TSTP Solution File: REL044-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL044-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 19:54:27 EDT 2022
% Result : Unsatisfiable 3.64s 3.92s
% Output : Refutation 3.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL044-2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n009.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 07:50:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.64/3.92 ============================== Prover9 ===============================
% 3.64/3.92 Prover9 (32) version 2009-11A, November 2009.
% 3.64/3.92 Process 15912 was started by sandbox2 on n009.cluster.edu,
% 3.64/3.92 Fri Jul 8 07:50:07 2022
% 3.64/3.92 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15759_n009.cluster.edu".
% 3.64/3.92 ============================== end of head ===========================
% 3.64/3.92
% 3.64/3.92 ============================== INPUT =================================
% 3.64/3.92
% 3.64/3.92 % Reading from file /tmp/Prover9_15759_n009.cluster.edu
% 3.64/3.92
% 3.64/3.92 set(prolog_style_variables).
% 3.64/3.92 set(auto2).
% 3.64/3.92 % set(auto2) -> set(auto).
% 3.64/3.92 % set(auto) -> set(auto_inference).
% 3.64/3.92 % set(auto) -> set(auto_setup).
% 3.64/3.92 % set(auto_setup) -> set(predicate_elim).
% 3.64/3.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.64/3.92 % set(auto) -> set(auto_limits).
% 3.64/3.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.64/3.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.64/3.92 % set(auto) -> set(auto_denials).
% 3.64/3.92 % set(auto) -> set(auto_process).
% 3.64/3.92 % set(auto2) -> assign(new_constants, 1).
% 3.64/3.92 % set(auto2) -> assign(fold_denial_max, 3).
% 3.64/3.92 % set(auto2) -> assign(max_weight, "200.000").
% 3.64/3.92 % set(auto2) -> assign(max_hours, 1).
% 3.64/3.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.64/3.92 % set(auto2) -> assign(max_seconds, 0).
% 3.64/3.92 % set(auto2) -> assign(max_minutes, 5).
% 3.64/3.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.64/3.92 % set(auto2) -> set(sort_initial_sos).
% 3.64/3.92 % set(auto2) -> assign(sos_limit, -1).
% 3.64/3.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.64/3.92 % set(auto2) -> assign(max_megs, 400).
% 3.64/3.92 % set(auto2) -> assign(stats, some).
% 3.64/3.92 % set(auto2) -> clear(echo_input).
% 3.64/3.92 % set(auto2) -> set(quiet).
% 3.64/3.92 % set(auto2) -> clear(print_initial_clauses).
% 3.64/3.92 % set(auto2) -> clear(print_given).
% 3.64/3.92 assign(lrs_ticks,-1).
% 3.64/3.92 assign(sos_limit,10000).
% 3.64/3.92 assign(order,kbo).
% 3.64/3.92 set(lex_order_vars).
% 3.64/3.92 clear(print_given).
% 3.64/3.92
% 3.64/3.92 % formulas(sos). % not echoed (18 formulas)
% 3.64/3.92
% 3.64/3.92 ============================== end of input ==========================
% 3.64/3.92
% 3.64/3.92 % From the command line: assign(max_seconds, 300).
% 3.64/3.92
% 3.64/3.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.64/3.92
% 3.64/3.92 % Formulas that are not ordinary clauses:
% 3.64/3.92
% 3.64/3.92 ============================== end of process non-clausal formulas ===
% 3.64/3.92
% 3.64/3.92 ============================== PROCESS INITIAL CLAUSES ===============
% 3.64/3.92
% 3.64/3.92 ============================== PREDICATE ELIMINATION =================
% 3.64/3.92
% 3.64/3.92 ============================== end predicate elimination =============
% 3.64/3.92
% 3.64/3.92 Auto_denials:
% 3.64/3.92 % copying label goals_18 to answer in negative clause
% 3.64/3.92
% 3.64/3.92 Term ordering decisions:
% 3.64/3.92 Function symbol KB weights: sk3=1. one=1. sk1=1. sk2=1. top=1. zero=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 3.64/3.92
% 3.64/3.92 ============================== end of process initial clauses ========
% 3.64/3.92
% 3.64/3.92 ============================== CLAUSES FOR SEARCH ====================
% 3.64/3.92
% 3.64/3.92 ============================== end of clauses for search =============
% 3.64/3.92
% 3.64/3.92 ============================== SEARCH ================================
% 3.64/3.92
% 3.64/3.92 % Starting search at 0.01 seconds.
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=86.000, iters=3408
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=84.000, iters=3350
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=76.000, iters=3496
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=70.000, iters=3388
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=68.000, iters=3345
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=67.000, iters=3363
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=66.000, iters=3343
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=65.000, iters=3401
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=61.000, iters=3396
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=60.000, iters=3342
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=58.000, iters=3378
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=57.000, iters=3390
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=56.000, iters=3346
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=55.000, iters=3343
% 3.64/3.92
% 3.64/3.92 Low Water (keep): wt=53.000, iters=3384
% 3.64/3.92
% 3.64/3.92 ============================== PROOF =================================
% 3.64/3.92 % SZS status Unsatisfiable
% 3.64/3.92 % SZS output start Refutation
% 3.64/3.92
% 3.64/3.92 % Proof 1 at 2.89 (+ 0.04) seconds: goals_18.
% 3.64/3.92 % Length of proof is 116.
% 3.64/3.92 % Level of proof is 36.
% 3.64/3.92 % Maximum clause weight is 48.000.
% 3.64/3.92 % Given clauses 505.
% 3.64/3.92
% 3.64/3.92 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 3.64/3.92 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 3.64/3.92 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 3.64/3.92 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 3.64/3.92 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 3.64/3.92 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 3.64/3.92 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 3.64/3.92 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 3.64/3.92 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 3.64/3.92 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 3.64/3.92 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 3.64/3.92 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 3.64/3.92 13 join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3) # label(goals_17) # label(negated_conjecture). [assumption].
% 3.64/3.92 14 join(complement(sk3),composition(complement(sk1),sk2)) = complement(sk3). [copy(13),rewrite([7(7)])].
% 3.64/3.92 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 3.64/3.92 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 3.64/3.92 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 3.64/3.92 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 3.64/3.92 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 3.64/3.92 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 3.64/3.92 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 3.64/3.92 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 3.64/3.92 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].
% 3.64/3.92 24 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(23),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 3.64/3.92 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].
% 3.64/3.92 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([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 3.64/3.92 27 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].
% 3.64/3.92 28 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(27),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 3.64/3.92 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].
% 3.64/3.92 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([8(2),7(4),8(8),8(14),8(22),8(28)])].
% 3.64/3.92 31 join(composition(sk3,converse(sk2)),sk1) != sk1 # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 3.64/3.92 32 join(sk1,composition(sk3,converse(sk2))) != sk1 # answer(goals_18). [copy(31),rewrite([7(6)])].
% 3.64/3.92 33 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 3.64/3.92 34 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),10(a,1,1)),rewrite([7(4)]),flip(a)].
% 3.64/3.92 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 3.64/3.92 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 3.64/3.92 37 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 3.64/3.92 38 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 3.64/3.92 43 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(18(a,1),20(a,1,1)),rewrite([7(6)])].
% 3.64/3.92 45 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(1(a,1),22(a,1,2,2,1))].
% 3.64/3.92 46 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),22(a,1,2,1))].
% 3.64/3.92 50 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1)),rewrite([33(2)])].
% 3.64/3.92 51 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),24(a,1,2,1)),rewrite([33(6),7(6)])].
% 3.64/3.92 64 join(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,C)))),converse(C)))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,C)))),converse(C))))). [para(2(a,1),28(a,1,2,1,2,1,1,1,2,1,2)),rewrite([2(22)])].
% 3.64/3.92 80 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(33(a,1),22(a,1,1)),rewrite([33(9)])].
% 3.64/3.92 90 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(34(a,1),10(a,1,1)),rewrite([7(7),16(7,R),7(6)]),flip(a)].
% 3.64/3.92 91 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(34(a,1),10(a,1,2)),rewrite([16(4,R),7(3),10(3),90(7)]),flip(a)].
% 3.64/3.92 99 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(34(a,1),34(a,2,2)),rewrite([91(4),34(4),16(6,R),7(5)])].
% 3.64/3.92 100 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))). [back_rewrite(90),rewrite([99(8),10(7)])].
% 3.64/3.92 107 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(35(a,1),10(a,1,1)),rewrite([7(7)]),flip(a)].
% 3.64/3.92 115 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 3.64/3.92 124 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(24(a,1),37(a,1,2)),rewrite([7(4),37(4),7(3),7(8)]),flip(a)].
% 3.64/3.92 125 join(top,complement(complement(A))) = top. [para(26(a,1),37(a,1,2)),rewrite([4(22),7(8),124(8)]),flip(a)].
% 3.64/3.92 126 converse(one) = one. [para(115(a,1),1(a,1)),flip(a)].
% 3.64/3.92 128 composition(join(A,one),B) = join(B,composition(A,B)). [para(115(a,1),20(a,1,1)),rewrite([126(4),7(4)]),flip(a)].
% 3.64/3.92 130 join(complement(A),complement(composition(one,A))) = complement(A). [para(115(a,1),22(a,1,2))].
% 3.64/3.92 144 composition(one,A) = A. [para(115(a,1),38(a,2)),rewrite([126(2),38(4)])].
% 3.64/3.92 150 join(complement(A),complement(A)) = complement(A). [back_rewrite(130),rewrite([144(3)])].
% 3.64/3.92 151 join(zero,complement(complement(A))) = A. [back_rewrite(50),rewrite([150(4)])].
% 3.64/3.92 152 converse(join(A,one)) = join(one,converse(A)). [para(126(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 3.64/3.92 153 join(zero,complement(A)) = complement(A). [para(125(a,1),24(a,1,1,1)),rewrite([33(2),33(3),151(5)])].
% 3.64/3.92 155 join(top,complement(A)) = join(top,top). [para(125(a,1),37(a,1,2)),rewrite([7(3)])].
% 3.64/3.92 156 complement(complement(A)) = A. [back_rewrite(151),rewrite([153(4)])].
% 3.64/3.92 166 complement(join(A,A)) = complement(A). [back_rewrite(51),rewrite([156(3),153(4)])].
% 3.64/3.92 168 join(A,top) = top. [back_rewrite(125),rewrite([156(3),7(2)])].
% 3.64/3.92 174 join(top,complement(A)) = top. [back_rewrite(155),rewrite([168(6)])].
% 3.64/3.92 184 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(156(a,1),24(a,1,1,1,2)),rewrite([156(5),7(4)])].
% 3.64/3.92 192 complement(zero) = top. [para(33(a,1),156(a,1,1))].
% 3.64/3.92 207 join(A,A) = A. [para(166(a,1),24(a,1,1,1,2)),rewrite([166(6),24(8)]),flip(a)].
% 3.64/3.92 214 join(A,join(A,B)) = join(A,B). [para(207(a,1),16(a,1)),rewrite([7(3),16(4,R),7(3),16(3,R),207(2)]),flip(a)].
% 3.64/3.92 249 join(complement(one),composition(A,complement(converse(A)))) = complement(one). [para(2(a,1),45(a,1,2,1))].
% 3.64/3.92 255 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(156(a,1),45(a,1,2,2))].
% 3.64/3.92 268 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(152(a,1),80(a,1,2,1))].
% 3.64/3.92 304 join(complement(one),converse(complement(one))) = complement(one). [para(1(a,1),255(a,1,2))].
% 3.64/3.92 308 converse(complement(one)) = complement(one). [para(304(a,1),10(a,2,1)),rewrite([2(7),7(6),304(6)]),flip(a)].
% 3.64/3.92 317 converse(top) = top. [para(308(a,1),152(a,2,2)),rewrite([7(4),4(4),4(6)])].
% 3.64/3.92 328 join(top,converse(A)) = top. [para(317(a,1),10(a,1,1)),rewrite([7(5),168(5),317(5)])].
% 3.64/3.92 335 join(top,composition(A,converse(B))) = top. [para(35(a,1),328(a,1,2))].
% 3.64/3.92 337 join(top,composition(A,B)) = top. [para(2(a,1),335(a,1,2,2))].
% 3.64/3.92 338 composition(join(A,one),top) = top. [para(317(a,1),335(a,1,2,2)),rewrite([128(4,R)])].
% 3.64/3.92 339 composition(join(one,converse(A)),zero) = zero. [back_rewrite(268),rewrite([338(8),33(6),128(7,R),7(5),214(5)])].
% 3.64/3.92 366 composition(top,zero) = zero. [para(308(a,1),339(a,1,1,2)),rewrite([4(4)])].
% 3.64/3.92 371 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(366(a,1),30(a,1,1,1,2,1)),rewrite([192(3),7(3),174(3),33(2),33(3),153(7),156(6),192(6),317(7),174(9),33(6),18(6),33(9),153(13),156(12),192(12),317(13),174(15),33(12),18(12)])].
% 3.64/3.92 375 join(zero,composition(A,composition(B,zero))) = zero. [para(366(a,1),43(a,1,2)),rewrite([7(5),337(8),366(8)])].
% 3.64/3.92 378 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(371),rewrite([375(7)]),flip(a)].
% 3.64/3.92 457 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(378(a,1),18(a,1,1)),rewrite([18(7)]),flip(a)].
% 3.64/3.92 458 composition(A,zero) = zero. [para(378(a,1),18(a,1)),rewrite([378(6)]),flip(a)].
% 3.64/3.92 459 composition(converse(zero),A) = converse(zero). [para(378(a,1),36(a,1,1)),rewrite([458(6)]),flip(a)].
% 3.64/3.92 464 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(457),rewrite([459(5)]),flip(a)].
% 3.64/3.92 466 composition(zero,A) = c_0. [new_symbol(464)].
% 3.64/3.92 482 c_0 = zero. [para(466(a,1),1(a,1))].
% 3.64/3.92 486 composition(zero,A) = zero. [back_rewrite(466),rewrite([482(3)])].
% 3.64/3.92 2478 join(A,join(complement(A),converse(B))) = top. [para(4(a,1),99(a,1,1)),rewrite([328(3)]),flip(a)].
% 3.64/3.92 2563 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(35(a,1),2478(a,1,2,2))].
% 3.64/3.92 3159 join(A,join(complement(A),composition(B,C))) = top. [para(2(a,1),2563(a,1,2,2,2))].
% 3.64/3.92 3162 join(A,composition(join(B,one),complement(A))) = top. [para(128(a,2),3159(a,1,2))].
% 3.64/3.92 3216 join(A,join(B,composition(join(C,one),complement(A)))) = top. [para(3162(a,1),16(a,2,2)),rewrite([7(5),168(8)])].
% 3.64/3.92 7390 join(complement(A),composition(join(one,converse(B)),A)) = top. [para(46(a,1),3216(a,1,2)),rewrite([152(3),7(6)])].
% 3.64/3.92 7400 join(converse(complement(converse(A))),composition(A,join(B,one))) = top. [para(7390(a,1),107(a,1,1)),rewrite([317(2),34(5),126(3),7(8)]),flip(a)].
% 3.64/3.92 9367 join(A,converse(complement(converse(A)))) = top. [para(207(a,1),7400(a,1,2,2)),rewrite([1(5),7(4)])].
% 3.64/3.92 9395 join(complement(converse(A)),converse(join(B,A))) = top. [para(9367(a,1),100(a,1,1,2)),rewrite([168(2),317(2)]),flip(a)].
% 3.64/3.92 9401 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))). [para(9367(a,1),184(a,1,1,1)),rewrite([33(2),7(6),153(8)])].
% 3.64/3.92 9452 join(converse(complement(sk3)),complement(converse(composition(complement(sk1),sk2)))) = top. [para(14(a,1),9395(a,1,2,1)),rewrite([7(10)])].
% 3.64/3.92 9462 join(complement(one),complement(composition(converse(complement(A)),A))) = top. [para(45(a,1),9395(a,1,2,1)),rewrite([36(4),308(7),7(7)])].
% 3.64/3.92 9465 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top. [para(249(a,1),9395(a,1,2,1)),rewrite([308(8),7(8)])].
% 3.64/3.92 9548 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero. [para(9462(a,1),28(a,1,2,1,2,1,1,1)),rewrite([144(6),7(6),33(13),486(13),192(13),7(13),174(13),33(9),7(9),153(9),12(18),9465(19),33(13),486(13),192(13),7(13),174(13),33(9)])].
% 3.64/3.92 9623 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))). [para(9548(a,1),24(a,1,1)),rewrite([156(3),153(8)])].
% 3.64/3.92 9636 complement(converse(complement(converse(A)))) = A. [para(9548(a,1),184(a,1,2)),rewrite([7(5),9401(6),7(6),153(6),156(6)])].
% 3.64/3.92 9639 converse(complement(converse(A))) = complement(A). [back_rewrite(9623),rewrite([9636(4),207(1)]),flip(a)].
% 3.64/3.92 9669 complement(converse(A)) = converse(complement(A)). [para(9639(a,1),2(a,1,1)),flip(a)].
% 3.64/3.92 9768 converse(join(complement(sk3),complement(composition(complement(sk1),sk2)))) = top. [back_rewrite(9452),rewrite([9669(9),10(10)])].
% 3.64/3.92 12546 join(complement(sk3),complement(composition(complement(sk1),sk2))) = top. [para(9768(a,1),2(a,1,1)),rewrite([317(2)]),flip(a)].
% 3.64/3.92 12548 complement(join(sk1,complement(composition(sk3,converse(sk2))))) = zero. [para(12546(a,1),64(a,1,2,1,2,1,1,1)),rewrite([156(3),156(11),33(11),486(13),192(11),168(11),33(10),7(10),153(10),156(11),12546(17),33(11),486(13),192(11),168(11),33(10)])].
% 3.64/3.92 12555 complement(join(sk1,composition(sk3,converse(sk2)))) = complement(sk1). [para(12548(a,1),184(a,1,2)),rewrite([7(6),7(9),153(9)])].
% 3.64/3.92 12697 join(sk1,composition(sk3,converse(sk2))) = sk1. [para(12555(a,1),24(a,1,1,1,2)),rewrite([12555(12),24(10)]),flip(a)].
% 3.64/3.92 12698 $F # answer(goals_18). [resolve(12697,a,32,a)].
% 3.64/3.92
% 3.64/3.92 % SZS output end Refutation
% 3.64/3.92 ============================== end of proof ==========================
% 3.64/3.92
% 3.64/3.92 ============================== STATISTICS ============================
% 3.64/3.92
% 3.64/3.92 Given=505. Generated=75074. Kept=12683. proofs=1.
% 3.64/3.92 Usable=345. Sos=7277. Demods=7438. Limbo=1, Disabled=5077. Hints=0.
% 3.64/3.92 Megabytes=23.57.
% 3.64/3.92 User_CPU=2.89, System_CPU=0.04, Wall_clock=3.
% 3.64/3.92
% 3.64/3.92 ============================== end of statistics =====================
% 3.64/3.92
% 3.64/3.92 ============================== end of search =========================
% 3.64/3.92
% 3.64/3.92 THEOREM PROVED
% 3.64/3.92 % SZS status Unsatisfiable
% 3.64/3.92
% 3.64/3.92 Exiting with 1 proof.
% 3.64/3.92
% 3.64/3.92 Process 15912 exit (max_proofs) Fri Jul 8 07:50:10 2022
% 3.64/3.92 Prover9 interrupted
%------------------------------------------------------------------------------