TSTP Solution File: REL050-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL050-3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 19:54:33 EDT 2022
% Result : Unsatisfiable 4.60s 4.89s
% Output : Refutation 4.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL050-3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 09:49:40 EDT 2022
% 0.12/0.35 % CPUTime :
% 4.28/4.57 ============================== Prover9 ===============================
% 4.28/4.57 Prover9 (32) version 2009-11A, November 2009.
% 4.28/4.57 Process 18400 was started by sandbox2 on n018.cluster.edu,
% 4.28/4.57 Fri Jul 8 09:49:41 2022
% 4.28/4.57 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18247_n018.cluster.edu".
% 4.28/4.57 ============================== end of head ===========================
% 4.28/4.57
% 4.28/4.57 ============================== INPUT =================================
% 4.28/4.57
% 4.28/4.57 % Reading from file /tmp/Prover9_18247_n018.cluster.edu
% 4.28/4.57
% 4.28/4.57 set(prolog_style_variables).
% 4.28/4.57 set(auto2).
% 4.28/4.57 % set(auto2) -> set(auto).
% 4.28/4.57 % set(auto) -> set(auto_inference).
% 4.28/4.57 % set(auto) -> set(auto_setup).
% 4.28/4.57 % set(auto_setup) -> set(predicate_elim).
% 4.28/4.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.28/4.57 % set(auto) -> set(auto_limits).
% 4.28/4.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.28/4.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.28/4.57 % set(auto) -> set(auto_denials).
% 4.28/4.57 % set(auto) -> set(auto_process).
% 4.28/4.57 % set(auto2) -> assign(new_constants, 1).
% 4.28/4.57 % set(auto2) -> assign(fold_denial_max, 3).
% 4.28/4.57 % set(auto2) -> assign(max_weight, "200.000").
% 4.28/4.57 % set(auto2) -> assign(max_hours, 1).
% 4.28/4.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.28/4.57 % set(auto2) -> assign(max_seconds, 0).
% 4.28/4.57 % set(auto2) -> assign(max_minutes, 5).
% 4.28/4.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.28/4.57 % set(auto2) -> set(sort_initial_sos).
% 4.28/4.57 % set(auto2) -> assign(sos_limit, -1).
% 4.28/4.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.28/4.57 % set(auto2) -> assign(max_megs, 400).
% 4.28/4.57 % set(auto2) -> assign(stats, some).
% 4.28/4.57 % set(auto2) -> clear(echo_input).
% 4.28/4.57 % set(auto2) -> set(quiet).
% 4.28/4.57 % set(auto2) -> clear(print_initial_clauses).
% 4.28/4.57 % set(auto2) -> clear(print_given).
% 4.28/4.57 assign(lrs_ticks,-1).
% 4.28/4.57 assign(sos_limit,10000).
% 4.28/4.57 assign(order,kbo).
% 4.28/4.57 set(lex_order_vars).
% 4.28/4.57 clear(print_given).
% 4.28/4.57
% 4.28/4.57 % formulas(sos). % not echoed (17 formulas)
% 4.28/4.57
% 4.28/4.57 ============================== end of input ==========================
% 4.28/4.57
% 4.28/4.57 % From the command line: assign(max_seconds, 300).
% 4.28/4.57
% 4.28/4.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.28/4.57
% 4.28/4.57 % Formulas that are not ordinary clauses:
% 4.28/4.57
% 4.28/4.57 ============================== end of process non-clausal formulas ===
% 4.28/4.57
% 4.28/4.57 ============================== PROCESS INITIAL CLAUSES ===============
% 4.28/4.57
% 4.28/4.57 ============================== PREDICATE ELIMINATION =================
% 4.28/4.57
% 4.28/4.57 ============================== end predicate elimination =============
% 4.28/4.57
% 4.28/4.57 Auto_denials:
% 4.28/4.57 % copying label goals_17 to answer in negative clause
% 4.28/4.57
% 4.28/4.57 Term ordering decisions:
% 4.28/4.57 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 4.28/4.57
% 4.28/4.57 ============================== end of process initial clauses ========
% 4.28/4.57
% 4.28/4.57 ============================== CLAUSES FOR SEARCH ====================
% 4.28/4.57
% 4.28/4.57 ============================== end of clauses for search =============
% 4.28/4.57
% 4.28/4.57 ============================== SEARCH ================================
% 4.28/4.57
% 4.28/4.57 % Starting search at 0.01 seconds.
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=86.000, iters=3414
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=84.000, iters=3355
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=76.000, iters=3491
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=70.000, iters=3384
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=69.000, iters=3385
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=68.000, iters=3407
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=67.000, iters=3383
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=66.000, iters=3339
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=65.000, iters=3396
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=61.000, iters=3390
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=60.000, iters=3336
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=58.000, iters=3372
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=57.000, iters=3340
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=56.000, iters=3334
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=55.000, iters=3356
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=53.000, iters=3399
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=51.000, iters=3357
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=50.000, iters=3335
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=49.000, iters=3359
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=48.000, iters=3370
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=45.000, iters=3383
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=40.000, iters=3436
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=38.000, iters=3562
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=33.000, iters=3377
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=31.000, iters=3341
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=30.000, iters=3340
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=29.000, iters=3359
% 4.28/4.57
% 4.28/4.57 Low Water (keep): wt=28.000, iters=3432
% 4.60/4.89
% 4.60/4.89 Low Water (keep): wt=27.000, iters=3349
% 4.60/4.89
% 4.60/4.89 Low Water (keep): wt=26.000, iters=3394
% 4.60/4.89
% 4.60/4.89 Low Water (keep): wt=25.000, iters=3333
% 4.60/4.89
% 4.60/4.89 ============================== PROOF =================================
% 4.60/4.89 % SZS status Unsatisfiable
% 4.60/4.89 % SZS output start Refutation
% 4.60/4.89
% 4.60/4.89 % Proof 1 at 3.83 (+ 0.07) seconds: goals_17.
% 4.60/4.89 % Length of proof is 132.
% 4.60/4.89 % Level of proof is 36.
% 4.60/4.89 % Maximum clause weight is 48.000.
% 4.60/4.89 % Given clauses 614.
% 4.60/4.89
% 4.60/4.89 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 4.60/4.89 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 4.60/4.89 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 4.60/4.89 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 4.60/4.89 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 4.60/4.89 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 4.60/4.89 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 4.60/4.89 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 4.60/4.89 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 4.60/4.89 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 4.60/4.89 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 4.60/4.89 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 4.60/4.89 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 4.60/4.89 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 4.60/4.89 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 4.60/4.89 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 4.60/4.89 17 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 4.60/4.89 18 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(17),flip(a)].
% 4.60/4.89 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 4.60/4.89 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 4.60/4.89 21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 4.60/4.89 22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 4.60/4.89 23 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].
% 4.60/4.89 24 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(23),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 4.60/4.89 25 join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C) # label(modular_law_2_16) # label(axiom). [assumption].
% 4.60/4.89 26 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))). [copy(25),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 4.60/4.89 27 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].
% 4.60/4.89 28 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(27),rewrite([8(2),7(4),8(8),8(14),8(22),8(28)])].
% 4.60/4.89 29 complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top) # label(goals_17) # label(negated_conjecture) # answer(goals_17). [assumption].
% 4.60/4.89 30 composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)) # answer(goals_17). [copy(29),flip(a)].
% 4.60/4.89 31 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 4.60/4.89 32 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),10(a,1,1)),rewrite([7(4)]),flip(a)].
% 4.60/4.89 33 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 4.60/4.89 34 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 4.60/4.89 35 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 4.60/4.89 36 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 4.60/4.89 38 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(12(a,1),18(a,1,1)),rewrite([7(7)])].
% 4.60/4.89 40 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(16(a,1),18(a,1,1)),rewrite([7(6)])].
% 4.60/4.89 42 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),20(a,1,2,2,1))].
% 4.60/4.89 43 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),20(a,1,2,1))].
% 4.60/4.89 47 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([31(2)])].
% 4.60/4.89 48 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),22(a,1,2,1)),rewrite([31(6),7(6)])].
% 4.60/4.89 51 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(22(a,1),22(a,1,2,1)),rewrite([7(10)])].
% 4.60/4.89 77 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(31(a,1),20(a,1,1)),rewrite([31(9)])].
% 4.60/4.89 79 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(31(a,1),22(a,1,2,1,1))].
% 4.60/4.89 87 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(32(a,1),10(a,1,1)),rewrite([7(7),14(7,R),7(6)]),flip(a)].
% 4.60/4.89 88 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(32(a,1),10(a,1,2)),rewrite([14(4,R),7(3),10(3),87(7)]),flip(a)].
% 4.60/4.89 96 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(32(a,1),32(a,2,2)),rewrite([88(4),32(4),14(6,R),7(5)])].
% 4.60/4.89 97 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(87),rewrite([96(8),10(7)])].
% 4.60/4.89 104 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(33(a,1),10(a,1,1)),rewrite([7(7)]),flip(a)].
% 4.60/4.89 112 composition(converse(one),A) = A. [para(1(a,1),34(a,1,1)),rewrite([2(2)]),flip(a)].
% 4.60/4.89 121 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(22(a,1),35(a,1,2)),rewrite([7(4),35(4),7(3),7(8)]),flip(a)].
% 4.60/4.89 122 join(top,complement(complement(A))) = top. [para(24(a,1),35(a,1,2)),rewrite([4(22),7(8),121(8)]),flip(a)].
% 4.60/4.89 123 converse(one) = one. [para(112(a,1),1(a,1)),flip(a)].
% 4.60/4.89 125 composition(join(A,one),B) = join(B,composition(A,B)). [para(112(a,1),18(a,1,1)),rewrite([123(4),7(4)]),flip(a)].
% 4.60/4.89 127 join(complement(A),complement(composition(one,A))) = complement(A). [para(112(a,1),20(a,1,2))].
% 4.60/4.89 141 composition(one,A) = A. [para(112(a,1),36(a,2)),rewrite([123(2),36(4)])].
% 4.60/4.89 147 join(complement(A),complement(A)) = complement(A). [back_rewrite(127),rewrite([141(3)])].
% 4.60/4.89 148 join(zero,complement(complement(A))) = A. [back_rewrite(47),rewrite([147(4)])].
% 4.60/4.89 149 converse(join(A,one)) = join(one,converse(A)). [para(123(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 4.60/4.89 150 join(zero,complement(A)) = complement(A). [para(122(a,1),22(a,1,1,1)),rewrite([31(2),31(3),148(5)])].
% 4.60/4.89 152 join(top,complement(A)) = join(top,top). [para(122(a,1),35(a,1,2)),rewrite([7(3)])].
% 4.60/4.89 153 complement(complement(A)) = A. [back_rewrite(148),rewrite([150(4)])].
% 4.60/4.89 161 join(A,complement(join(top,top))) = A. [back_rewrite(79),rewrite([152(3),150(7),153(6),7(5)])].
% 4.60/4.89 163 complement(join(A,A)) = complement(A). [back_rewrite(48),rewrite([153(3),150(4)])].
% 4.60/4.89 165 join(A,top) = top. [back_rewrite(122),rewrite([153(3),7(2)])].
% 4.60/4.89 170 join(A,zero) = A. [back_rewrite(161),rewrite([165(3),31(2)])].
% 4.60/4.89 171 join(top,complement(A)) = top. [back_rewrite(152),rewrite([165(6)])].
% 4.60/4.89 180 join(A,composition(converse(B),complement(composition(B,complement(A))))) = A. [para(153(a,1),20(a,1,1)),rewrite([153(8)])].
% 4.60/4.89 181 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(153(a,1),22(a,1,1,1,2)),rewrite([153(5),7(4)])].
% 4.60/4.89 189 complement(zero) = top. [para(31(a,1),153(a,1,1))].
% 4.60/4.89 199 converse(join(A,composition(A,B))) = composition(join(one,converse(B)),converse(A)). [para(141(a,1),38(a,1,2)),rewrite([7(4),10(4)])].
% 4.60/4.89 204 join(A,A) = A. [para(163(a,1),22(a,1,1,1,2)),rewrite([163(6),22(8)]),flip(a)].
% 4.60/4.89 211 join(A,join(A,B)) = join(A,B). [para(204(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),204(2)]),flip(a)].
% 4.60/4.89 217 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))). [para(149(a,1),12(a,1,1))].
% 4.60/4.89 228 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))). [back_rewrite(199),rewrite([217(8)]),flip(a)].
% 4.60/4.89 229 join(A,complement(join(B,complement(A)))) = A. [para(22(a,1),211(a,1,2)),rewrite([7(4),22(12)])].
% 4.60/4.89 246 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(2(a,1),42(a,1,2,1))].
% 4.60/4.89 252 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(153(a,1),42(a,1,2,2))].
% 4.60/4.89 259 join(converse(zero),composition(converse(complement(composition(A,top))),A)) = converse(zero). [para(77(a,1),10(a,2,1)),rewrite([34(8)])].
% 4.60/4.89 265 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(149(a,1),77(a,1,2,1))].
% 4.60/4.89 301 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),252(a,1,2))].
% 4.60/4.89 305 converse(complement(one)) = complement(one). [para(301(a,1),10(a,2,1)),rewrite([2(7),7(6),301(6)]),flip(a)].
% 4.60/4.89 314 converse(top) = top. [para(305(a,1),149(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 4.60/4.89 325 join(top,converse(A)) = top. [para(314(a,1),10(a,1,1)),rewrite([7(5),165(5),314(5)])].
% 4.60/4.89 332 join(top,composition(A,converse(B))) = top. [para(33(a,1),325(a,1,2))].
% 4.60/4.89 334 join(top,composition(A,B)) = top. [para(2(a,1),332(a,1,2,2))].
% 4.60/4.89 335 composition(join(A,one),top) = top. [para(314(a,1),332(a,1,2,2)),rewrite([125(4,R)])].
% 4.60/4.89 336 composition(join(one,converse(A)),zero) = zero. [back_rewrite(265),rewrite([335(8),31(6),125(7,R),7(5),211(5)])].
% 4.60/4.89 363 composition(top,zero) = zero. [para(305(a,1),336(a,1,1,2)),rewrite([4(4)])].
% 4.60/4.89 368 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(363(a,1),28(a,1,1,1,2,1)),rewrite([189(3),7(3),171(3),31(2),31(3),150(7),153(6),189(6),314(7),171(9),31(6),16(6),31(9),150(13),153(12),189(12),314(13),171(15),31(12),16(12)])].
% 4.60/4.89 372 join(zero,composition(A,composition(B,zero))) = zero. [para(363(a,1),40(a,1,2)),rewrite([7(5),334(8),363(8)])].
% 4.60/4.89 375 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(368),rewrite([372(7)]),flip(a)].
% 4.60/4.89 434 join(complement(A),complement(join(B,A))) = complement(A). [para(229(a,1),51(a,2)),rewrite([153(2),153(4),153(8),51(13)])].
% 4.60/4.89 454 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(375(a,1),16(a,1,1)),rewrite([16(7)]),flip(a)].
% 4.60/4.89 455 composition(A,zero) = zero. [para(375(a,1),16(a,1)),rewrite([375(6)]),flip(a)].
% 4.60/4.89 456 composition(converse(zero),A) = converse(zero). [para(375(a,1),34(a,1,1)),rewrite([455(6)]),flip(a)].
% 4.60/4.89 461 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(454),rewrite([456(5)]),flip(a)].
% 4.60/4.89 463 composition(zero,A) = c_0. [new_symbol(461)].
% 4.60/4.89 464 composition(A,converse(zero)) = c_0. [back_rewrite(461),rewrite([463(2)]),flip(a)].
% 4.60/4.89 479 c_0 = zero. [para(463(a,1),1(a,1))].
% 4.60/4.89 480 converse(zero) = zero. [para(463(a,1),12(a,2,1)),rewrite([464(4),479(1),479(2)]),flip(a)].
% 4.60/4.89 481 join(zero,composition(A,B)) = composition(A,B). [para(463(a,1),18(a,1,1)),rewrite([479(1),7(5),170(5)])].
% 4.60/4.89 483 composition(zero,A) = zero. [back_rewrite(463),rewrite([479(3)])].
% 4.60/4.89 484 composition(converse(complement(composition(A,top))),A) = zero. [back_rewrite(259),rewrite([480(2),481(7),480(7)])].
% 4.60/4.89 603 composition(converse(complement(composition(A,top))),composition(A,B)) = zero. [para(484(a,1),16(a,1,1)),rewrite([483(2)]),flip(a)].
% 4.60/4.89 756 join(one,complement(composition(A,complement(converse(A))))) = complement(composition(A,complement(converse(A)))). [para(246(a,1),434(a,1,2,1)),rewrite([153(7),7(6)])].
% 4.60/4.89 2473 join(A,join(complement(A),converse(B))) = top. [para(4(a,1),96(a,1,1)),rewrite([325(3)]),flip(a)].
% 4.60/4.89 2557 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(33(a,1),2473(a,1,2,2))].
% 4.60/4.89 3153 join(A,join(complement(A),composition(B,C))) = top. [para(2(a,1),2557(a,1,2,2,2))].
% 4.60/4.89 3156 join(A,composition(join(B,one),complement(A))) = top. [para(125(a,2),3153(a,1,2))].
% 4.60/4.89 3210 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3156(a,1),14(a,2,2)),rewrite([7(5),165(8)])].
% 4.60/4.89 7329 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(43(a,1),3210(a,1,2)),rewrite([149(3),7(6)])].
% 4.60/4.89 7390 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7329(a,1),104(a,1,1)),rewrite([314(2),32(5),123(3),7(8)]),flip(a)].
% 4.60/4.89 9335 join(A,converse(complement(converse(A)))) = top. [para(204(a,1),7390(a,1,2,2)),rewrite([1(5),7(4)])].
% 4.60/4.89 9374 join(complement(converse(A)),converse(join(B,A))) = top. [para(9335(a,1),97(a,1,1,2)),rewrite([165(2),314(2)]),flip(a)].
% 4.60/4.89 9380 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))). [para(9335(a,1),181(a,1,1,1)),rewrite([31(2),7(6),150(8)])].
% 4.60/4.89 9415 join(complement(one),complement(composition(converse(complement(A)),A))) = top. [para(42(a,1),9374(a,1,2,1)),rewrite([34(4),305(7),7(7)])].
% 4.60/4.89 9418 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top. [para(246(a,1),9374(a,1,2,1)),rewrite([305(8),7(8)])].
% 4.60/4.89 9526 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero. [para(9415(a,1),26(a,1,2,1,2,1,1,1)),rewrite([141(6),7(6),31(13),483(13),189(13),7(13),171(13),31(9),7(9),150(9),12(18),9418(19),31(13),483(13),189(13),7(13),171(13),31(9)])].
% 4.60/4.89 9601 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))). [para(9526(a,1),22(a,1,1)),rewrite([153(3),150(8)])].
% 4.60/4.89 9614 complement(converse(complement(converse(A)))) = A. [para(9526(a,1),181(a,1,2)),rewrite([7(5),9380(6),7(6),150(6),153(6)])].
% 4.60/4.89 9617 converse(complement(converse(A))) = complement(A). [back_rewrite(9601),rewrite([9614(4),204(1)]),flip(a)].
% 4.60/4.89 9647 complement(converse(A)) = converse(complement(A)). [para(9617(a,1),2(a,1,1)),flip(a)].
% 4.60/4.89 9651 converse(complement(composition(A,converse(B)))) = complement(composition(B,converse(A))). [para(33(a,1),9617(a,1,1,1))].
% 4.60/4.89 9652 converse(complement(composition(converse(A),B))) = complement(composition(converse(B),A)). [para(34(a,1),9617(a,1,1,1))].
% 4.60/4.89 10533 join(one,complement(composition(A,converse(complement(A))))) = complement(composition(A,converse(complement(A)))). [back_rewrite(756),rewrite([9647(3),9647(8)])].
% 4.60/4.89 11768 composition(complement(composition(complement(A),converse(A))),A) = A. [para(180(a,1),228(a,2,1)),rewrite([9647(3),7(7),10533(7),34(7),9651(5),2(7)])].
% 4.60/4.89 11929 composition(A,complement(composition(converse(A),complement(A)))) = A. [para(11768(a,1),33(a,1,1)),rewrite([2(2),9647(2),2(4),9652(5)]),flip(a)].
% 4.60/4.89 12012 composition(complement(A),complement(composition(converse(complement(A)),A))) = complement(A). [para(153(a,1),11929(a,1,2,1,2))].
% 4.60/4.89 15883 composition(complement(composition(A,top)),top) = complement(composition(A,top)). [para(603(a,1),12012(a,1,2,1)),rewrite([189(5)])].
% 4.60/4.89 15884 $F # answer(goals_17). [resolve(15883,a,30,a)].
% 4.60/4.89
% 4.60/4.89 % SZS output end Refutation
% 4.60/4.89 ============================== end of proof ==========================
% 4.60/4.89
% 4.60/4.89 ============================== STATISTICS ============================
% 4.60/4.89
% 4.60/4.89 Given=614. Generated=107885. Kept=15870. proofs=1.
% 4.60/4.89 Usable=446. Sos=9510. Demods=9566. Limbo=3, Disabled=5927. Hints=0.
% 4.60/4.89 Megabytes=26.35.
% 4.60/4.89 User_CPU=3.83, System_CPU=0.07, Wall_clock=4.
% 4.60/4.89
% 4.60/4.89 ============================== end of statistics =====================
% 4.60/4.89
% 4.60/4.89 ============================== end of search =========================
% 4.60/4.89
% 4.60/4.89 THEOREM PROVED
% 4.60/4.89 % SZS status Unsatisfiable
% 4.60/4.89
% 4.60/4.89 Exiting with 1 proof.
% 4.60/4.89
% 4.60/4.89 Process 18400 exit (max_proofs) Fri Jul 8 09:49:45 2022
% 4.60/4.89 Prover9 interrupted
%------------------------------------------------------------------------------