TSTP Solution File: REL045+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL045+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 19:54:29 EDT 2022
% Result : Theorem 0.90s 1.23s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : REL045+2 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 09:21:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/1.04 ============================== Prover9 ===============================
% 0.47/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.04 Process 18655 was started by sandbox2 on n005.cluster.edu,
% 0.47/1.04 Fri Jul 8 09:21:38 2022
% 0.47/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18349_n005.cluster.edu".
% 0.47/1.04 ============================== end of head ===========================
% 0.47/1.04
% 0.47/1.04 ============================== INPUT =================================
% 0.47/1.04
% 0.47/1.04 % Reading from file /tmp/Prover9_18349_n005.cluster.edu
% 0.47/1.04
% 0.47/1.04 set(prolog_style_variables).
% 0.47/1.04 set(auto2).
% 0.47/1.04 % set(auto2) -> set(auto).
% 0.47/1.04 % set(auto) -> set(auto_inference).
% 0.47/1.04 % set(auto) -> set(auto_setup).
% 0.47/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.04 % set(auto) -> set(auto_limits).
% 0.47/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.04 % set(auto) -> set(auto_denials).
% 0.47/1.04 % set(auto) -> set(auto_process).
% 0.47/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.04 % set(auto2) -> assign(stats, some).
% 0.47/1.04 % set(auto2) -> clear(echo_input).
% 0.47/1.04 % set(auto2) -> set(quiet).
% 0.47/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.04 % set(auto2) -> clear(print_given).
% 0.47/1.04 assign(lrs_ticks,-1).
% 0.47/1.04 assign(sos_limit,10000).
% 0.47/1.04 assign(order,kbo).
% 0.47/1.04 set(lex_order_vars).
% 0.47/1.04 clear(print_given).
% 0.47/1.04
% 0.47/1.04 % formulas(sos). % not echoed (17 formulas)
% 0.47/1.04
% 0.47/1.04 ============================== end of input ==========================
% 0.47/1.04
% 0.47/1.04 % From the command line: assign(max_seconds, 300).
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.04
% 0.47/1.04 % Formulas that are not ordinary clauses:
% 0.47/1.04 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 17 -(all X0 join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.90/1.23
% 0.90/1.23 ============================== end of process non-clausal formulas ===
% 0.90/1.23
% 0.90/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.90/1.23
% 0.90/1.23 ============================== PREDICATE ELIMINATION =================
% 0.90/1.23
% 0.90/1.23 ============================== end predicate elimination =============
% 0.90/1.23
% 0.90/1.23 Auto_denials:
% 0.90/1.23 % copying label goals to answer in negative clause
% 0.90/1.23
% 0.90/1.23 Term ordering decisions:
% 0.90/1.23 Function symbol KB weights: one=1. top=1. zero=1. c1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 0.90/1.23
% 0.90/1.23 ============================== end of process initial clauses ========
% 0.90/1.23
% 0.90/1.23 ============================== CLAUSES FOR SEARCH ====================
% 0.90/1.23
% 0.90/1.23 ============================== end of clauses for search =============
% 0.90/1.23
% 0.90/1.23 ============================== SEARCH ================================
% 0.90/1.23
% 0.90/1.23 % Starting search at 0.01 seconds.
% 0.90/1.23
% 0.90/1.23 ============================== PROOF =================================
% 0.90/1.23 % SZS status Theorem
% 0.90/1.23 % SZS output start Refutation
% 0.90/1.23
% 0.90/1.23 % Proof 1 at 0.19 (+ 0.01) seconds: goals.
% 0.90/1.23 % Length of proof is 91.
% 0.90/1.23 % Level of proof is 25.
% 0.90/1.23 % Maximum clause weight is 48.000.
% 0.90/1.23 % Given clauses 109.
% 0.90/1.23
% 0.90/1.23 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause). [assumption].
% 0.90/1.23 17 -(all X0 join(X0,composition(composition(X0,converse(X0)),X0)) = composition(composition(X0,converse(X0)),X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.90/1.23 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 0.90/1.23 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 0.90/1.23 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 0.90/1.23 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 0.90/1.23 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 0.90/1.23 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 0.90/1.23 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 0.90/1.23 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 0.90/1.23 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 0.90/1.23 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 0.90/1.23 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 0.90/1.23 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 0.90/1.23 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 0.90/1.23 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 0.90/1.23 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 0.90/1.23 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 0.90/1.23 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 0.90/1.23 35 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 0.90/1.23 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 0.90/1.23 37 meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) # label(modular_law_1) # label(axiom). [clausify(15)].
% 0.90/1.23 38 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(37),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 0.90/1.23 39 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom). [clausify(16)].
% 0.90/1.23 40 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(39),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
% 0.90/1.23 41 composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))) # label(dedekind_law) # label(axiom). [clausify(14)].
% 0.90/1.23 42 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(41),rewrite([23(3),23(9),23(15),22(17),23(21),23(27)]),flip(a)].
% 0.90/1.23 43 composition(composition(c1,converse(c1)),c1) != join(c1,composition(composition(c1,converse(c1)),c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 0.90/1.23 44 join(c1,composition(c1,composition(converse(c1),c1))) != composition(c1,composition(converse(c1),c1)) # answer(goals). [copy(43),rewrite([30(6),30(13)]),flip(a)].
% 0.90/1.23 45 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 0.90/1.23 47 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(19(a,1),27(a,1,1)),flip(a)].
% 0.90/1.23 48 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 0.90/1.23 49 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 0.90/1.23 50 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 0.90/1.23 56 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(18(a,1),34(a,1,2,2,1))].
% 0.90/1.23 61 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
% 0.90/1.23 62 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(20(a,1),36(a,1,2,1)),rewrite([45(6),22(6)])].
% 0.90/1.23 65 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(36(a,1),36(a,1,2,1)),rewrite([22(10)])].
% 0.90/1.23 91 join(zero,composition(converse(A),complement(composition(A,top)))) = zero. [para(45(a,1),34(a,1,1)),rewrite([45(9)])].
% 0.90/1.23 126 composition(converse(one),A) = A. [para(18(a,1),48(a,1,1)),rewrite([19(2)]),flip(a)].
% 0.90/1.23 135 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(36(a,1),49(a,1,2)),rewrite([22(4),49(4),22(3),22(8)]),flip(a)].
% 0.90/1.23 136 join(top,complement(complement(A))) = top. [para(38(a,1),49(a,1,2)),rewrite([20(22),22(8),135(8)]),flip(a)].
% 0.90/1.23 137 converse(one) = one. [para(126(a,1),18(a,1)),flip(a)].
% 0.90/1.23 139 composition(join(A,one),B) = join(B,composition(A,B)). [para(126(a,1),32(a,1,1)),rewrite([137(4),22(4)]),flip(a)].
% 0.90/1.23 141 join(complement(A),complement(composition(one,A))) = complement(A). [para(126(a,1),34(a,1,2))].
% 0.90/1.23 155 composition(one,A) = A. [para(126(a,1),50(a,2)),rewrite([137(2),50(4)])].
% 0.90/1.23 161 join(complement(A),complement(A)) = complement(A). [back_rewrite(141),rewrite([155(3)])].
% 0.90/1.23 162 join(zero,complement(complement(A))) = A. [back_rewrite(61),rewrite([161(4)])].
% 0.90/1.23 163 converse(join(A,one)) = join(one,converse(A)). [para(137(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
% 0.90/1.23 164 join(zero,complement(A)) = complement(A). [para(136(a,1),36(a,1,1,1)),rewrite([45(2),45(3),162(5)])].
% 0.90/1.23 167 complement(complement(A)) = A. [back_rewrite(162),rewrite([164(4)])].
% 0.90/1.23 177 complement(join(A,A)) = complement(A). [back_rewrite(62),rewrite([167(3),164(4)])].
% 0.90/1.23 179 join(A,top) = top. [back_rewrite(136),rewrite([167(3),22(2)])].
% 0.90/1.23 195 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(167(a,1),36(a,1,1,1,2)),rewrite([167(5),22(4)])].
% 0.90/1.23 203 complement(zero) = top. [para(45(a,1),167(a,1,1))].
% 0.90/1.23 218 join(A,A) = A. [para(177(a,1),36(a,1,1,1,2)),rewrite([177(6),36(8)]),flip(a)].
% 0.90/1.23 225 join(A,join(A,B)) = join(A,B). [para(218(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),218(2)]),flip(a)].
% 0.90/1.23 243 join(A,complement(join(B,complement(A)))) = A. [para(36(a,1),225(a,1,2)),rewrite([22(4),36(12)])].
% 0.90/1.23 248 join(complement(A),complement(join(A,B))) = complement(A). [para(167(a,1),243(a,1,2,1,2)),rewrite([22(2)])].
% 0.90/1.23 266 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(167(a,1),56(a,1,2,2))].
% 0.90/1.23 279 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero. [para(163(a,1),91(a,1,2,1))].
% 0.90/1.23 315 join(complement(one),converse(complement(one))) = complement(one). [para(18(a,1),266(a,1,2))].
% 0.90/1.23 319 converse(complement(one)) = complement(one). [para(315(a,1),25(a,2,1)),rewrite([19(7),22(6),315(6)]),flip(a)].
% 0.90/1.23 328 converse(top) = top. [para(319(a,1),163(a,2,2)),rewrite([22(4),20(4),20(6)])].
% 0.90/1.23 339 join(top,converse(A)) = top. [para(328(a,1),25(a,1,1)),rewrite([22(5),179(5),328(5)])].
% 0.90/1.23 346 join(top,composition(A,converse(B))) = top. [para(47(a,1),339(a,1,2))].
% 0.90/1.23 349 composition(join(A,one),top) = top. [para(328(a,1),346(a,1,2,2)),rewrite([139(4,R)])].
% 0.90/1.23 350 composition(join(one,converse(A)),zero) = zero. [back_rewrite(279),rewrite([349(8),45(6),139(7,R),22(5),225(5)])].
% 0.90/1.23 377 composition(top,zero) = zero. [para(319(a,1),350(a,1,1,2)),rewrite([20(4)])].
% 0.90/1.23 381 composition(top,top) = top. [para(377(a,1),34(a,1,2,2,1)),rewrite([203(2),328(3),203(4),139(5,R),22(3),179(3),203(5)])].
% 0.90/1.23 393 join(A,complement(join(complement(A),complement(composition(A,top))))) = complement(join(complement(A),complement(composition(A,top)))). [para(381(a,1),40(a,1,1,1,2,1)),rewrite([45(3),22(3),164(3),167(2),45(3),328(4),164(6),167(5),30(5),381(4),45(10),328(11),164(13),167(12),30(12),381(11)])].
% 0.90/1.23 449 join(A,complement(join(complement(A),complement(B)))) = A. [para(65(a,1),248(a,1,2,1)),rewrite([167(2),22(3),167(7)])].
% 0.90/1.23 458 complement(join(complement(A),complement(composition(A,top)))) = A. [back_rewrite(393),rewrite([449(7)]),flip(a)].
% 0.90/1.23 811 join(complement(A),complement(composition(A,top))) = complement(A). [para(458(a,1),36(a,1,1,1,2)),rewrite([458(9),22(4),195(6)]),flip(a)].
% 0.90/1.23 814 join(A,composition(A,composition(converse(A),A))) = composition(A,composition(converse(A),A)). [para(458(a,1),42(a,1,1)),rewrite([328(3),811(5),167(2),45(2),164(5),167(4),328(7),811(9),167(6),45(6),164(9),167(8)])].
% 0.90/1.23 815 $F # answer(goals). [resolve(814,a,44,a)].
% 0.90/1.23
% 0.90/1.23 % SZS output end Refutation
% 0.90/1.23 ============================== end of proof ==========================
% 0.90/1.23
% 0.90/1.23 ============================== STATISTICS ============================
% 0.90/1.23
% 0.90/1.23 Given=109. Generated=4163. Kept=787. proofs=1.
% 0.90/1.23 Usable=88. Sos=477. Demods=552. Limbo=5, Disabled=233. Hints=0.
% 0.90/1.23 Megabytes=1.53.
% 0.90/1.23 User_CPU=0.19, System_CPU=0.01, Wall_clock=0.
% 0.90/1.23
% 0.90/1.23 ============================== end of statistics =====================
% 0.90/1.23
% 0.90/1.23 ============================== end of search =========================
% 0.90/1.23
% 0.90/1.23 THEOREM PROVED
% 0.90/1.23 % SZS status Theorem
% 0.90/1.23
% 0.90/1.23 Exiting with 1 proof.
% 0.90/1.23
% 0.90/1.23 Process 18655 exit (max_proofs) Fri Jul 8 09:21:38 2022
% 0.90/1.23 Prover9 interrupted
%------------------------------------------------------------------------------