TSTP Solution File: REL027+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL027+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 1.35s 1.68s
% Output : Refutation 1.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : REL027+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.32 % Computer : n025.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Fri Jul 8 15:02:45 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.69/0.99 ============================== Prover9 ===============================
% 0.69/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.69/0.99 Process 8173 was started by sandbox2 on n025.cluster.edu,
% 0.69/0.99 Fri Jul 8 15:02:45 2022
% 0.69/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8020_n025.cluster.edu".
% 0.69/0.99 ============================== end of head ===========================
% 0.69/0.99
% 0.69/0.99 ============================== INPUT =================================
% 0.69/0.99
% 0.69/0.99 % Reading from file /tmp/Prover9_8020_n025.cluster.edu
% 0.69/0.99
% 0.69/0.99 set(prolog_style_variables).
% 0.69/0.99 set(auto2).
% 0.69/0.99 % set(auto2) -> set(auto).
% 0.69/0.99 % set(auto) -> set(auto_inference).
% 0.69/0.99 % set(auto) -> set(auto_setup).
% 0.69/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.69/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/0.99 % set(auto) -> set(auto_limits).
% 0.69/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/0.99 % set(auto) -> set(auto_denials).
% 0.69/0.99 % set(auto) -> set(auto_process).
% 0.69/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.69/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.69/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.69/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.69/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.69/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.69/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.69/0.99 % set(auto2) -> assign(stats, some).
% 0.69/0.99 % set(auto2) -> clear(echo_input).
% 0.69/0.99 % set(auto2) -> set(quiet).
% 0.69/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.69/0.99 % set(auto2) -> clear(print_given).
% 0.69/0.99 assign(lrs_ticks,-1).
% 0.69/0.99 assign(sos_limit,10000).
% 0.69/0.99 assign(order,kbo).
% 0.69/0.99 set(lex_order_vars).
% 0.69/0.99 clear(print_given).
% 0.69/0.99
% 0.69/0.99 % formulas(sos). % not echoed (14 formulas)
% 0.69/0.99
% 0.69/0.99 ============================== end of input ==========================
% 0.69/0.99
% 0.69/0.99 % From the command line: assign(max_seconds, 300).
% 0.69/0.99
% 0.69/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/0.99
% 0.69/0.99 % Formulas that are not ordinary clauses:
% 0.69/0.99 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 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].
% 0.69/0.99 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].
% 0.69/0.99 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].
% 0.69/0.99 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 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].
% 0.69/0.99 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.69/0.99 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.35/1.68 14 -(all X0 (join(X0,one) = one -> meet(complement(composition(X0,top)),one) = meet(complement(X0),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.35/1.68
% 1.35/1.68 ============================== end of process non-clausal formulas ===
% 1.35/1.68
% 1.35/1.68 ============================== PROCESS INITIAL CLAUSES ===============
% 1.35/1.68
% 1.35/1.68 ============================== PREDICATE ELIMINATION =================
% 1.35/1.68
% 1.35/1.68 ============================== end predicate elimination =============
% 1.35/1.68
% 1.35/1.68 Auto_denials:
% 1.35/1.68 % copying label goals to answer in negative clause
% 1.35/1.68
% 1.35/1.68 Term ordering decisions:
% 1.35/1.68 Function symbol KB weights: one=1. top=1. zero=1. c1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.35/1.68
% 1.35/1.68 ============================== end of process initial clauses ========
% 1.35/1.68
% 1.35/1.68 ============================== CLAUSES FOR SEARCH ====================
% 1.35/1.68
% 1.35/1.68 ============================== end of clauses for search =============
% 1.35/1.68
% 1.35/1.68 ============================== SEARCH ================================
% 1.35/1.68
% 1.35/1.68 % Starting search at 0.01 seconds.
% 1.35/1.68
% 1.35/1.68 ============================== PROOF =================================
% 1.35/1.68 % SZS status Theorem
% 1.35/1.68 % SZS output start Refutation
% 1.35/1.68
% 1.35/1.68 % Proof 1 at 0.68 (+ 0.02) seconds: goals.
% 1.35/1.68 % Length of proof is 98.
% 1.35/1.68 % Level of proof is 26.
% 1.35/1.68 % Maximum clause weight is 21.000.
% 1.35/1.68 % Given clauses 378.
% 1.35/1.68
% 1.35/1.68 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.35/1.68 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].
% 1.35/1.68 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].
% 1.35/1.68 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].
% 1.35/1.68 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].
% 1.39/1.68 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 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].
% 1.39/1.68 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 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].
% 1.39/1.68 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.39/1.68 14 -(all X0 (join(X0,one) = one -> meet(complement(composition(X0,top)),one) = meet(complement(X0),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.39/1.68 15 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 1.39/1.68 16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 1.39/1.68 17 join(c1,one) = one # label(goals) # label(negated_conjecture). [clausify(14)].
% 1.39/1.68 18 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 1.39/1.68 19 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 1.39/1.68 20 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 1.39/1.68 21 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 1.39/1.68 22 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 1.39/1.68 23 join(converse(A),converse(B)) = converse(join(A,B)). [copy(22),flip(a)].
% 1.39/1.68 24 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 1.39/1.68 25 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(24),flip(a)].
% 1.39/1.68 26 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 1.39/1.68 27 join(A,join(B,C)) = join(C,join(A,B)). [copy(26),rewrite([20(2)]),flip(a)].
% 1.39/1.68 28 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 1.39/1.68 29 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 1.39/1.68 30 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(29),flip(a)].
% 1.39/1.68 31 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 1.39/1.68 32 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(31),rewrite([20(7)]),flip(a)].
% 1.39/1.68 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)].
% 1.39/1.68 34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(33),rewrite([20(6),20(8)]),rewrite([20(6)])].
% 1.39/1.68 35 meet(complement(composition(c1,top)),one) != meet(complement(c1),one) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 1.39/1.68 36 complement(join(complement(one),complement(complement(composition(c1,top))))) != complement(join(complement(one),complement(complement(c1)))) # answer(goals). [copy(35),rewrite([21(6),20(8),21(13),20(15)])].
% 1.39/1.68 37 join(one,c1) = one. [back_rewrite(17),rewrite([20(3)])].
% 1.39/1.68 38 complement(top) = zero. [back_rewrite(19),rewrite([21(2),18(4)])].
% 1.39/1.68 39 converse(join(A,converse(B))) = join(B,converse(A)). [para(16(a,1),23(a,1,1)),rewrite([20(4)]),flip(a)].
% 1.39/1.68 40 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(16(a,1),25(a,1,1)),flip(a)].
% 1.39/1.68 41 converse(composition(converse(A),B)) = composition(converse(B),A). [para(16(a,1),25(a,1,2)),flip(a)].
% 1.39/1.68 42 join(A,join(B,complement(A))) = join(B,top). [para(18(a,1),27(a,2,2)),rewrite([20(2)])].
% 1.39/1.68 43 composition(A,composition(one,B)) = composition(A,B). [para(15(a,1),28(a,1,1)),flip(a)].
% 1.39/1.68 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)])].
% 1.39/1.68 49 join(complement(one),composition(converse(A),complement(A))) = complement(one). [para(15(a,1),32(a,1,2,2,1))].
% 1.39/1.68 54 join(zero,complement(join(complement(A),complement(A)))) = A. [para(18(a,1),34(a,1,1,1)),rewrite([38(2)])].
% 1.39/1.68 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)])].
% 1.39/1.68 62 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(38(a,1),34(a,1,2,1,1))].
% 1.39/1.68 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)].
% 1.39/1.68 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)].
% 1.39/1.68 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)])].
% 1.39/1.68 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)].
% 1.39/1.68 75 composition(converse(one),A) = A. [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 1.39/1.68 81 converse(one) = one. [para(75(a,1),15(a,1)),flip(a)].
% 1.39/1.68 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)].
% 1.39/1.68 85 join(complement(A),complement(composition(one,A))) = complement(A). [para(75(a,1),32(a,1,2))].
% 1.39/1.68 86 composition(one,A) = A. [para(75(a,1),43(a,2)),rewrite([81(2),43(4)])].
% 1.39/1.68 87 join(complement(A),complement(A)) = complement(A). [back_rewrite(85),rewrite([86(3)])].
% 1.39/1.68 88 join(zero,complement(complement(A))) = A. [back_rewrite(54),rewrite([87(4)])].
% 1.39/1.68 89 converse(join(A,one)) = join(one,converse(A)). [para(81(a,1),23(a,1,1)),rewrite([20(5)]),flip(a)].
% 1.39/1.68 93 join(top,complement(A)) = top. [para(87(a,1),42(a,1,2)),rewrite([18(2),20(4)]),flip(a)].
% 1.39/1.68 94 join(zero,complement(join(zero,complement(A)))) = A. [back_rewrite(62),rewrite([93(3),38(2)])].
% 1.39/1.68 95 join(top,top) = join(A,top). [para(93(a,1),42(a,1,2)),flip(a)].
% 1.39/1.68 100 join(A,top) = join(B,top). [para(95(a,1),42(a,2)),rewrite([93(3)])].
% 1.39/1.68 101 join(A,top) = c_0. [new_symbol(100)].
% 1.39/1.68 104 join(A,join(B,complement(A))) = c_0. [back_rewrite(42),rewrite([101(5)])].
% 1.39/1.68 115 c_0 = top. [para(88(a,1),104(a,1,2)),rewrite([20(2),18(2)]),flip(a)].
% 1.39/1.68 116 join(A,join(B,complement(A))) = top. [back_rewrite(104),rewrite([115(4)])].
% 1.39/1.68 128 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)].
% 1.39/1.68 139 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)].
% 1.39/1.68 143 join(zero,complement(A)) = complement(A). [para(88(a,1),94(a,1,2,1))].
% 1.39/1.68 144 complement(complement(A)) = A. [back_rewrite(94),rewrite([143(4),143(4)])].
% 1.39/1.68 145 join(A,zero) = A. [back_rewrite(88),rewrite([144(3),20(2)])].
% 1.39/1.68 149 complement(join(complement(one),composition(c1,top))) != complement(join(c1,complement(one))) # answer(goals). [back_rewrite(36),rewrite([144(7),144(12),20(11)])].
% 1.39/1.68 153 join(A,A) = A. [para(144(a,1),87(a,1,1)),rewrite([144(2),144(3)])].
% 1.39/1.68 157 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)].
% 1.39/1.68 158 join(A,complement(join(B,complement(A)))) = A. [para(34(a,1),157(a,1,2)),rewrite([20(4),34(12)])].
% 1.39/1.68 163 join(complement(A),complement(join(A,B))) = complement(A). [para(144(a,1),158(a,1,2,1,2)),rewrite([20(2)])].
% 1.39/1.68 171 join(complement(one),composition(converse(complement(A)),A)) = complement(one). [para(144(a,1),49(a,1,2,2))].
% 1.39/1.68 198 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)].
% 1.39/1.68 225 join(complement(one),converse(complement(one))) = complement(one). [para(15(a,1),171(a,1,2))].
% 1.39/1.68 229 converse(complement(one)) = complement(one). [para(225(a,1),23(a,2,1)),rewrite([16(7),20(6),225(6)]),flip(a)].
% 1.39/1.68 234 converse(top) = top. [para(229(a,1),89(a,2,2)),rewrite([20(4),18(4),18(6)])].
% 1.39/1.68 303 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)])].
% 1.39/1.68 304 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)])].
% 1.39/1.68 561 join(complement(one),complement(c1)) = complement(c1). [para(37(a,1),303(a,1,2,1)),rewrite([20(5)])].
% 1.39/1.68 575 join(A,join(complement(A),complement(B))) = top. [para(304(a,1),116(a,1,2)),rewrite([20(4)])].
% 1.39/1.68 593 join(one,complement(c1)) = top. [para(561(a,1),575(a,1,2))].
% 1.39/1.68 596 join(zero,c1) = c1. [para(593(a,1),34(a,1,1,1)),rewrite([38(2),561(6),144(4)])].
% 1.39/1.68 999 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)].
% 1.39/1.68 1012 join(A,composition(converse(c1),A)) = A. [para(999(a,1),30(a,2,1)),rewrite([86(2),86(6)])].
% 1.39/1.68 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)].
% 1.39/1.68 1771 join(A,composition(c1,A)) = A. [para(1018(a,1),139(a,1,1)),rewrite([86(2),86(4)]),flip(a)].
% 1.39/1.68 1798 join(A,join(B,composition(c1,A))) = join(A,B). [para(1771(a,1),27(a,2,2)),rewrite([20(3),20(5)])].
% 1.39/1.68 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)].
% 1.39/1.68 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)].
% 1.39/1.68 4578 join(complement(one),composition(c1,top)) = join(c1,complement(one)). [para(3746(a,1),1798(a,1,2)),rewrite([20(10)])].
% 1.39/1.68 4581 $F # answer(goals). [back_rewrite(149),rewrite([4578(6)]),xx(a)].
% 1.39/1.68
% 1.39/1.68 % SZS output end Refutation
% 1.39/1.68 ============================== end of proof ==========================
% 1.39/1.68
% 1.39/1.68 ============================== STATISTICS ============================
% 1.39/1.68
% 1.39/1.68 Given=378. Generated=29947. Kept=4559. proofs=1.
% 1.39/1.68 Usable=319. Sos=3690. Demods=3698. Limbo=3, Disabled=562. Hints=0.
% 1.39/1.68 Megabytes=5.82.
% 1.39/1.68 User_CPU=0.68, System_CPU=0.02, Wall_clock=1.
% 1.39/1.68
% 1.39/1.68 ============================== end of statistics =====================
% 1.39/1.68
% 1.39/1.68 ============================== end of search =========================
% 1.39/1.68
% 1.39/1.68 THEOREM PROVED
% 1.39/1.68 % SZS status Theorem
% 1.39/1.68
% 1.39/1.68 Exiting with 1 proof.
% 1.39/1.68
% 1.39/1.68 Process 8173 exit (max_proofs) Fri Jul 8 15:02:46 2022
% 1.39/1.68 Prover9 interrupted
%------------------------------------------------------------------------------