57 2022
% 11.82/12.10 Prover9 interrupted
%------------------------------------------------------------------------------