TSTP Solution File: REL008+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL008+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 19:53:32 EDT 2022
% Result : Theorem 1.42s 1.77s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL008+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n003.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 11:15:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 23578 was started by sandbox2 on n003.cluster.edu,
% 0.43/0.99 Fri Jul 8 11:15:28 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23423_n003.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_23423_n003.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (17 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 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].
% 1.42/1.77 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].
% 1.42/1.77 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].
% 1.42/1.77 17 -(all X0 all X1 all X2 (join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) & join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.42/1.77
% 1.42/1.77 ============================== end of process non-clausal formulas ===
% 1.42/1.77
% 1.42/1.77 ============================== PROCESS INITIAL CLAUSES ===============
% 1.42/1.77
% 1.42/1.77 ============================== PREDICATE ELIMINATION =================
% 1.42/1.77
% 1.42/1.77 ============================== end predicate elimination =============
% 1.42/1.77
% 1.42/1.77 Auto_denials:
% 1.42/1.77 % copying label goals to answer in negative clause
% 1.42/1.77
% 1.42/1.77 Term ordering decisions:
% 1.42/1.77 Function symbol KB weights: one=1. top=1. zero=1. c1=1. c2=1. c3=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 1.42/1.77
% 1.42/1.77 ============================== end of process initial clauses ========
% 1.42/1.77
% 1.42/1.77 ============================== CLAUSES FOR SEARCH ====================
% 1.42/1.77
% 1.42/1.77 ============================== end of clauses for search =============
% 1.42/1.77
% 1.42/1.77 ============================== SEARCH ================================
% 1.42/1.77
% 1.42/1.77 % Starting search at 0.01 seconds.
% 1.42/1.77
% 1.42/1.77 ============================== PROOF =================================
% 1.42/1.77 % SZS status Theorem
% 1.42/1.77 % SZS output start Refutation
% 1.42/1.77
% 1.42/1.77 % Proof 1 at 0.77 (+ 0.02) seconds: goals.
% 1.42/1.77 % Length of proof is 61.
% 1.42/1.77 % Level of proof is 14.
% 1.42/1.77 % Maximum clause weight is 42.000.
% 1.42/1.77 % Given clauses 248.
% 1.42/1.77
% 1.42/1.77 1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 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].
% 1.42/1.77 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].
% 1.42/1.77 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].
% 1.42/1.77 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].
% 1.42/1.77 6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 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].
% 1.42/1.77 8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 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].
% 1.42/1.77 12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause). [assumption].
% 1.42/1.77 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].
% 1.42/1.77 17 -(all X0 all X1 all X2 (join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) & join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.42/1.77 18 composition(A,one) = A # label(composition_identity) # label(axiom). [clausify(6)].
% 1.42/1.77 19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom). [clausify(8)].
% 1.42/1.77 20 join(A,complement(A)) = top # label(def_top) # label(axiom). [clausify(12)].
% 1.42/1.77 21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom). [clausify(13)].
% 1.42/1.77 22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom). [clausify(1)].
% 1.42/1.77 23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom). [clausify(4)].
% 1.42/1.77 24 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom). [clausify(9)].
% 1.42/1.77 25 join(converse(A),converse(B)) = converse(join(A,B)). [copy(24),flip(a)].
% 1.42/1.77 26 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom). [clausify(10)].
% 1.42/1.77 27 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(26),flip(a)].
% 1.42/1.77 28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom). [clausify(2)].
% 1.42/1.77 29 join(A,join(B,C)) = join(C,join(A,B)). [copy(28),rewrite([22(2)]),flip(a)].
% 1.42/1.77 30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom). [clausify(5)].
% 1.42/1.77 31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom). [clausify(7)].
% 1.42/1.77 32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(31),flip(a)].
% 1.42/1.77 33 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom). [clausify(11)].
% 1.42/1.77 34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(33),rewrite([22(7)]),flip(a)].
% 1.42/1.77 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)].
% 1.42/1.77 36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
% 1.42/1.77 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)].
% 1.42/1.77 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)].
% 1.42/1.77 43 join(composition(c1,c2),composition(c1,c3)) != join(join(composition(c1,join(c2,c3)),composition(c1,c2)),composition(c1,c3)) | composition(c1,join(c2,c3)) != join(join(composition(c1,c2),composition(c1,c3)),composition(c1,join(c2,c3))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 1.42/1.77 44 join(composition(c1,c2),join(composition(c1,c3),composition(c1,join(c2,c3)))) != join(composition(c1,c2),composition(c1,c3)) | join(composition(c1,c2),join(composition(c1,c3),composition(c1,join(c2,c3)))) != composition(c1,join(c2,c3)) # answer(goals). [copy(43),rewrite([22(16),22(20),29(20,R),22(19),22(39),29(39),22(38),29(39,R),22(38)]),flip(a),flip(b)].
% 1.42/1.77 45 complement(top) = zero. [back_rewrite(21),rewrite([23(2),20(4)])].
% 1.42/1.77 48 converse(composition(converse(A),B)) = composition(converse(B),A). [para(19(a,1),27(a,1,2)),flip(a)].
% 1.42/1.77 49 join(A,join(B,complement(A))) = join(B,top). [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
% 1.42/1.77 50 composition(A,composition(one,B)) = composition(A,B). [para(18(a,1),30(a,1,1)),flip(a)].
% 1.42/1.77 52 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)). [para(27(a,1),32(a,1,1)),rewrite([22(7)])].
% 1.42/1.77 61 join(zero,complement(join(complement(A),complement(A)))) = A. [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
% 1.42/1.77 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)])].
% 1.42/1.77 126 composition(converse(one),A) = A. [para(18(a,1),48(a,1,1)),rewrite([19(2)]),flip(a)].
% 1.42/1.77 127 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)). [para(48(a,1),25(a,1,1)),rewrite([22(7)]),flip(a)].
% 1.42/1.77 135 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)].
% 1.42/1.77 136 join(top,complement(complement(A))) = top. [para(38(a,1),49(a,1,2)),rewrite([20(22),22(8),135(8)]),flip(a)].
% 1.42/1.77 137 converse(one) = one. [para(126(a,1),18(a,1)),flip(a)].
% 1.42/1.77 141 join(complement(A),complement(composition(one,A))) = complement(A). [para(126(a,1),34(a,1,2))].
% 1.42/1.77 155 composition(one,A) = A. [para(126(a,1),50(a,2)),rewrite([137(2),50(4)])].
% 1.42/1.77 161 join(complement(A),complement(A)) = complement(A). [back_rewrite(141),rewrite([155(3)])].
% 1.42/1.77 162 join(zero,complement(complement(A))) = A. [back_rewrite(61),rewrite([161(4)])].
% 1.42/1.77 164 join(zero,complement(A)) = complement(A). [para(136(a,1),36(a,1,1,1)),rewrite([45(2),45(3),162(5)])].
% 1.42/1.77 167 complement(complement(A)) = A. [back_rewrite(162),rewrite([164(4)])].
% 1.42/1.77 177 complement(join(A,A)) = complement(A). [back_rewrite(62),rewrite([167(3),164(4)])].
% 1.42/1.77 218 join(A,A) = A. [para(177(a,1),36(a,1,1,1,2)),rewrite([177(6),36(8)]),flip(a)].
% 1.42/1.77 225 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)].
% 1.42/1.77 3456 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)). [para(52(a,1),127(a,1,1)),rewrite([25(3),27(4),19(4),19(4),19(6)]),flip(a)].
% 1.42/1.77 3574 $F # answer(goals). [back_rewrite(44),rewrite([3456(12),29(9,R),218(8),3456(9),225(6),3456(12),3456(23),29(20,R),218(19),3456(20),225(17)]),xx(a),xx(b)].
% 1.42/1.77
% 1.42/1.77 % SZS output end Refutation
% 1.42/1.77 ============================== end of proof ==========================
% 1.42/1.77
% 1.42/1.77 ============================== STATISTICS ============================
% 1.42/1.77
% 1.42/1.77 Given=248. Generated=20947. Kept=3546. proofs=1.
% 1.42/1.77 Usable=207. Sos=2837. Demods=3129. Limbo=118, Disabled=401. Hints=0.
% 1.42/1.77 Megabytes=8.40.
% 1.42/1.77 User_CPU=0.77, System_CPU=0.02, Wall_clock=1.
% 1.42/1.77
% 1.42/1.77 ============================== end of statistics =====================
% 1.42/1.77
% 1.42/1.77 ============================== end of search =========================
% 1.42/1.77
% 1.42/1.77 THEOREM PROVED
% 1.42/1.77 % SZS status Theorem
% 1.42/1.77
% 1.42/1.77 Exiting with 1 proof.
% 1.42/1.77
% 1.42/1.77 Process 23578 exit (max_proofs) Fri Jul 8 11:15:29 2022
% 1.42/1.77 Prover9 interrupted
%------------------------------------------------------------------------------