TSTP Solution File: REL004-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : REL004-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 19:53:24 EDT 2022
% Result : Unsatisfiable 2.14s 2.47s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL004-2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n019.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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 600
% 0.19/0.34 % DateTime : Fri Jul 8 08:53:23 EDT 2022
% 0.19/0.34 % CPUTime :
% 2.14/2.47 ============================== Prover9 ===============================
% 2.14/2.47 Prover9 (32) version 2009-11A, November 2009.
% 2.14/2.47 Process 6658 was started by sandbox on n019.cluster.edu,
% 2.14/2.47 Fri Jul 8 08:53:24 2022
% 2.14/2.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6505_n019.cluster.edu".
% 2.14/2.47 ============================== end of head ===========================
% 2.14/2.47
% 2.14/2.47 ============================== INPUT =================================
% 2.14/2.47
% 2.14/2.47 % Reading from file /tmp/Prover9_6505_n019.cluster.edu
% 2.14/2.47
% 2.14/2.47 set(prolog_style_variables).
% 2.14/2.47 set(auto2).
% 2.14/2.47 % set(auto2) -> set(auto).
% 2.14/2.47 % set(auto) -> set(auto_inference).
% 2.14/2.47 % set(auto) -> set(auto_setup).
% 2.14/2.47 % set(auto_setup) -> set(predicate_elim).
% 2.14/2.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.14/2.47 % set(auto) -> set(auto_limits).
% 2.14/2.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.14/2.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.14/2.47 % set(auto) -> set(auto_denials).
% 2.14/2.47 % set(auto) -> set(auto_process).
% 2.14/2.47 % set(auto2) -> assign(new_constants, 1).
% 2.14/2.47 % set(auto2) -> assign(fold_denial_max, 3).
% 2.14/2.47 % set(auto2) -> assign(max_weight, "200.000").
% 2.14/2.47 % set(auto2) -> assign(max_hours, 1).
% 2.14/2.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.14/2.47 % set(auto2) -> assign(max_seconds, 0).
% 2.14/2.47 % set(auto2) -> assign(max_minutes, 5).
% 2.14/2.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.14/2.47 % set(auto2) -> set(sort_initial_sos).
% 2.14/2.47 % set(auto2) -> assign(sos_limit, -1).
% 2.14/2.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.14/2.47 % set(auto2) -> assign(max_megs, 400).
% 2.14/2.47 % set(auto2) -> assign(stats, some).
% 2.14/2.47 % set(auto2) -> clear(echo_input).
% 2.14/2.47 % set(auto2) -> set(quiet).
% 2.14/2.47 % set(auto2) -> clear(print_initial_clauses).
% 2.14/2.47 % set(auto2) -> clear(print_given).
% 2.14/2.47 assign(lrs_ticks,-1).
% 2.14/2.47 assign(sos_limit,10000).
% 2.14/2.47 assign(order,kbo).
% 2.14/2.47 set(lex_order_vars).
% 2.14/2.47 clear(print_given).
% 2.14/2.47
% 2.14/2.47 % formulas(sos). % not echoed (17 formulas)
% 2.14/2.47
% 2.14/2.47 ============================== end of input ==========================
% 2.14/2.47
% 2.14/2.47 % From the command line: assign(max_seconds, 300).
% 2.14/2.47
% 2.14/2.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.14/2.47
% 2.14/2.47 % Formulas that are not ordinary clauses:
% 2.14/2.47
% 2.14/2.47 ============================== end of process non-clausal formulas ===
% 2.14/2.47
% 2.14/2.47 ============================== PROCESS INITIAL CLAUSES ===============
% 2.14/2.47
% 2.14/2.47 ============================== PREDICATE ELIMINATION =================
% 2.14/2.47
% 2.14/2.47 ============================== end predicate elimination =============
% 2.14/2.47
% 2.14/2.47 Auto_denials:
% 2.14/2.47 % copying label goals_17 to answer in negative clause
% 2.14/2.47
% 2.14/2.47 Term ordering decisions:
% 2.14/2.47 Function symbol KB weights: one=1. top=1. zero=1. sk1=1. composition=1. join=1. meet=1. converse=1. complement=1.
% 2.14/2.47
% 2.14/2.47 ============================== end of process initial clauses ========
% 2.14/2.47
% 2.14/2.47 ============================== CLAUSES FOR SEARCH ====================
% 2.14/2.47
% 2.14/2.47 ============================== end of clauses for search =============
% 2.14/2.47
% 2.14/2.47 ============================== SEARCH ================================
% 2.14/2.47
% 2.14/2.47 % Starting search at 0.01 seconds.
% 2.14/2.47
% 2.14/2.47 Low Water (keep): wt=125.000, iters=3594
% 2.14/2.47
% 2.14/2.47 Low Water (keep): wt=105.000, iters=3578
% 2.14/2.47
% 2.14/2.47 ============================== PROOF =================================
% 2.14/2.47 % SZS status Unsatisfiable
% 2.14/2.47 % SZS output start Refutation
% 2.14/2.47
% 2.14/2.47 % Proof 1 at 1.46 (+ 0.03) seconds: goals_17.
% 2.14/2.47 % Length of proof is 99.
% 2.14/2.47 % Level of proof is 35.
% 2.14/2.47 % Maximum clause weight is 48.000.
% 2.14/2.47 % Given clauses 430.
% 2.14/2.47
% 2.14/2.47 1 composition(A,one) = A # label(composition_identity_6) # label(axiom). [assumption].
% 2.14/2.47 2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom). [assumption].
% 2.14/2.47 3 top = join(A,complement(A)) # label(def_top_12) # label(axiom). [assumption].
% 2.14/2.47 4 join(A,complement(A)) = top. [copy(3),flip(a)].
% 2.14/2.47 5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom). [assumption].
% 2.14/2.47 6 meet(A,complement(A)) = zero. [copy(5),flip(a)].
% 2.14/2.47 7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom). [assumption].
% 2.14/2.47 8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom). [assumption].
% 2.14/2.47 9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom). [assumption].
% 2.14/2.47 10 join(converse(A),converse(B)) = converse(join(A,B)). [copy(9),flip(a)].
% 2.14/2.47 11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom). [assumption].
% 2.14/2.47 12 composition(converse(A),converse(B)) = converse(composition(B,A)). [copy(11),flip(a)].
% 2.14/2.47 13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom). [assumption].
% 2.14/2.47 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(4)])].
% 2.14/2.47 15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom). [assumption].
% 2.14/2.47 16 composition(composition(A,B),C) = composition(A,composition(B,C)). [copy(15),flip(a)].
% 2.14/2.47 17 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom). [assumption].
% 2.14/2.47 18 join(composition(A,B),composition(C,B)) = composition(join(A,C),B). [copy(17),flip(a)].
% 2.14/2.47 19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom). [assumption].
% 2.14/2.47 20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A). [copy(19),rewrite([7(6)])].
% 2.14/2.47 21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom). [assumption].
% 2.14/2.47 22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B. [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 2.14/2.47 23 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].
% 2.14/2.47 24 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(23),rewrite([8(2),7(4),8(8),8(13),7(15),8(20),8(25),7(27)])].
% 2.14/2.47 27 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].
% 2.14/2.47 28 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(27),rewrite([8(2),7(4),8(8),8(14),8(22),8(28)])].
% 2.14/2.47 29 converse(complement(sk1)) != complement(converse(sk1)) # label(goals_17) # label(negated_conjecture) # answer(goals_17). [assumption].
% 2.14/2.47 30 complement(converse(sk1)) != converse(complement(sk1)) # answer(goals_17). [copy(29),flip(a)].
% 2.14/2.47 31 complement(top) = zero. [back_rewrite(6),rewrite([8(2),4(4)])].
% 2.14/2.47 32 complement(converse(sk1)) = c_0. [new_symbol(30)].
% 2.14/2.47 33 converse(complement(sk1)) != c_0 # answer(goals_17). [back_rewrite(30),rewrite([32(3)]),flip(a)].
% 2.14/2.47 35 converse(composition(A,converse(B))) = composition(B,converse(A)). [para(2(a,1),12(a,1,1)),flip(a)].
% 2.14/2.47 36 converse(composition(converse(A),B)) = composition(converse(B),A). [para(2(a,1),12(a,1,2)),flip(a)].
% 2.14/2.47 37 join(A,join(B,complement(A))) = join(B,top). [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 2.14/2.47 38 composition(A,composition(one,B)) = composition(A,B). [para(1(a,1),16(a,1,1)),flip(a)].
% 2.14/2.47 42 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C). [para(16(a,1),18(a,1,1)),rewrite([7(6)])].
% 2.14/2.47 49 join(zero,complement(join(complement(A),complement(A)))) = A. [para(4(a,1),22(a,1,1,1)),rewrite([31(2)])].
% 2.14/2.47 50 join(zero,complement(join(A,complement(complement(A))))) = complement(A). [para(4(a,1),22(a,1,2,1)),rewrite([31(6),7(6)])].
% 2.14/2.47 81 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A. [para(31(a,1),22(a,1,2,1,1))].
% 2.14/2.47 89 join(c_0,converse(sk1)) = top. [para(32(a,1),4(a,1,2)),rewrite([7(4)])].
% 2.14/2.47 111 join(sk1,converse(c_0)) = converse(top). [para(89(a,1),10(a,2,1)),rewrite([2(5),7(4)])].
% 2.14/2.47 126 composition(converse(one),A) = A. [para(1(a,1),36(a,1,1)),rewrite([2(2)]),flip(a)].
% 2.14/2.47 134 converse(one) = one. [para(126(a,1),1(a,1)),flip(a)].
% 2.14/2.47 136 composition(join(A,one),B) = join(B,composition(A,B)). [para(126(a,1),18(a,1,1)),rewrite([134(4),7(4)]),flip(a)].
% 2.14/2.47 138 join(complement(A),complement(composition(one,A))) = complement(A). [para(126(a,1),20(a,1,2))].
% 2.14/2.47 152 composition(one,A) = A. [para(126(a,1),38(a,2)),rewrite([134(2),38(4)])].
% 2.14/2.47 158 join(complement(A),complement(A)) = complement(A). [back_rewrite(138),rewrite([152(3)])].
% 2.14/2.47 159 join(zero,complement(complement(A))) = A. [back_rewrite(49),rewrite([158(4)])].
% 2.14/2.47 160 converse(join(A,one)) = join(one,converse(A)). [para(134(a,1),10(a,1,1)),rewrite([7(5)]),flip(a)].
% 2.14/2.47 162 join(top,complement(join(A,complement(B)))) = join(top,complement(A)). [para(22(a,1),37(a,1,2)),rewrite([7(4),37(4),7(3),7(8)]),flip(a)].
% 2.14/2.47 163 join(top,complement(complement(A))) = top. [para(24(a,1),37(a,1,2)),rewrite([4(22),7(8),162(8)]),flip(a)].
% 2.14/2.47 165 join(zero,complement(c_0)) = converse(sk1). [para(32(a,1),159(a,1,2,1))].
% 2.14/2.47 166 join(zero,complement(A)) = complement(A). [para(163(a,1),22(a,1,1,1)),rewrite([31(2),31(3),159(5)])].
% 2.14/2.47 169 join(top,complement(A)) = join(top,top). [para(163(a,1),37(a,1,2)),rewrite([7(3)])].
% 2.14/2.47 170 complement(c_0) = converse(sk1). [back_rewrite(165),rewrite([166(4)])].
% 2.14/2.47 171 complement(complement(A)) = A. [back_rewrite(159),rewrite([166(4)])].
% 2.14/2.47 179 join(A,complement(join(top,top))) = A. [back_rewrite(81),rewrite([169(3),166(7),171(6),7(5)])].
% 2.14/2.47 181 complement(join(A,A)) = complement(A). [back_rewrite(50),rewrite([171(3),166(4)])].
% 2.14/2.47 184 join(A,top) = top. [back_rewrite(163),rewrite([171(3),7(2)])].
% 2.14/2.47 190 join(A,zero) = A. [back_rewrite(179),rewrite([184(3),31(2)])].
% 2.14/2.47 191 join(top,complement(A)) = top. [back_rewrite(169),rewrite([184(6)])].
% 2.14/2.47 193 join(A,join(B,complement(A))) = top. [back_rewrite(37),rewrite([184(5)])].
% 2.14/2.47 195 join(complement(join(A,converse(sk1))),complement(join(complement(A),converse(sk1)))) = c_0. [para(170(a,1),22(a,1,1,1,2)),rewrite([170(7)])].
% 2.14/2.47 204 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B). [para(171(a,1),22(a,1,1,1,2)),rewrite([171(5),7(4)])].
% 2.14/2.47 212 complement(zero) = top. [para(31(a,1),171(a,1,1))].
% 2.14/2.47 241 join(A,A) = A. [para(181(a,1),22(a,1,1,1,2)),rewrite([181(6),22(8)]),flip(a)].
% 2.14/2.47 248 join(A,join(A,B)) = join(A,B). [para(241(a,1),14(a,1)),rewrite([7(3),14(4,R),7(3),14(3,R),241(2)]),flip(a)].
% 2.14/2.47 266 join(A,complement(join(B,complement(A)))) = A. [para(22(a,1),248(a,1,2)),rewrite([7(4),22(12)])].
% 2.14/2.47 273 join(c_0,complement(join(A,converse(sk1)))) = c_0. [para(170(a,1),266(a,1,2,1,2))].
% 2.14/2.47 275 join(c_0,complement(converse(join(A,sk1)))) = c_0. [para(10(a,1),273(a,1,2,1))].
% 2.14/2.47 278 join(c_0,converse(join(A,sk1))) = top. [para(275(a,1),193(a,1,2)),rewrite([7(5)])].
% 2.14/2.47 279 join(A,converse(top)) = converse(top). [para(278(a,1),10(a,2,1)),rewrite([2(6),14(5),7(4),14(5,R),7(4),111(4)])].
% 2.14/2.47 291 join(top,converse(A)) = top. [para(279(a,1),10(a,2,1)),rewrite([2(4),7(3),2(6)])].
% 2.14/2.47 292 join(top,composition(A,converse(B))) = top. [para(35(a,1),291(a,1,2))].
% 2.14/2.47 294 converse(top) = top. [para(291(a,1),279(a,1)),flip(a)].
% 2.14/2.47 298 join(sk1,converse(c_0)) = top. [back_rewrite(111),rewrite([294(6)])].
% 2.14/2.47 312 join(top,composition(A,B)) = top. [para(2(a,1),292(a,1,2,2))].
% 2.14/2.47 313 composition(join(A,one),top) = top. [para(294(a,1),292(a,1,2,2)),rewrite([136(4,R)])].
% 2.14/2.47 314 composition(top,join(one,converse(A))) = top. [para(313(a,1),12(a,2,1)),rewrite([294(2),160(4),294(7)])].
% 2.14/2.47 341 composition(top,top) = top. [para(294(a,1),314(a,1,2,2)),rewrite([184(4)])].
% 2.14/2.47 344 composition(top,zero) = zero. [para(341(a,1),20(a,1,2,2,1)),rewrite([31(2),294(3),31(4),136(5,R),7(3),184(3),31(5)])].
% 2.14/2.47 353 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)). [para(344(a,1),28(a,1,1,1,2,1)),rewrite([212(3),7(3),191(3),31(2),31(3),166(7),171(6),212(6),294(7),191(9),31(6),16(6),31(9),166(13),171(12),212(12),294(13),191(15),31(12),16(12)])].
% 2.14/2.47 357 join(zero,composition(A,composition(B,zero))) = zero. [para(344(a,1),42(a,1,2)),rewrite([7(5),312(8),344(8)])].
% 2.14/2.47 359 composition(A,composition(converse(zero),zero)) = zero. [back_rewrite(353),rewrite([357(7)]),flip(a)].
% 2.14/2.47 415 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B). [para(359(a,1),16(a,1,1)),rewrite([16(7)]),flip(a)].
% 2.14/2.47 416 composition(A,zero) = zero. [para(359(a,1),16(a,1)),rewrite([359(6)]),flip(a)].
% 2.14/2.47 417 composition(converse(zero),A) = converse(zero). [para(359(a,1),36(a,1,1)),rewrite([416(6)]),flip(a)].
% 2.14/2.47 422 composition(zero,A) = composition(B,converse(zero)). [back_rewrite(415),rewrite([417(5)]),flip(a)].
% 2.14/2.47 424 composition(zero,A) = c_1. [new_symbol(422)].
% 2.14/2.47 425 composition(A,converse(zero)) = c_1. [back_rewrite(422),rewrite([424(2)]),flip(a)].
% 2.14/2.47 440 c_1 = zero. [para(424(a,1),1(a,1))].
% 2.14/2.47 441 converse(zero) = zero. [para(424(a,1),12(a,2,1)),rewrite([425(4),440(1),440(2)]),flip(a)].
% 2.14/2.47 469 join(zero,converse(A)) = converse(A). [para(441(a,1),10(a,1,1)),rewrite([7(5),190(5)])].
% 2.14/2.47 6581 complement(join(converse(c_0),complement(sk1))) = complement(converse(c_0)). [para(298(a,1),204(a,1,1,1)),rewrite([31(2),166(8)])].
% 2.14/2.47 6728 join(converse(c_0),complement(sk1)) = converse(c_0). [para(6581(a,1),22(a,1,1,1,2)),rewrite([6581(12),22(12)]),flip(a)].
% 2.14/2.47 6741 join(c_0,converse(complement(sk1))) = c_0. [para(6728(a,1),10(a,2,1)),rewrite([2(3),2(8)])].
% 2.14/2.47 6746 complement(converse(complement(sk1))) = converse(sk1). [para(6741(a,1),204(a,1,1,1)),rewrite([170(2),170(7),7(8),10(8),4(6),294(4),31(4),7(4),469(4)]),flip(a)].
% 2.14/2.47 6863 converse(complement(sk1)) = c_0. [para(6746(a,1),22(a,1,1,1,2)),rewrite([6746(9),195(10)]),flip(a)].
% 2.14/2.47 6864 $F # answer(goals_17). [resolve(6863,a,33,a)].
% 2.14/2.47
% 2.14/2.47 % SZS output end Refutation
% 2.14/2.47 ============================== end of proof ==========================
% 2.14/2.47
% 2.14/2.47 ============================== STATISTICS ============================
% 2.14/2.47
% 2.14/2.47 Given=430. Generated=39104. Kept=6850. proofs=1.
% 2.14/2.47 Usable=374. Sos=5905. Demods=6243. Limbo=1, Disabled=586. Hints=0.
% 2.14/2.47 Megabytes=16.44.
% 2.14/2.47 User_CPU=1.46, System_CPU=0.03, Wall_clock=1.
% 2.14/2.47
% 2.14/2.47 ============================== end of statistics =====================
% 2.14/2.47
% 2.14/2.47 ============================== end of search =========================
% 2.14/2.47
% 2.14/2.47 THEOREM PROVED
% 2.14/2.47 % SZS status Unsatisfiable
% 2.14/2.47
% 2.14/2.47 Exiting with 1 proof.
% 2.14/2.47
% 2.14/2.47 Process 6658 exit (max_proofs) Fri Jul 8 08:53:25 2022
% 2.14/2.47 Prover9 interrupted
%------------------------------------------------------------------------------