TSTP Solution File: REL011+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL011+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n009.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 : 300s
% DateTime : Tue Aug 22 10:54:27 EDT 2023
% Result : Theorem 13.00s 4.77s
% Output : CNFRefutation 13.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 26
% Syntax : Number of formulae : 134 ( 122 unt; 11 typ; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 150 (; 150 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(top,type,
top: $i ).
tff(converse,type,
converse: $i > $i ).
tff(join,type,
join: ( $i * $i ) > $i ).
tff(composition,type,
composition: ( $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(meet,type,
meet: ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(f_54,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_60,axiom,
! [X0,X1] : ( meet(X0,X1) = complement(join(complement(X0),complement(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
tff(f_121,negated_conjecture,
~ ! [X0,X1,X2] :
( ( meet(X0,composition(converse(X1),X2)) = zero )
=> ( meet(composition(X1,X0),X2) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_81,axiom,
! [X0] : ( zero = meet(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
tff(f_79,axiom,
! [X0] : ( top = join(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
tff(f_58,axiom,
! [X0,X1] : ( X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
tff(f_56,axiom,
! [X0,X1,X2] : ( join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
tff(f_70,axiom,
! [X0] : ( converse(converse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
tff(f_65,axiom,
! [X0] : ( composition(X0,one) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
tff(f_74,axiom,
! [X0,X1] : ( converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
tff(f_63,axiom,
! [X0,X1,X2] : ( composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
tff(f_76,axiom,
! [X0,X1] : ( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
tff(f_72,axiom,
! [X0,X1] : ( converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
tff(f_67,axiom,
! [X0,X1,X2] : ( composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
tff(f_112,axiom,
! [X0,X1,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) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
tff(c_2,plain,
! [X1_2,X0_1] : ( join(X1_2,X0_1) = join(X0_1,X1_2) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_115,plain,
! [X0_41,X1_42] : ( complement(join(complement(X0_41),complement(X1_42))) = meet(X0_41,X1_42) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_646,plain,
! [X1_62,X0_63] : ( complement(join(complement(X1_62),complement(X0_63))) = meet(X0_63,X1_62) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_115]) ).
tff(c_8,plain,
! [X0_8,X1_9] : ( complement(join(complement(X0_8),complement(X1_9))) = meet(X0_8,X1_9) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_673,plain,
! [X1_62,X0_63] : ( meet(X1_62,X0_63) = meet(X0_63,X1_62) ),
inference(superposition,[status(thm),theory(equality)],[c_646,c_8]) ).
tff(c_34,plain,
meet(composition('#skF_2','#skF_1'),'#skF_3') != zero,
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_776,plain,
meet('#skF_3',composition('#skF_2','#skF_1')) != zero,
inference(demodulation,[status(thm),theory(equality)],[c_673,c_34]) ).
tff(c_26,plain,
! [X0_25] : ( meet(X0_25,complement(X0_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_24,plain,
! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_149,plain,
! [X0_41] : ( meet(X0_41,complement(X0_41)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_115]) ).
tff(c_152,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_149]) ).
tff(c_6,plain,
! [X0_6,X1_7] : ( join(complement(join(complement(X0_6),complement(X1_7))),complement(join(complement(X0_6),X1_7))) = X0_6 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_844,plain,
! [X0_67,X1_68] : ( join(meet(X0_67,X1_68),complement(join(complement(X0_67),X1_68))) = X0_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_910,plain,
! [X0_67] : ( join(meet(X0_67,complement(complement(X0_67))),complement(top)) = X0_67 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_844]) ).
tff(c_920,plain,
! [X0_67] : ( join(zero,meet(X0_67,complement(complement(X0_67)))) = X0_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_152,c_910]) ).
tff(c_162,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_152,c_24]) ).
tff(c_360,plain,
! [X0_50,X1_51,X2_52] : ( join(join(X0_50,X1_51),X2_52) = join(X0_50,join(X1_51,X2_52)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_414,plain,
! [X2_53] : ( join(top,join(zero,X2_53)) = join(top,X2_53) ),
inference(superposition,[status(thm),theory(equality)],[c_162,c_360]) ).
tff(c_435,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_414]) ).
tff(c_159,plain,
! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_8]) ).
tff(c_193,plain,
! [X0_45] : ( complement(join(zero,complement(X0_45))) = meet(X0_45,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_227,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_193]) ).
tff(c_230,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_227]) ).
tff(c_880,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_230,c_844]) ).
tff(c_918,plain,
join(zero,complement(join(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_435,c_2,c_880]) ).
tff(c_388,plain,
! [X2_52] : ( join(top,join(zero,X2_52)) = join(top,X2_52) ),
inference(superposition,[status(thm),theory(equality)],[c_162,c_360]) ).
tff(c_985,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm),theory(equality)],[c_918,c_388]) ).
tff(c_997,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_162,c_985]) ).
tff(c_168,plain,
! [X0_8] : ( complement(join(zero,complement(X0_8))) = meet(X0_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_994,plain,
meet(join(top,top),top) = complement(zero),
inference(superposition,[status(thm),theory(equality)],[c_918,c_168]) ).
tff(c_37,plain,
! [X0_6,X1_7] : ( join(meet(X0_6,X1_7),complement(join(complement(X0_6),X1_7))) = X0_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_1017,plain,
join(complement(zero),complement(join(complement(join(top,top)),top))) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_994,c_37]) ).
tff(c_1032,plain,
join(top,top) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_152,c_2,c_997,c_2,c_1017]) ).
tff(c_1093,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_1032,c_918]) ).
tff(c_1096,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_1093]) ).
tff(c_4,plain,
! [X0_3,X1_4,X2_5] : ( join(join(X0_3,X1_4),X2_5) = join(X0_3,join(X1_4,X2_5)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_1380,plain,
! [X2_79] : ( join(zero,join(zero,X2_79)) = join(zero,X2_79) ),
inference(superposition,[status(thm),theory(equality)],[c_1096,c_4]) ).
tff(c_1407,plain,
! [X0_67] : ( join(zero,meet(X0_67,complement(complement(X0_67)))) = join(zero,X0_67) ),
inference(superposition,[status(thm),theory(equality)],[c_920,c_1380]) ).
tff(c_1440,plain,
! [X0_67] : ( join(zero,X0_67) = X0_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_920,c_1407]) ).
tff(c_156,plain,
! [X1_9] : ( complement(join(zero,complement(X1_9))) = meet(top,X1_9) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_8]) ).
tff(c_1451,plain,
! [X1_9] : ( complement(complement(X1_9)) = meet(top,X1_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_1440,c_156]) ).
tff(c_1453,plain,
! [X0_80] : ( join(zero,X0_80) = X0_80 ),
inference(demodulation,[status(thm),theory(equality)],[c_920,c_1407]) ).
tff(c_1462,plain,
! [X0_67] : ( meet(X0_67,complement(complement(X0_67))) = X0_67 ),
inference(superposition,[status(thm),theory(equality)],[c_1453,c_920]) ).
tff(c_2050,plain,
! [X0_91] : ( meet(X0_91,meet(top,X0_91)) = X0_91 ),
inference(demodulation,[status(thm),theory(equality)],[c_1451,c_1462]) ).
tff(c_2090,plain,
! [X1_62] : ( meet(X1_62,meet(X1_62,top)) = X1_62 ),
inference(superposition,[status(thm),theory(equality)],[c_673,c_2050]) ).
tff(c_1976,plain,
! [X0_90] : ( complement(complement(X0_90)) = meet(X0_90,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_1440,c_168]) ).
tff(c_731,plain,
! [X1_62] : ( meet(complement(X1_62),X1_62) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_646]) ).
tff(c_739,plain,
! [X1_62] : ( meet(complement(X1_62),X1_62) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_152,c_731]) ).
tff(c_2367,plain,
! [X0_97] : ( meet(meet(X0_97,top),complement(X0_97)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_1976,c_739]) ).
tff(c_2372,plain,
! [X0_97] : ( join(zero,complement(join(complement(meet(X0_97,top)),complement(X0_97)))) = meet(X0_97,top) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_37]) ).
tff(c_2431,plain,
! [X0_97] : ( meet(X0_97,top) = X0_97 ),
inference(demodulation,[status(thm),theory(equality)],[c_2090,c_1440,c_8,c_2,c_2372]) ).
tff(c_1452,plain,
! [X0_8] : ( complement(complement(X0_8)) = meet(X0_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_1440,c_168]) ).
tff(c_2446,plain,
! [X0_8] : ( complement(complement(X0_8)) = X0_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_2431,c_1452]) ).
tff(c_16,plain,
! [X0_17] : ( converse(converse(X0_17)) = X0_17 ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_12,plain,
! [X0_13] : ( composition(X0_13,one) = X0_13 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_170,plain,
! [X1_43,X0_44] : ( composition(converse(X1_43),converse(X0_44)) = converse(composition(X0_44,X1_43)) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_3492,plain,
! [X0_113,X1_114] : ( converse(composition(converse(X0_113),X1_114)) = composition(converse(X1_114),X0_113) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_170]) ).
tff(c_3551,plain,
! [X0_113] : ( composition(converse(one),X0_113) = converse(converse(X0_113)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_3492]) ).
tff(c_3568,plain,
! [X0_113] : ( composition(converse(one),X0_113) = X0_113 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3551]) ).
tff(c_3570,plain,
! [X0_115] : ( composition(converse(one),X0_115) = X0_115 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3551]) ).
tff(c_502,plain,
! [X0_55,X1_56,X2_57] : ( composition(composition(X0_55,X1_56),X2_57) = composition(X0_55,composition(X1_56,X2_57)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_524,plain,
! [X0_13,X2_57] : ( composition(X0_13,composition(one,X2_57)) = composition(X0_13,X2_57) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_502]) ).
tff(c_3620,plain,
! [X2_57] : ( composition(converse(one),X2_57) = composition(one,X2_57) ),
inference(superposition,[status(thm),theory(equality)],[c_3570,c_524]) ).
tff(c_3657,plain,
! [X2_57] : ( composition(one,X2_57) = X2_57 ),
inference(demodulation,[status(thm),theory(equality)],[c_3568,c_3620]) ).
tff(c_3631,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_3570,c_12]) ).
tff(c_3718,plain,
! [X2_116] : ( composition(one,X2_116) = X2_116 ),
inference(demodulation,[status(thm),theory(equality)],[c_3568,c_3620]) ).
tff(c_22,plain,
! [X0_22,X1_23] : ( join(composition(converse(X0_22),complement(composition(X0_22,X1_23))),complement(X1_23)) = complement(X1_23) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_3751,plain,
! [X2_116] : ( join(composition(converse(one),complement(X2_116)),complement(X2_116)) = complement(X2_116) ),
inference(superposition,[status(thm),theory(equality)],[c_3718,c_22]) ).
tff(c_4174,plain,
! [X2_122] : ( join(complement(X2_122),complement(X2_122)) = complement(X2_122) ),
inference(demodulation,[status(thm),theory(equality)],[c_3657,c_2,c_3631,c_3751]) ).
tff(c_4204,plain,
! [X0_8] : ( join(complement(complement(X0_8)),X0_8) = complement(complement(X0_8)) ),
inference(superposition,[status(thm),theory(equality)],[c_2446,c_4174]) ).
tff(c_4270,plain,
! [X0_123] : ( join(X0_123,X0_123) = X0_123 ),
inference(demodulation,[status(thm),theory(equality)],[c_2446,c_2446,c_4204]) ).
tff(c_376,plain,
! [X0_50,X1_51] : ( join(X0_50,join(X1_51,complement(join(X0_50,X1_51)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_360,c_24]) ).
tff(c_4288,plain,
! [X0_123] : ( join(X0_123,join(X0_123,complement(X0_123))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_4270,c_376]) ).
tff(c_4388,plain,
! [X0_124] : ( join(X0_124,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4288]) ).
tff(c_4426,plain,
! [X0_124] : ( join(top,X0_124) = top ),
inference(superposition,[status(thm),theory(equality)],[c_4388,c_2]) ).
tff(c_405,plain,
! [X0_24,X2_52] : ( join(X0_24,join(complement(X0_24),X2_52)) = join(top,X2_52) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_360]) ).
tff(c_4802,plain,
! [X0_127,X2_128] : ( join(X0_127,join(complement(X0_127),X2_128)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_4426,c_405]) ).
tff(c_4828,plain,
! [X0_6,X2_128] : ( join(meet(X0_6,join(complement(complement(X0_6)),X2_128)),complement(top)) = X0_6 ),
inference(superposition,[status(thm),theory(equality)],[c_4802,c_37]) ).
tff(c_4934,plain,
! [X0_129,X2_130] : ( meet(X0_129,join(X0_129,X2_130)) = X0_129 ),
inference(demodulation,[status(thm),theory(equality)],[c_2446,c_1440,c_2,c_152,c_4828]) ).
tff(c_5067,plain,
! [X0_131] : ( meet(zero,X0_131) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_1440,c_4934]) ).
tff(c_5122,plain,
! [X0_131] : ( meet(X0_131,zero) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_5067,c_673]) ).
tff(c_254,plain,
! [X0_46,X1_47] : ( join(converse(X0_46),converse(X1_47)) = converse(join(X0_46,X1_47)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_275,plain,
! [X0_17,X1_47] : ( converse(join(converse(X0_17),X1_47)) = join(X0_17,converse(X1_47)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_254]) ).
tff(c_4594,plain,
! [X0_126] : ( join(X0_126,converse(top)) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_4388,c_275]) ).
tff(c_4599,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_4594,c_4426]) ).
tff(c_20,plain,
! [X1_21,X0_20] : ( composition(converse(X1_21),converse(X0_20)) = converse(composition(X0_20,X1_21)) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_26917,plain,
! [X0_279] : ( composition(top,converse(X0_279)) = converse(composition(X0_279,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_4599,c_20]) ).
tff(c_26989,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_4599,c_26917]) ).
tff(c_585,plain,
! [X0_60,X1_61] : ( join(composition(converse(X0_60),complement(composition(X0_60,X1_61))),complement(X1_61)) = complement(X1_61) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_618,plain,
! [X1_21,X0_20] : ( join(composition(converse(converse(X1_21)),complement(converse(composition(X0_20,X1_21)))),complement(converse(X0_20))) = complement(converse(X0_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_585]) ).
tff(c_642,plain,
! [X0_20,X1_21] : ( join(complement(converse(X0_20)),composition(X1_21,complement(converse(composition(X0_20,X1_21))))) = complement(converse(X0_20)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_618]) ).
tff(c_27643,plain,
join(complement(converse(top)),composition(top,complement(composition(top,top)))) = complement(converse(top)),
inference(superposition,[status(thm),theory(equality)],[c_26989,c_642]) ).
tff(c_27750,plain,
composition(top,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_4599,c_1440,c_152,c_4599,c_27643]) ).
tff(c_14,plain,
! [X0_14,X2_16,X1_15] : ( join(composition(X0_14,X2_16),composition(X1_15,X2_16)) = composition(join(X0_14,X1_15),X2_16) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_27794,plain,
! [X1_15] : ( join(zero,composition(X1_15,complement(composition(top,top)))) = composition(join(top,X1_15),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_27750,c_14]) ).
tff(c_27813,plain,
! [X1_15] : ( composition(X1_15,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27750,c_4426,c_1440,c_27794]) ).
tff(c_27866,plain,
! [X1_283] : ( composition(X1_283,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27750,c_4426,c_1440,c_27794]) ).
tff(c_10,plain,
! [X0_10,X1_11,X2_12] : ( composition(composition(X0_10,X1_11),X2_12) = composition(X0_10,composition(X1_11,X2_12)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_27944,plain,
! [X0_10,X1_11] : ( composition(X0_10,composition(X1_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_27866,c_10]) ).
tff(c_27975,plain,
! [X0_10] : ( composition(X0_10,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27813,c_27944]) ).
tff(c_36,plain,
meet('#skF_1',composition(converse('#skF_2'),'#skF_3')) = zero,
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_30,plain,
! [X0_29,X1_30,X2_31] : ( join(meet(composition(X0_29,X1_30),X2_31),meet(composition(X0_29,meet(X1_30,composition(converse(X0_29),X2_31))),X2_31)) = meet(composition(X0_29,meet(X1_30,composition(converse(X0_29),X2_31))),X2_31) ),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_1200,plain,
! [X0_74,X1_75,X2_76] : ( join(meet(composition(X0_74,X1_75),X2_76),meet(X2_76,composition(X0_74,meet(X1_75,composition(converse(X0_74),X2_76))))) = meet(X2_76,composition(X0_74,meet(X1_75,composition(converse(X0_74),X2_76)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_673,c_673,c_30]) ).
tff(c_1252,plain,
meet('#skF_3',composition('#skF_2',meet('#skF_1',composition(converse('#skF_2'),'#skF_3')))) = join(meet(composition('#skF_2','#skF_1'),'#skF_3'),meet('#skF_3',composition('#skF_2',zero))),
inference(superposition,[status(thm),theory(equality)],[c_36,c_1200]) ).
tff(c_1275,plain,
join(meet('#skF_3',composition('#skF_2','#skF_1')),meet('#skF_3',composition('#skF_2',zero))) = meet('#skF_3',composition('#skF_2',zero)),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_673,c_36,c_2,c_1252]) ).
tff(c_27986,plain,
join(meet('#skF_3',composition('#skF_2','#skF_1')),meet('#skF_3',zero)) = meet('#skF_3',zero),
inference(demodulation,[status(thm),theory(equality)],[c_27975,c_27975,c_1275]) ).
tff(c_27992,plain,
meet('#skF_3',composition('#skF_2','#skF_1')) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_5122,c_1440,c_2,c_5122,c_27986]) ).
tff(c_27994,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_776,c_27992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL011+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n009.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 : 300
% 0.13/0.35 % DateTime : Thu Aug 3 15:27:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 13.00/4.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.00/4.79
% 13.00/4.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.18/4.83
% 13.18/4.83 Inference rules
% 13.18/4.83 ----------------------
% 13.18/4.83 #Ref : 0
% 13.18/4.83 #Sup : 7006
% 13.18/4.83 #Fact : 0
% 13.18/4.83 #Define : 0
% 13.18/4.83 #Split : 0
% 13.18/4.83 #Chain : 0
% 13.18/4.83 #Close : 0
% 13.18/4.83
% 13.18/4.83 Ordering : KBO
% 13.18/4.83
% 13.18/4.83 Simplification rules
% 13.18/4.83 ----------------------
% 13.18/4.83 #Subsume : 126
% 13.18/4.83 #Demod : 9226
% 13.18/4.83 #Tautology : 4426
% 13.18/4.83 #SimpNegUnit : 1
% 13.18/4.83 #BackRed : 46
% 13.18/4.83
% 13.18/4.83 #Partial instantiations: 0
% 13.18/4.83 #Strategies tried : 1
% 13.18/4.83
% 13.18/4.83 Timing (in seconds)
% 13.18/4.83 ----------------------
% 13.18/4.83 Preprocessing : 0.49
% 13.18/4.83 Parsing : 0.26
% 13.18/4.83 CNF conversion : 0.03
% 13.18/4.83 Main loop : 3.27
% 13.18/4.83 Inferencing : 0.72
% 13.18/4.83 Reduction : 1.83
% 13.18/4.83 Demodulation : 1.64
% 13.18/4.83 BG Simplification : 0.08
% 13.18/4.83 Subsumption : 0.46
% 13.18/4.83 Abstraction : 0.11
% 13.18/4.83 MUC search : 0.00
% 13.18/4.83 Cooper : 0.00
% 13.18/4.83 Total : 3.83
% 13.18/4.83 Index Insertion : 0.00
% 13.18/4.83 Index Deletion : 0.00
% 13.18/4.83 Index Matching : 0.00
% 13.18/4.83 BG Taut test : 0.00
%------------------------------------------------------------------------------