TSTP Solution File: REL027+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL027+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 19:54:00 EDT 2022
% Result : Theorem 1.52s 1.79s
% Output : Refutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : REL027+2 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Fri Jul 8 11:09:52 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.50/1.05 ============================== Prover9 ===============================
% 0.50/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.50/1.05 Process 14808 was started by sandbox on n005.cluster.edu,
% 0.50/1.05 Fri Jul 8 11:09:52 2022
% 0.50/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14655_n005.cluster.edu".
% 0.50/1.05 ============================== end of head ===========================
% 0.50/1.05
% 0.50/1.05 ============================== INPUT =================================
% 0.50/1.05
% 0.50/1.05 % Reading from file /tmp/Prover9_14655_n005.cluster.edu
% 0.50/1.05
% 0.50/1.05 set(prolog_style_variables).
% 0.50/1.05 set(auto2).
% 0.50/1.05 % set(auto2) -> set(auto).
% 0.50/1.05 % set(auto) -> set(auto_inference).
% 0.50/1.05 % set(auto) -> set(auto_setup).
% 0.50/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.50/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/1.05 % set(auto) -> set(auto_limits).
% 0.50/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/1.05 % set(auto) -> set(auto_denials).
% 0.50/1.05 % set(auto) -> set(auto_process).
% 0.50/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.50/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.50/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.50/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.50/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.50/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.50/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.50/1.05 % set(auto2) -> assign(stats, some).
% 0.50/1.05 % set(auto2) -> clear(echo_input).
% 0.50/1.05 % set(auto2) -> set(quiet).
% 0.50/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.50/1.05 % set(auto2) -> clear(print_given).
% 0.50/1.05 assign(lrs_ticks,-1).
% 0.50/1.05 assign(sos_limit,10000).
% 0.50/1.05 assign(order,kbo).
% 0.50/1.05 set(lex_order_vars).
% 0.50/1.05 clear(print_given).
% 0.50/1.05
% 0.50/1.05 % formulas(sos). % not echoed (14 formulas)
% 0.50/1.05
% 0.50/1.05 ============================== end of input ==========================
% 0.50/1.05
% 0.50/1.05 % From the command line: assign(max_seconds, 300).
% 0.50/1.05
% 0.50/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/1.05
% 0.50/1.05 % Formulas that are not ordinary clauses:
% 0.50/1.05 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 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].
% 0.50/1.05 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].
% 0.50/1.05 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].
% 0.50/1.05 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].
% 0.50/1.05 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 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].
% 0.50/1.05 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 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].
% 0.50/1.05 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.50/1.05 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 14 -(all X0 (join(X0,one) = one -> join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) & join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.52/1.79
% 1.52/1.79 ============================== end of process non-clausal formulas ===
% 1.52/1.79
% 1.52/1.79 ============================== PROCESS INITIAL CLAUSES ===============
% 1.52/1.79
% 1.52/1.79 ============================== PREDICATE ELIMINATION =================
% 1.52/1.79
% 1.52/1.79 ============================== end predicate elimination =============
% 1.52/1.79
% 1.52/1.79 Auto_denials:
% 1.52/1.79 % copying label goals to answer in negative clause
% 1.52/1.79
% 1.52/1.79 Term ordering decisions:
% 1.52/1.79 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.52/1.79
% 1.52/1.79 ============================== end of process initial clauses ========
% 1.52/1.79
% 1.52/1.79 ============================== CLAUSES FOR SEARCH ====================
% 1.52/1.79
% 1.52/1.79 ============================== end of clauses for search =============
% 1.52/1.79
% 1.52/1.79 ============================== SEARCH ================================
% 1.52/1.79
% 1.52/1.79 % Starting search at 0.01 seconds.
% 1.52/1.79
% 1.52/1.79 ============================== PROOF =================================
% 1.52/1.79 % SZS status Theorem
% 1.52/1.79 % SZS output start Refutation
% 1.52/1.79
% 1.52/1.79 % Proof 1 at 0.73 (+ 0.03) seconds: goals.
% 1.52/1.79 % Length of proof is 98.
% 1.52/1.79 % Level of proof is 26.
% 1.52/1.79 % Maximum clause weight is 52.000.
% 1.52/1.79 % Given clauses 378.
% 1.52/1.79
% 1.52/1.79 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 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].
% 1.52/1.79 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].
% 1.52/1.79 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].
% 1.52/1.79 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].
% 1.52/1.79 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 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].
% 1.52/1.79 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 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].
% 1.52/1.79 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.52/1.79 14 -(all X0 (join(X0,one) = one -> join(meet(complement(composition(X0,top)),one),meet(complement(X0),one)) = meet(complement(X0),one) & join(meet(complement(X0),one),meet(complement(composition(X0,top)),one)) = meet(complement(composition(X0,top)),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.52/1.79 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 1.52/1.79 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 1.52/1.79 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 1.52/1.79 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 1.52/1.79 19 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 1.52/1.79 20 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 1.52/1.79 21 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 1.52/1.79 22 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 1.52/1.79 23 join(converse(A),converse(B)) = converse(join(A,B)). [copy(22),flip(a)].
% 1.52/1.79 24 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 1.52/1.79 25 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(24),flip(a)].
% 1.52/1.79 26 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 1.52/1.79 27 join(A,join(B,C)) = join(C,join(A,B)). [copy(26),rewrite([20(2)]),flip(a)].
% 1.52/1.79 28 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 1.52/1.79 29 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 1.52/1.79 30 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(29),flip(a)].
% 1.52/1.79 31 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 1.52/1.79 32 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(31),rewrite([20(7)]),flip(a)].
% 1.52/1.79 33 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom). [clausify(3)].
% 1.52/1.79 34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(33),rewrite([20(6),20(8)]),rewrite([20(6)])].
% 1.52/1.79 35 meet(complement(c1),one) != join(meet(complement(composition(c1,top)),one),meet(complement(c1),one)) | meet(complement(composition(c1,top)),one) != join(meet(complement(c1),one),meet(complement(composition(c1,top)),one)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 1.52/1.79 36 join(complement(join(complement(one),complement(complement(c1)))),complement(join(complement(one),complement(complement(composition(c1,top)))))) != complement(join(complement(one),complement(complement(c1)))) | join(complement(join(complement(one),complement(complement(c1)))),complement(join(complement(one),complement(complement(composition(c1,top)))))) != complement(join(complement(one),complement(complement(composition(c1,top))))) # answer(goals). [copy(35),rewrite([21(4),20(6),21(13),20(15),21(20),20(22),20(24),21(31),20(33),21(38),20(40),21(47),20(49)]),flip(a),flip(b)].
% 1.52/1.79 37 join(one,c1) = one. [back_rewrite(17),rewrite([20(3)])].
% 1.52/1.79 38 complement(top) = zero. [back_rewrite(19),rewrite([21(2),18(4)])].
% 1.52/1.79 39 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),23(a,1,1)),rewrite([20(4)]),flip(a)].
% 1.52/1.79 40 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),25(a,1,1)),flip(a)].
% 1.52/1.79 41 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),25(a,1,2)),flip(a)].
% 1.52/1.79 42 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),27(a,2,2)),rewrite([20(2)])].
% 1.52/1.79 43 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),28(a,1,1)),flip(a)].
% 1.52/1.79 47 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(28(a,1),30(a,1,1)),rewrite([20(6)])].
% 1.52/1.79 49 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),32(a,1,2,2,1))].
% 1.52/1.79 54 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),34(a,1,1,1)),rewrite([38(2)])].
% 1.52/1.79 58 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)). [para(34(a,1),34(a,1,2,1)),rewrite([20(10)])].
% 1.52/1.79 62 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(38(a,1),34(a,1,2,1,1))].
% 1.52/1.79 63 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)). [para(39(a,1),23(a,1,1)),rewrite([20(7),27(7,R),20(6)]),flip(a)].
% 1.52/1.79 64 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))). [para(39(a,1),23(a,1,2)),rewrite([27(4,R),20(3),23(3),63(7)]),flip(a)].
% 1.52/1.79 68 join(join(A,B),converse(C)) = join(A,join(B,converse(C))). [para(39(a,1),39(a,2,2)),rewrite([64(4),39(4),27(6,R),20(5)])].
% 1.52/1.79 71 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)). [para(40(a,1),23(a,1,1)),rewrite([20(7)]),flip(a)].
% 1.52/1.79 75 composition(converse(one),A) = A. [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 1.52/1.79 81 converse(one) = one. [para(75(a,1),15(a,1)),flip(a)].
% 1.52/1.79 83 composition(join(A,one),B) = join(B,composition(A,B)). [para(75(a,1),30(a,1,1)),rewrite([81(4),20(4)]),flip(a)].
% 1.52/1.79 85 join(complement(A),complement(composition(one,A))) = complement(A). [para(75(a,1),32(a,1,2))].
% 1.52/1.79 86 composition(one,A) = A. [para(75(a,1),43(a,2)),rewrite([81(2),43(4)])].
% 1.52/1.79 87 join(complement(A),complement(A)) = complement(A). [back_rewrite(85),rewrite([86(3)])].
% 1.52/1.79 88 join(zero,complement(complement(A))) = A. [back_rewrite(54),rewrite([87(4)])].
% 1.52/1.79 89 converse(join(A,one)) = join(one,converse(A)). [para(81(a,1),23(a,1,1)),rewrite([20(5)]),flip(a)].
% 1.52/1.79 93 join(top,complement(A)) = top. [para(87(a,1),42(a,1,2)),rewrite([18(2),20(4)]),flip(a)].
% 1.52/1.79 94 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(62),rewrite([93(3),38(2)])].
% 1.52/1.79 95 join(top,top) = join(A,top). [para(93(a,1),42(a,1,2)),flip(a)].
% 1.52/1.79 100 join(A,top) = join(B,top). [para(95(a,1),42(a,2)),rewrite([93(3)])].
% 1.52/1.79 101 join(A,top) = c_0. [new_symbol(100)].
% 1.52/1.79 104 join(A,join(B,complement(A))) = c_0. [back_rewrite(42),rewrite([101(5)])].
% 1.52/1.79 115 c_0 = top. [para(88(a,1),104(a,1,2)),rewrite([20(2),18(2)]),flip(a)].
% 1.52/1.79 116 join(A,join(B,complement(A))) = top. [back_rewrite(104),rewrite([115(4)])].
% 1.52/1.79 128 converse(join(A,join(B,one))) = join(one,converse(join(A,B))). [para(89(a,1),23(a,1,1)),rewrite([68(5),23(4),20(7),27(7,R),20(6)]),flip(a)].
% 1.52/1.79 139 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))). [para(86(a,1),47(a,1,2)),rewrite([20(3)]),flip(a)].
% 1.52/1.79 143 join(zero,complement(A)) = complement(A). [para(88(a,1),94(a,1,2,1))].
% 1.52/1.79 144 complement(complement(A)) = A. [back_rewrite(94),rewrite([143(4),143(4)])].
% 1.52/1.79 145 join(A,zero) = A. [back_rewrite(88),rewrite([144(3),20(2)])].
% 1.52/1.79 149 join(complement(join(c1,complement(one))),complement(join(complement(one),composition(c1,top)))) != complement(join(c1,complement(one))) | join(complement(join(c1,complement(one))),complement(join(complement(one),composition(c1,top)))) != complement(join(complement(one),composition(c1,top))) # answer(goals). [back_rewrite(36),rewrite([144(5),20(4),144(12),144(18),20(17),144(24),20(23),144(31),144(39)])].
% 1.52/1.79 153 join(A,A) = A. [para(144(a,1),87(a,1,1)),rewrite([144(2),144(3)])].
% 1.52/1.79 157 join(A,join(A,B)) = join(A,B). [para(153(a,1),27(a,1)),rewrite([20(3),27(4,R),20(3),27(3,R),153(2)]),flip(a)].
% 1.52/1.79 158 join(A,complement(join(B,complement(A)))) = A. [para(34(a,1),157(a,1,2)),rewrite([20(4),34(12)])].
% 1.52/1.79 163 join(complement(A),complement(join(A,B))) = complement(A). [para(144(a,1),158(a,1,2,1,2)),rewrite([20(2)])].
% 1.52/1.79 171 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(144(a,1),49(a,1,2,2))].
% 1.52/1.79 198 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)). [para(83(a,1),30(a,1,2)),rewrite([27(4,R),30(3),20(1)]),flip(a)].
% 1.52/1.79 225 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),171(a,1,2))].
% 1.52/1.79 229 converse(complement(one)) = complement(one). [para(225(a,1),23(a,2,1)),rewrite([16(7),20(6),225(6)]),flip(a)].
% 1.52/1.79 234 converse(top) = top. [para(229(a,1),89(a,2,2)),rewrite([20(4),18(4),18(6)])].
% 1.52/1.79 303 join(complement(A),complement(join(B,A))) = complement(A). [para(158(a,1),58(a,2)),rewrite([144(2),144(4),144(8),58(13)])].
% 1.52/1.79 304 join(A,complement(join(complement(A),complement(B)))) = A. [para(58(a,1),163(a,1,2,1)),rewrite([144(2),20(3),144(7)])].
% 1.52/1.79 561 join(complement(one),complement(c1)) = complement(c1). [para(37(a,1),303(a,1,2,1)),rewrite([20(5)])].
% 1.52/1.79 575 join(A,join(complement(A),complement(B))) = top. [para(304(a,1),116(a,1,2)),rewrite([20(4)])].
% 1.52/1.79 593 join(one,complement(c1)) = top. [para(561(a,1),575(a,1,2))].
% 1.52/1.79 596 join(zero,c1) = c1. [para(593(a,1),34(a,1,1,1)),rewrite([38(2),561(6),144(4)])].
% 1.52/1.79 999 join(one,converse(c1)) = one. [para(596(a,1),128(a,2,2,1)),rewrite([20(4),37(4),20(3),145(3),81(2)]),flip(a)].
% 1.52/1.79 1012 join(A,composition(converse(c1),A)) = A. [para(999(a,1),30(a,2,1)),rewrite([86(2),86(6)])].
% 1.52/1.79 1018 join(A,composition(A,c1)) = A. [para(1012(a,1),71(a,1,1)),rewrite([16(2),16(3),16(4),20(3)]),flip(a)].
% 1.52/1.79 1771 join(A,composition(c1,A)) = A. [para(1018(a,1),139(a,1,1)),rewrite([86(2),86(4)]),flip(a)].
% 1.52/1.79 1798 join(A,join(B,composition(c1,A))) = join(A,B). [para(1771(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 1.52/1.79 3617 join(A,composition(complement(one),A)) = composition(top,A). [para(49(a,1),198(a,2,2,1)),rewrite([20(7),27(8,R),20(7),49(7),18(4)]),flip(a)].
% 1.52/1.79 3746 join(A,composition(A,complement(one))) = composition(A,top). [para(3617(a,1),71(a,1,1)),rewrite([40(4),234(2),229(5),16(7),20(6)]),flip(a)].
% 1.52/1.79 4578 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(3746(a,1),1798(a,1,2)),rewrite([20(10)])].
% 1.52/1.79 4581 $F # answer(goals). [back_rewrite(149),rewrite([4578(11),153(11),4578(22),153(22),4578(22)]),xx(a),xx(b)].
% 1.52/1.79
% 1.52/1.79 % SZS output end Refutation
% 1.52/1.79 ============================== end of proof ==========================
% 1.52/1.79
% 1.52/1.79 ============================== STATISTICS ============================
% 1.52/1.79
% 1.52/1.79 Given=378. Generated=29951. Kept=4559. proofs=1.
% 1.52/1.79 Usable=319. Sos=3690. Demods=3698. Limbo=3, Disabled=562. Hints=0.
% 1.52/1.79 Megabytes=5.89.
% 1.52/1.79 User_CPU=0.73, System_CPU=0.03, Wall_clock=1.
% 1.52/1.79
% 1.52/1.79 ============================== end of statistics =====================
% 1.52/1.79
% 1.52/1.79 ============================== end of search =========================
% 1.52/1.79
% 1.52/1.79 THEOREM PROVED
% 1.52/1.79 % SZS status Theorem
% 1.52/1.79
% 1.52/1.79 Exiting with 1 proof.
% 1.52/1.79
% 1.52/1.79 Process 14808 exit (max_proofs) Fri Jul 8 11:09:53 2022
% 1.52/1.79 Prover9 interrupted
%------------------------------------------------------------------------------