TSTP Solution File: REL011-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL011-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 19:53:36 EDT 2022
% Result : Unsatisfiable 2.14s 2.44s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL011-2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.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 14:12:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.14/2.44 ============================== Prover9 ===============================
% 2.14/2.44 Prover9 (32) version 2009-11A, November 2009.
% 2.14/2.44 Process 22439 was started by sandbox on n004.cluster.edu,
% 2.14/2.44 Fri Jul 8 14:12:53 2022
% 2.14/2.44 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22285_n004.cluster.edu".
% 2.14/2.44 ============================== end of head ===========================
% 2.14/2.44
% 2.14/2.44 ============================== INPUT =================================
% 2.14/2.44
% 2.14/2.44 % Reading from file /tmp/Prover9_22285_n004.cluster.edu
% 2.14/2.44
% 2.14/2.44 set(prolog_style_variables).
% 2.14/2.44 set(auto2).
% 2.14/2.44 % set(auto2) -> set(auto).
% 2.14/2.44 % set(auto) -> set(auto_inference).
% 2.14/2.44 % set(auto) -> set(auto_setup).
% 2.14/2.44 % set(auto_setup) -> set(predicate_elim).
% 2.14/2.44 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.14/2.44 % set(auto) -> set(auto_limits).
% 2.14/2.44 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.14/2.44 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.14/2.44 % set(auto) -> set(auto_denials).
% 2.14/2.44 % set(auto) -> set(auto_process).
% 2.14/2.44 % set(auto2) -> assign(new_constants, 1).
% 2.14/2.44 % set(auto2) -> assign(fold_denial_max, 3).
% 2.14/2.44 % set(auto2) -> assign(max_weight, "200.000").
% 2.14/2.44 % set(auto2) -> assign(max_hours, 1).
% 2.14/2.44 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.14/2.44 % set(auto2) -> assign(max_seconds, 0).
% 2.14/2.44 % set(auto2) -> assign(max_minutes, 5).
% 2.14/2.44 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.14/2.44 % set(auto2) -> set(sort_initial_sos).
% 2.14/2.44 % set(auto2) -> assign(sos_limit, -1).
% 2.14/2.44 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.14/2.44 % set(auto2) -> assign(max_megs, 400).
% 2.14/2.44 % set(auto2) -> assign(stats, some).
% 2.14/2.44 % set(auto2) -> clear(echo_input).
% 2.14/2.44 % set(auto2) -> set(quiet).
% 2.14/2.44 % set(auto2) -> clear(print_initial_clauses).
% 2.14/2.44 % set(auto2) -> clear(print_given).
% 2.14/2.44 assign(lrs_ticks,-1).
% 2.14/2.44 assign(sos_limit,10000).
% 2.14/2.44 assign(order,kbo).
% 2.14/2.44 set(lex_order_vars).
% 2.14/2.44 clear(print_given).
% 2.14/2.44
% 2.14/2.44 % formulas(sos). % not echoed (18 formulas)
% 2.14/2.44
% 2.14/2.44 ============================== end of input ==========================
% 2.14/2.44
% 2.14/2.44 % From the command line: assign(max_seconds, 300).
% 2.14/2.44
% 2.14/2.44 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.14/2.44
% 2.14/2.44 % Formulas that are not ordinary clauses:
% 2.14/2.44
% 2.14/2.44 ============================== end of process non-clausal formulas ===
% 2.14/2.44
% 2.14/2.44 ============================== PROCESS INITIAL CLAUSES ===============
% 2.14/2.44
% 2.14/2.44 ============================== PREDICATE ELIMINATION =================
% 2.14/2.44
% 2.14/2.44 ============================== end predicate elimination =============
% 2.14/2.44
% 2.14/2.44 Auto_denials:
% 2.14/2.44 % copying label goals_18 to answer in negative clause
% 2.14/2.44
% 2.14/2.44 Term ordering decisions:
% 2.14/2.44 Function symbol KB weights: zero=1. one=1. sk1=1. sk2=1. sk3=1. top=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 2.14/2.44
% 2.14/2.44 ============================== end of process initial clauses ========
% 2.14/2.44
% 2.14/2.44 ============================== CLAUSES FOR SEARCH ====================
% 2.14/2.44
% 2.14/2.44 ============================== end of clauses for search =============
% 2.14/2.44
% 2.14/2.44 ============================== SEARCH ================================
% 2.14/2.44
% 2.14/2.44 % Starting search at 0.01 seconds.
% 2.14/2.44
% 2.14/2.44 ============================== PROOF =================================
% 2.14/2.44 % SZS status Unsatisfiable
% 2.14/2.44 % SZS output start Refutation
% 2.14/2.44
% 2.14/2.44 % Proof 1 at 1.46 (+ 0.01) seconds: goals_18.
% 2.14/2.44 % Length of proof is 150.
% 2.14/2.44 % Level of proof is 37.
% 2.14/2.44 % Maximum clause weight is 49.000.
% 2.14/2.44 % Given clauses 302.
% 2.14/2.44
% 2.14/2.44 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 2.14/2.44 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 2.14/2.44 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 2.14/2.44 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 2.14/2.44 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 2.14/2.44 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 2.14/2.44 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 2.14/2.44 8 meet(sk1,composition(converse(sk2),sk3)) = zero # label(goals_17) # label(negated_conjecture). [assumption].
% 2.14/2.44 9 zero = meet(sk1,composition(converse(sk2),sk3)). [copy(8),flip(a)].
% 2.14/2.44 10 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 2.14/2.44 11 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 2.14/2.44 12 join(converse(A),converse(B)) = converse(join(A,B)). [copy(11),flip(a)].
% 2.14/2.44 13 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 2.14/2.44 14 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(13),flip(a)].
% 2.14/2.44 15 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 2.14/2.44 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([7(4)])].
% 2.14/2.44 17 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 2.14/2.44 18 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(17),flip(a)].
% 2.14/2.44 19 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 2.14/2.44 20 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(19),flip(a)].
% 2.14/2.44 21 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 2.14/2.44 22 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(21),rewrite([7(6)])].
% 2.14/2.44 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].
% 2.14/2.44 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)])].
% 2.14/2.44 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].
% 2.14/2.44 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),7(4),10(8),10(13),7(15),10(20),10(25),7(27)])].
% 2.14/2.44 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].
% 2.14/2.44 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([10(2),7(4),10(8),10(13),7(15),10(20),10(25),7(27)])].
% 2.14/2.44 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].
% 2.14/2.44 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),7(4),10(8),10(14),10(22),10(28)])].
% 2.14/2.44 31 meet(composition(sk2,sk1),sk3) != zero # label(goals_18) # label(negated_conjecture) # answer(goals_18). [assumption].
% 2.14/2.44 32 complement(join(complement(sk1),complement(composition(converse(sk2),sk3)))) != complement(join(complement(sk3),complement(composition(sk2,sk1)))) # answer(goals_18). [copy(31),rewrite([10(5),7(7),9(9),10(14)]),flip(a)].
% 2.14/2.44 33 complement(join(complement(sk1),complement(composition(converse(sk2),sk3)))) = complement(top). [back_rewrite(6),rewrite([10(2),4(4),9(3),10(8)]),flip(a)].
% 2.14/2.44 35 complement(join(complement(sk3),complement(composition(sk2,sk1)))) != complement(top) # answer(goals_18). [back_rewrite(32),rewrite([33(9)]),flip(a)].
% 2.14/2.44 36 converse(join(A,converse(B))) = join(B,converse(A)). [para(2(a,1),12(a,1,1)),rewrite([7(4)]),flip(a)].
% 2.14/2.44 37 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),14(a,1,1)),flip(a)].
% 2.14/2.44 38 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),14(a,1,2)),flip(a)].
% 2.14/2.44 39 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),16(a,2,2)),rewrite([7(2)])].
% 2.14/2.44 40 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),18(a,1,1)),flip(a)].
% 2.14/2.44 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([7(7)])].
% 2.14/2.44 45 join(composition(A,B),composition(C,composition(D,B))) = composition(join(A,composition(C,D)),B). [para(18(a,1),20(a,1,2))].
% 2.14/2.44 47 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A). [para(2(a,1),22(a,1,2,1))].
% 2.14/2.44 48 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)). [para(22(a,1),12(a,2,1)),rewrite([38(7)])].
% 2.14/2.44 49 join(complement(converse(A)),composition(B,complement(converse(composition(A,B))))) = complement(converse(A)). [para(14(a,1),22(a,1,2,2,1)),rewrite([2(4)])].
% 2.14/2.44 51 join(complement(top),complement(join(complement(A),complement(A)))) = A. [para(4(a,1),24(a,1,1,1))].
% 2.14/2.44 52 join(complement(top),complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),24(a,1,2,1)),rewrite([7(7)])].
% 2.14/2.44 53 join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B. [para(24(a,1),7(a,1)),rewrite([7(3),7(8)]),flip(a)].
% 2.14/2.44 54 join(complement(A),complement(join(complement(join(complement(A),complement(B))),complement(complement(join(B,complement(A))))))) = join(complement(A),complement(B)). [para(24(a,1),24(a,1,1,1)),rewrite([7(8),7(10),7(15)])].
% 2.14/2.44 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([7(10)])].
% 2.14/2.44 65 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)])].
% 2.14/2.44 75 join(complement(join(complement(A),complement(composition(converse(B),C)))),composition(complement(join(complement(converse(B)),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(B,A)))))) = composition(complement(join(complement(converse(B)),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(B,A))))). [para(2(a,1),30(a,1,2,2,1,2,1,1)),rewrite([2(30)])].
% 2.14/2.44 82 join(complement(sk1),complement(composition(converse(sk2),sk3))) = top. [para(33(a,1),24(a,1,1,1,2)),rewrite([33(14),24(10)]),flip(a)].
% 2.14/2.44 86 join(complement(join(complement(sk3),complement(composition(sk2,sk1)))),complement(join(complement(sk3),complement(composition(sk2,complement(top)))))) = complement(join(complement(sk3),complement(composition(sk2,complement(top))))). [para(33(a,1),26(a,1,2,1,2,1,2)),rewrite([82(29)])].
% 2.14/2.44 90 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(36(a,1),12(a,1,1)),rewrite([7(7),16(7,R),7(6)]),flip(a)].
% 2.14/2.44 91 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),7(3),12(3),90(7)]),flip(a)].
% 2.14/2.44 99 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(36(a,1),36(a,2,2)),rewrite([91(4),36(4),16(6,R),7(5)])].
% 2.14/2.44 107 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(37(a,1),12(a,1,1)),rewrite([7(7)]),flip(a)].
% 2.14/2.44 115 composition(converse(one),A) = A. [para(1(a,1),38(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.14/2.44 123 converse(one) = one. [para(115(a,1),1(a,1)),flip(a)].
% 2.14/2.44 125 composition(join(A,one),B) = join(B,composition(A,B)). [para(115(a,1),20(a,1,1)),rewrite([123(4),7(4)]),flip(a)].
% 2.14/2.44 126 composition(join(one,one),complement(A)) = complement(A). [para(115(a,1),22(a,1,2,2,1)),rewrite([123(3),123(3),125(5,R)])].
% 2.14/2.44 127 join(complement(A),complement(composition(one,A))) = complement(A). [para(115(a,1),22(a,1,2))].
% 2.14/2.44 141 composition(one,A) = A. [para(115(a,1),40(a,2)),rewrite([123(2),40(4)])].
% 2.14/2.44 147 join(complement(A),complement(A)) = complement(A). [back_rewrite(127),rewrite([141(3)])].
% 2.14/2.44 148 join(complement(top),complement(complement(A))) = A. [back_rewrite(51),rewrite([147(5)])].
% 2.14/2.44 150 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(24(a,1),39(a,1,2)),rewrite([7(4),39(4),7(3),7(8)]),flip(a)].
% 2.14/2.44 151 join(top,complement(complement(A))) = top. [para(26(a,1),39(a,1,2)),rewrite([4(22),7(8),150(8)]),flip(a)].
% 2.14/2.44 152 converse(join(A,one)) = join(one,converse(A)). [para(123(a,1),12(a,1,1)),rewrite([7(5)]),flip(a)].
% 2.14/2.44 153 join(complement(A),complement(top)) = complement(A). [para(151(a,1),24(a,1,1,1)),rewrite([148(7),7(4)])].
% 2.14/2.44 154 join(top,complement(A)) = join(top,top). [para(151(a,1),39(a,1,2)),rewrite([7(3)])].
% 2.14/2.44 155 join(top,top) = top. [back_rewrite(151),rewrite([154(4)])].
% 2.14/2.44 156 join(top,complement(A)) = top. [back_rewrite(154),rewrite([155(6)])].
% 2.14/2.44 157 join(A,top) = top. [para(155(a,1),39(a,2)),rewrite([156(3)])].
% 2.14/2.44 174 join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))). [para(42(a,1),12(a,2,1)),rewrite([2(3),37(4),37(9),36(7)])].
% 2.14/2.44 180 join(complement(complement(A)),complement(join(A,complement(top)))) = top. [para(153(a,1),24(a,1,2,1)),rewrite([7(7)])].
% 2.14/2.44 183 composition(join(A,join(one,one)),complement(B)) = composition(join(A,one),complement(B)). [para(126(a,1),20(a,1,1)),rewrite([125(4,R),7(8)]),flip(a)].
% 2.14/2.44 233 composition(join(one,one),A) = join(A,A). [para(141(a,1),125(a,2,2))].
% 2.14/2.44 259 composition(A,join(one,one)) = join(A,A). [para(233(a,2),36(a,1,1)),rewrite([37(6),152(4),123(3),2(6)])].
% 2.14/2.44 262 composition(join(one,one),top) = top. [para(233(a,2),157(a,1))].
% 2.14/2.44 273 composition(converse(top),join(one,one)) = converse(top). [para(262(a,1),14(a,2,1)),rewrite([152(6),123(5)])].
% 2.14/2.44 298 join(A,join(A,composition(B,join(one,one)))) = composition(join(B,A),join(one,one)). [para(259(a,1),20(a,1,2)),rewrite([16(6),7(5)])].
% 2.14/2.44 310 composition(top,join(one,one)) = top. [para(259(a,2),157(a,1))].
% 2.14/2.44 321 composition(join(one,one),A) = composition(A,join(one,one)). [para(259(a,2),233(a,2))].
% 2.14/2.44 343 composition(top,composition(A,join(one,one))) = composition(top,A). [para(310(a,1),18(a,1,1)),rewrite([321(7)]),flip(a)].
% 2.14/2.44 344 join(top,composition(A,join(one,one))) = top. [para(310(a,1),20(a,1,1)),rewrite([7(8),157(8),310(11)])].
% 2.14/2.44 386 join(top,converse(top)) = top. [para(273(a,1),344(a,1,2))].
% 2.14/2.44 388 converse(top) = top. [para(386(a,1),12(a,2,1)),rewrite([2(5),7(4),386(4)]),flip(a)].
% 2.14/2.44 398 join(top,converse(A)) = top. [para(388(a,1),12(a,1,1)),rewrite([7(5),157(5),388(5)])].
% 2.14/2.44 399 converse(composition(A,top)) = composition(top,converse(A)). [para(388(a,1),14(a,1,1)),flip(a)].
% 2.14/2.44 407 join(top,composition(A,converse(B))) = top. [para(37(a,1),398(a,1,2))].
% 2.14/2.44 416 join(top,composition(A,B)) = top. [para(2(a,1),407(a,1,2,2))].
% 2.14/2.44 417 composition(join(A,one),top) = top. [para(388(a,1),407(a,1,2,2)),rewrite([125(4,R)])].
% 2.14/2.44 420 composition(top,join(one,converse(A))) = top. [para(417(a,1),14(a,2,1)),rewrite([388(2),152(4),388(7)])].
% 2.14/2.44 431 composition(top,join(A,one)) = top. [para(2(a,1),420(a,1,2,2)),rewrite([7(3)])].
% 2.14/2.44 441 composition(top,top) = top. [para(388(a,1),420(a,1,2,2)),rewrite([157(4)])].
% 2.14/2.44 451 composition(top,complement(top)) = complement(top). [para(441(a,1),22(a,1,2,2,1)),rewrite([388(4),125(7,R),7(3),157(3)])].
% 2.14/2.44 470 composition(join(A,one),complement(top)) = complement(top). [para(431(a,1),49(a,1,2,2,1,1)),rewrite([388(2),388(6),125(8,R),7(4),16(4,R),183(7),388(7)])].
% 2.14/2.44 471 composition(converse(complement(top)),top) = converse(complement(top)). [para(451(a,1),14(a,2,1)),rewrite([388(5)])].
% 2.14/2.44 472 composition(top,composition(complement(top),A)) = composition(complement(top),A). [para(451(a,1),18(a,1,1)),flip(a)].
% 2.14/2.44 552 join(A,complement(complement(A))) = A. [para(52(a,1),24(a,1,2,1)),rewrite([156(6),148(5)]),flip(a)].
% 2.14/2.44 553 complement(complement(top)) = top. [para(148(a,1),52(a,1,2,1)),rewrite([4(6)]),flip(a)].
% 2.14/2.44 560 join(A,join(B,complement(complement(A)))) = join(A,B). [para(552(a,1),16(a,2,2)),rewrite([7(3),7(5)])].
% 2.14/2.44 679 join(complement(top),complement(join(A,complement(top)))) = complement(A). [para(153(a,1),55(a,1,2,1,2,1)),rewrite([7(8),16(8),7(7),552(7),7(5),153(11)])].
% 2.14/2.44 929 join(complement(top),complement(join(complement(complement(complement(A))),complement(join(A,complement(top)))))) = join(A,complement(top)). [para(180(a,1),24(a,1,1,1))].
% 2.14/2.44 931 join(complement(complement(complement(A))),complement(join(A,complement(top)))) = complement(A). [para(180(a,1),54(a,1,2,1,2,1,1)),rewrite([7(12),553(16),7(15),156(15),7(7),679(7),7(9)]),flip(a)].
% 2.14/2.44 932 join(A,complement(top)) = A. [back_rewrite(929),rewrite([931(10),148(5)]),flip(a)].
% 2.14/2.44 1204 composition(top,join(A,A)) = composition(top,A). [para(259(a,1),343(a,1,2))].
% 2.14/2.44 1224 join(join(A,A),composition(top,A)) = composition(top,A). [para(1204(a,1),125(a,2,2)),rewrite([7(3),157(3),1204(3)]),flip(a)].
% 2.14/2.44 1547 join(complement(join(complement(top),complement(composition(A,top)))),complement(join(complement(top),complement(composition(complement(complement(A)),top))))) = complement(join(complement(top),complement(composition(complement(complement(A)),top)))). [para(441(a,1),65(a,1,2,1,2,1,1,1,2,1)),rewrite([388(4),932(13),388(13),441(23),932(23),388(23)])].
% 2.14/2.44 1760 join(A,A) = A. [para(148(a,1),560(a,1,2)),rewrite([932(4)])].
% 2.14/2.44 1798 join(A,composition(top,A)) = composition(top,A). [back_rewrite(1224),rewrite([1760(1)])].
% 2.14/2.44 1820 join(A,join(A,B)) = join(A,B). [back_rewrite(298),rewrite([1760(3),1(2),7(3),1760(6),1(5)])].
% 2.14/2.44 1832 join(A,complement(join(B,complement(A)))) = A. [para(24(a,1),1820(a,1,2)),rewrite([7(4),24(12)])].
% 2.14/2.44 2493 join(complement(join(complement(top),complement(composition(top,A)))),composition(complement(join(complement(top),complement(composition(top,converse(A))))),complement(complement(A)))) = composition(complement(join(complement(top),complement(composition(top,converse(A))))),complement(complement(A))). [para(441(a,1),75(a,1,2,2,1,2,1)),rewrite([388(4),388(9),932(19),388(21),441(31),932(31)])].
% 2.14/2.44 3568 join(complement(complement(join(complement(sk3),complement(composition(sk2,complement(top)))))),complement(join(join(complement(sk3),complement(composition(sk2,complement(top)))),complement(join(complement(sk3),complement(composition(sk2,sk1))))))) = join(complement(sk3),complement(composition(sk2,sk1))). [para(86(a,1),53(a,1,2,1)),rewrite([7(29)])].
% 2.14/2.44 4310 join(A,join(complement(A),converse(B))) = top. [para(4(a,1),99(a,1,1)),rewrite([398(3)]),flip(a)].
% 2.14/2.44 4384 join(A,join(complement(A),composition(B,converse(C)))) = top. [para(37(a,1),4310(a,1,2,2))].
% 2.14/2.44 4439 join(A,join(complement(A),composition(B,C))) = top. [para(2(a,1),4384(a,1,2,2,2))].
% 2.14/2.44 4445 join(A,composition(top,complement(A))) = top. [para(1798(a,1),4439(a,1,2))].
% 2.14/2.44 4456 join(A,join(composition(top,complement(A)),converse(B))) = top. [para(4445(a,1),99(a,1,1)),rewrite([398(3)]),flip(a)].
% 2.14/2.44 4602 join(A,composition(top,join(complement(A),converse(B)))) = top. [para(399(a,1),4456(a,1,2,2)),rewrite([174(7)])].
% 2.14/2.44 4603 join(A,composition(top,join(B,complement(A)))) = top. [para(2(a,1),4602(a,1,2,2,2)),rewrite([7(3)])].
% 2.14/2.44 4611 join(complement(A),join(complement(B),composition(top,A))) = top. [para(53(a,1),4603(a,1,2,2)),rewrite([7(6),16(6,R)])].
% 2.14/2.44 4637 join(A,composition(A,top)) = composition(A,top). [para(1798(a,1),107(a,1,1)),rewrite([37(4),388(2),388(4),2(6),7(5)]),flip(a)].
% 2.14/2.44 4675 join(A,composition(complement(A),top)) = top. [para(4637(a,1),4439(a,1,2))].
% 2.14/2.44 4677 join(A,join(B,composition(complement(A),top))) = top. [para(4675(a,1),16(a,2,2)),rewrite([7(4),157(7)])].
% 2.14/2.44 4749 join(A,composition(join(B,complement(A)),top)) = top. [para(20(a,1),4677(a,1,2))].
% 2.14/2.44 4797 join(complement(A),composition(A,top)) = top. [para(148(a,1),4749(a,1,2,1))].
% 2.14/2.44 4857 join(complement(A),join(composition(A,top),converse(B))) = top. [para(4797(a,1),99(a,1,1)),rewrite([398(3)]),flip(a)].
% 2.14/2.44 4866 join(complement(A),complement(complement(composition(top,A)))) = top. [para(47(a,1),4611(a,1,2)),rewrite([388(2),7(6)])].
% 2.14/2.44 4877 join(complement(top),complement(composition(top,A))) = complement(composition(top,A)). [para(4866(a,1),1832(a,1,2,1)),rewrite([7(6)])].
% 2.14/2.44 4890 join(complement(complement(composition(top,A))),composition(complement(complement(composition(top,converse(A)))),complement(complement(A)))) = composition(complement(complement(composition(top,converse(A)))),complement(complement(A))). [back_rewrite(2493),rewrite([4877(6),4877(11),4877(20)])].
% 2.14/2.44 4968 join(complement(converse(complement(top))),converse(A)) = top. [para(471(a,1),4857(a,1,2,1)),rewrite([7(9),12(9),932(7)])].
% 2.14/2.44 5007 join(A,complement(converse(complement(top)))) = top. [para(2(a,1),4968(a,1,2)),rewrite([7(5)])].
% 2.14/2.44 5068 converse(complement(top)) = complement(top). [para(5007(a,1),24(a,1,1,1)),rewrite([5007(8),1760(5)]),flip(a)].
% 2.14/2.44 5234 join(complement(top),converse(A)) = converse(A). [para(5068(a,1),12(a,1,1)),rewrite([7(7),932(7)])].
% 2.14/2.44 5240 join(complement(top),composition(converse(complement(composition(A,top))),A)) = complement(top). [para(5068(a,1),48(a,1,1)),rewrite([5068(11)])].
% 2.14/2.44 5331 join(complement(top),composition(converse(A),B)) = composition(converse(A),B). [para(38(a,1),5234(a,1,2)),rewrite([38(8)])].
% 2.14/2.44 5333 composition(converse(complement(composition(A,top))),A) = complement(top). [back_rewrite(5240),rewrite([5331(8)])].
% 2.14/2.44 5376 complement(complement(composition(A,top))) = composition(A,top). [para(5333(a,1),49(a,1,2,2,1,1)),rewrite([2(5),5068(7),553(7),7(7),552(7),2(7)]),flip(a)].
% 2.14/2.44 5533 join(complement(top),complement(composition(A,top))) = complement(composition(A,top)). [para(5376(a,1),148(a,1,2,1))].
% 2.14/2.44 5612 composition(complement(complement(A)),top) = composition(A,top). [back_rewrite(1547),rewrite([5533(6),5376(4),5533(10),5376(8),20(7),552(3),5533(10),5376(8)]),flip(a)].
% 2.14/2.44 5656 join(composition(A,top),complement(complement(complement(A)))) = top. [para(5612(a,1),4797(a,1,2)),rewrite([7(6)])].
% 2.14/2.44 5879 complement(complement(A)) = A. [para(5656(a,1),1832(a,1,2,1)),rewrite([7(5),148(5)]),flip(a)].
% 2.14/2.44 5943 composition(top,composition(converse(A),A)) = composition(top,A). [back_rewrite(4890),rewrite([5879(4),5879(7),5879(7),18(6),45(7),416(5),5879(7),5879(7),18(6)]),flip(a)].
% 2.14/2.44 6083 join(join(complement(sk3),complement(composition(sk2,complement(top)))),complement(join(join(complement(sk3),complement(composition(sk2,complement(top)))),complement(join(complement(sk3),complement(composition(sk2,sk1))))))) = join(complement(sk3),complement(composition(sk2,sk1))). [back_rewrite(3568),rewrite([5879(10)])].
% 2.14/2.44 6738 composition(complement(top),complement(top)) = complement(top). [para(451(a,1),5943(a,2)),rewrite([5068(4),472(7)])].
% 2.14/2.44 6818 composition(A,complement(top)) = complement(top). [para(6738(a,1),20(a,1,1)),rewrite([125(6,R),470(5),7(5),932(5)]),flip(a)].
% 2.14/2.44 6825 join(complement(sk3),complement(composition(sk2,sk1))) = top. [back_rewrite(6083),rewrite([6818(6),5879(5),7(4),156(4),6818(7),5879(6),7(5),156(5),156(11),4(4)]),flip(a)].
% 2.14/2.44 6869 $F # answer(goals_18). [back_rewrite(35),rewrite([6825(7)]),xx(a)].
% 2.14/2.44
% 2.14/2.44 % SZS output end Refutation
% 2.14/2.44 ============================== end of proof ==========================
% 2.14/2.44
% 2.14/2.44 ============================== STATISTICS ============================
% 2.14/2.44
% 2.14/2.44 Given=302. Generated=29743. Kept=6854. proofs=1.
% 2.14/2.44 Usable=209. Sos=3364. Demods=3579. Limbo=44, Disabled=3255. Hints=0.
% 2.14/2.44 Megabytes=15.69.
% 2.14/2.44 User_CPU=1.46, System_CPU=0.01, Wall_clock=1.
% 2.14/2.44
% 2.14/2.44 ============================== end of statistics =====================
% 2.14/2.44
% 2.14/2.44 ============================== end of search =========================
% 2.14/2.44
% 2.14/2.44 THEOREM PROVED
% 2.14/2.44 % SZS status Unsatisfiable
% 2.14/2.44
% 2.14/2.44 Exiting with 1 proof.
% 2.14/2.44
% 2.14/2.44 Process 22439 exit (max_proofs) Fri Jul 8 14:12:54 2022
% 2.14/2.44 Prover9 interrupted
%------------------------------------------------------------------------------