TSTP Solution File: REL042+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL042+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 10:54:37 EDT 2023
% Result : Theorem 53.71s 40.56s
% Output : CNFRefutation 53.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 24
% Syntax : Number of formulae : 121 ( 111 unt; 9 typ; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 166 (; 166 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #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_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(meet,type,
meet: ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(f_56,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_124,negated_conjecture,
~ ! [X0] :
( ! [X1] : ( meet(composition(X0,X1),composition(X0,complement(X1))) = zero )
=> ( join(composition(converse(X0),X0),one) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_83,axiom,
! [X0] : ( zero = meet(X0,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
tff(f_81,axiom,
! [X0] : ( top = join(X0,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
tff(f_62,axiom,
! [X0,X1] : ( meet(X0,X1) = complement(join(complement(X0),complement(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
tff(f_60,axiom,
! [X0,X1] : ( X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
tff(f_72,axiom,
! [X0] : ( converse(converse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
tff(f_67,axiom,
! [X0] : ( composition(X0,one) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
tff(f_76,axiom,
! [X0,X1] : ( converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
tff(f_78,axiom,
! [X0,X1] : ( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
tff(f_58,axiom,
! [X0,X1,X2] : ( join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
tff(f_74,axiom,
! [X0,X1] : ( converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
tff(f_69,axiom,
! [X0,X1,X2] : ( composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
tff(f_65,axiom,
! [X0,X1,X2] : ( composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
tff(f_111,axiom,
! [X0,X1,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))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
tff(c_2,plain,
! [X1_2,X0_1] : ( join(X1_2,X0_1) = join(X0_1,X1_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_34,plain,
join(composition(converse('#skF_1'),'#skF_1'),one) != one,
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_38,plain,
join(one,composition(converse('#skF_1'),'#skF_1')) != one,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_34]) ).
tff(c_26,plain,
! [X0_25] : ( meet(X0_25,complement(X0_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_24,plain,
! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_112,plain,
! [X0_43,X1_44] : ( complement(join(complement(X0_43),complement(X1_44))) = meet(X0_43,X1_44) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_146,plain,
! [X0_43] : ( meet(X0_43,complement(X0_43)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_112]) ).
tff(c_149,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_146]) ).
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_62]) ).
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_60]) ).
tff(c_1024,plain,
! [X0_74,X1_75] : ( join(meet(X0_74,X1_75),complement(join(complement(X0_74),X1_75))) = X0_74 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_1102,plain,
! [X0_74] : ( join(meet(X0_74,complement(complement(X0_74))),complement(top)) = X0_74 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1024]) ).
tff(c_1115,plain,
! [X0_74] : ( join(zero,meet(X0_74,complement(complement(X0_74)))) = X0_74 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149,c_1102]) ).
tff(c_399,plain,
! [X1_53,X0_54] : ( complement(join(complement(X1_53),complement(X0_54))) = meet(X0_54,X1_53) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_112]) ).
tff(c_426,plain,
! [X1_53,X0_54] : ( meet(X1_53,X0_54) = meet(X0_54,X1_53) ),
inference(superposition,[status(thm),theory(equality)],[c_399,c_8]) ).
tff(c_484,plain,
! [X1_53] : ( meet(complement(X1_53),X1_53) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_399]) ).
tff(c_491,plain,
! [X1_53] : ( meet(complement(X1_53),X1_53) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_149,c_484]) ).
tff(c_3469,plain,
! [X0_117,X1_118] : ( join(meet(X0_117,complement(X1_118)),meet(X0_117,X1_118)) = X0_117 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1024]) ).
tff(c_3548,plain,
! [X1_118] : ( join(zero,meet(complement(complement(X1_118)),X1_118)) = complement(complement(X1_118)) ),
inference(superposition,[status(thm),theory(equality)],[c_491,c_3469]) ).
tff(c_3607,plain,
! [X1_118] : ( complement(complement(X1_118)) = X1_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_1115,c_426,c_3548]) ).
tff(c_16,plain,
! [X0_17] : ( converse(converse(X0_17)) = X0_17 ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_12,plain,
! [X0_13] : ( composition(X0_13,one) = X0_13 ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_263,plain,
! [X1_47,X0_48] : ( composition(converse(X1_47),converse(X0_48)) = converse(composition(X0_48,X1_47)) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_763,plain,
! [X0_66,X1_67] : ( converse(composition(converse(X0_66),X1_67)) = composition(converse(X1_67),X0_66) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_263]) ).
tff(c_807,plain,
! [X0_66] : ( composition(converse(one),X0_66) = converse(converse(X0_66)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_763]) ).
tff(c_821,plain,
! [X0_68] : ( composition(converse(one),X0_68) = X0_68 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_807]) ).
tff(c_842,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_821,c_12]) ).
tff(c_819,plain,
! [X0_66] : ( composition(converse(one),X0_66) = X0_66 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_807]) ).
tff(c_866,plain,
! [X0_66] : ( composition(one,X0_66) = X0_66 ),
inference(demodulation,[status(thm),theory(equality)],[c_842,c_819]) ).
tff(c_1347,plain,
! [X0_82,X1_83] : ( join(composition(converse(X0_82),complement(composition(X0_82,X1_83))),complement(X1_83)) = complement(X1_83) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1365,plain,
! [X0_66] : ( join(composition(converse(one),complement(X0_66)),complement(X0_66)) = complement(X0_66) ),
inference(superposition,[status(thm),theory(equality)],[c_866,c_1347]) ).
tff(c_1423,plain,
! [X0_84] : ( join(complement(X0_84),complement(X0_84)) = complement(X0_84) ),
inference(demodulation,[status(thm),theory(equality)],[c_866,c_2,c_842,c_1365]) ).
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_1429,plain,
! [X0_84] : ( join(meet(X0_84,complement(X0_84)),complement(complement(X0_84))) = X0_84 ),
inference(superposition,[status(thm),theory(equality)],[c_1423,c_37]) ).
tff(c_1479,plain,
! [X0_84] : ( join(zero,complement(complement(X0_84))) = X0_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1429]) ).
tff(c_3613,plain,
! [X0_84] : ( join(zero,X0_84) = X0_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_3607,c_1479]) ).
tff(c_153,plain,
! [X1_9] : ( complement(join(zero,complement(X1_9))) = meet(top,X1_9) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_8]) ).
tff(c_3885,plain,
! [X1_9] : ( complement(complement(X1_9)) = meet(top,X1_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_3613,c_153]) ).
tff(c_3887,plain,
! [X1_9] : ( meet(top,X1_9) = X1_9 ),
inference(demodulation,[status(thm),theory(equality)],[c_3607,c_3885]) ).
tff(c_3618,plain,
! [X1_119] : ( complement(complement(X1_119)) = X1_119 ),
inference(demodulation,[status(thm),theory(equality)],[c_1115,c_426,c_3548]) ).
tff(c_1413,plain,
! [X0_66] : ( join(complement(X0_66),complement(X0_66)) = complement(X0_66) ),
inference(demodulation,[status(thm),theory(equality)],[c_866,c_2,c_842,c_1365]) ).
tff(c_3678,plain,
! [X1_119] : ( join(complement(complement(X1_119)),X1_119) = complement(complement(X1_119)) ),
inference(superposition,[status(thm),theory(equality)],[c_3618,c_1413]) ).
tff(c_3748,plain,
! [X1_119] : ( join(X1_119,X1_119) = X1_119 ),
inference(demodulation,[status(thm),theory(equality)],[c_3607,c_3607,c_3678]) ).
tff(c_896,plain,
! [X0_69,X1_70,X2_71] : ( join(join(X0_69,X1_70),X2_71) = join(X0_69,join(X1_70,X2_71)) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_4249,plain,
! [X0_124,X2_125] : ( join(X0_124,join(complement(X0_124),X2_125)) = join(top,X2_125) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_896]) ).
tff(c_4286,plain,
! [X0_124] : ( join(top,complement(X0_124)) = join(X0_124,complement(X0_124)) ),
inference(superposition,[status(thm),theory(equality)],[c_3748,c_4249]) ).
tff(c_5023,plain,
! [X0_136] : ( join(top,complement(X0_136)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_4286]) ).
tff(c_5055,plain,
! [X1_137] : ( join(top,X1_137) = top ),
inference(superposition,[status(thm),theory(equality)],[c_3607,c_5023]) ).
tff(c_372,plain,
! [X0_51,X1_52] : ( join(converse(X0_51),converse(X1_52)) = converse(join(X0_51,X1_52)) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_396,plain,
! [X0_51,X0_17] : ( converse(join(X0_51,converse(X0_17))) = join(converse(X0_51),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_372]) ).
tff(c_5916,plain,
! [X0_146] : ( join(converse(top),X0_146) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_5055,c_396]) ).
tff(c_958,plain,
! [X0_69,X1_70] : ( join(X0_69,join(X1_70,complement(join(X0_69,X1_70)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_896]) ).
tff(c_5934,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_5916,c_958]) ).
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_76]) ).
tff(c_35194,plain,
! [X1_329] : ( composition(converse(X1_329),top) = converse(composition(top,X1_329)) ),
inference(superposition,[status(thm),theory(equality)],[c_5934,c_20]) ).
tff(c_35284,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_5934,c_35194]) ).
tff(c_1386,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_1347]) ).
tff(c_1418,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_1386]) ).
tff(c_35345,plain,
join(complement(converse(top)),composition(top,complement(composition(top,top)))) = complement(converse(top)),
inference(superposition,[status(thm),theory(equality)],[c_35284,c_1418]) ).
tff(c_35457,plain,
composition(top,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_149,c_5934,c_3613,c_149,c_5934,c_35345]) ).
tff(c_5075,plain,
! [X1_137] : ( join(X1_137,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_5055,c_2]) ).
tff(c_1750,plain,
! [X0_88,X2_89,X1_90] : ( join(composition(X0_88,X2_89),composition(X1_90,X2_89)) = composition(join(X0_88,X1_90),X2_89) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_1789,plain,
! [X1_90,X2_89,X0_88] : ( join(composition(X1_90,X2_89),composition(X0_88,X2_89)) = composition(join(X0_88,X1_90),X2_89) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1750]) ).
tff(c_35771,plain,
! [X0_88] : ( join(zero,composition(X0_88,complement(composition(top,top)))) = composition(join(X0_88,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_35457,c_1789]) ).
tff(c_35805,plain,
! [X0_88] : ( composition(X0_88,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_35457,c_5075,c_3613,c_35771]) ).
tff(c_35885,plain,
! [X0_333] : ( composition(X0_333,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_35457,c_5075,c_3613,c_35771]) ).
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_65]) ).
tff(c_36021,plain,
! [X0_10,X1_11] : ( composition(X0_10,composition(X1_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_35885,c_10]) ).
tff(c_36076,plain,
! [X0_10] : ( composition(X0_10,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_35805,c_36021]) ).
tff(c_171,plain,
! [X1_45] : ( meet(composition('#skF_1',X1_45),composition('#skF_1',complement(X1_45))) = zero ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_185,plain,
meet('#skF_1',composition('#skF_1',complement(one))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_12,c_171]) ).
tff(c_3050,plain,
! [X0_111,X1_112,X2_113] : ( join(meet(composition(X0_111,X1_112),X2_113),composition(meet(X0_111,composition(X2_113,converse(X1_112))),meet(X1_112,composition(converse(X0_111),X2_113)))) = composition(meet(X0_111,composition(X2_113,converse(X1_112))),meet(X1_112,composition(converse(X0_111),X2_113))) ),
inference(cnfTransformation,[status(thm)],[f_111]) ).
tff(c_3188,plain,
! [X0_17,X1_112,X2_113] : ( join(meet(composition(converse(X0_17),X1_112),X2_113),composition(meet(converse(X0_17),composition(X2_113,converse(X1_112))),meet(X1_112,composition(X0_17,X2_113)))) = composition(meet(converse(X0_17),composition(X2_113,converse(X1_112))),meet(X1_112,composition(converse(converse(X0_17)),X2_113))) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_3050]) ).
tff(c_46099,plain,
! [X0_385,X1_386,X2_387] : ( join(meet(composition(converse(X0_385),X1_386),X2_387),composition(meet(converse(X0_385),composition(X2_387,converse(X1_386))),meet(X1_386,composition(X0_385,X2_387)))) = composition(meet(converse(X0_385),composition(X2_387,converse(X1_386))),meet(X1_386,composition(X0_385,X2_387))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3188]) ).
tff(c_46534,plain,
join(meet(composition(converse('#skF_1'),'#skF_1'),complement(one)),composition(meet(converse('#skF_1'),composition(complement(one),converse('#skF_1'))),zero)) = composition(meet(converse('#skF_1'),composition(complement(one),converse('#skF_1'))),meet('#skF_1',composition('#skF_1',complement(one)))),
inference(superposition,[status(thm),theory(equality)],[c_185,c_46099]) ).
tff(c_46656,plain,
meet(complement(one),composition(converse('#skF_1'),'#skF_1')) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_36076,c_3613,c_2,c_36076,c_426,c_185,c_46534]) ).
tff(c_130,plain,
! [X0_8,X1_9,X1_44] : ( meet(join(complement(X0_8),complement(X1_9)),X1_44) = complement(join(meet(X0_8,X1_9),complement(X1_44))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_112]) ).
tff(c_1087,plain,
! [X0_8,X1_9,X1_75] : ( join(meet(join(complement(X0_8),complement(X1_9)),X1_75),complement(join(meet(X0_8,X1_9),X1_75))) = join(complement(X0_8),complement(X1_9)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1024]) ).
tff(c_39977,plain,
! [X0_8,X1_9,X1_75] : ( join(complement(join(meet(X0_8,X1_9),X1_75)),complement(join(meet(X0_8,X1_9),complement(X1_75)))) = join(complement(X0_8),complement(X1_9)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_130,c_1087]) ).
tff(c_81443,plain,
! [X1_75] : ( join(complement(join(zero,X1_75)),complement(join(meet(complement(one),composition(converse('#skF_1'),'#skF_1')),complement(X1_75)))) = join(complement(complement(one)),complement(composition(converse('#skF_1'),'#skF_1'))) ),
inference(superposition,[status(thm),theory(equality)],[c_46656,c_39977]) ).
tff(c_81552,plain,
join(one,complement(composition(converse('#skF_1'),'#skF_1'))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_3613,c_46656,c_3613,c_3607,c_81443]) ).
tff(c_152664,plain,
! [X1_669,X1_670] : ( complement(join(X1_669,complement(X1_670))) = meet(complement(X1_669),X1_670) ),
inference(superposition,[status(thm),theory(equality)],[c_3618,c_8]) ).
tff(c_153050,plain,
! [X1_669,X1_670] : ( complement(meet(complement(X1_669),X1_670)) = join(X1_669,complement(X1_670)) ),
inference(superposition,[status(thm),theory(equality)],[c_152664,c_3607]) ).
tff(c_3711,plain,
! [X0_8,X1_119] : ( complement(join(complement(X0_8),X1_119)) = meet(X0_8,complement(X1_119)) ),
inference(superposition,[status(thm),theory(equality)],[c_3618,c_8]) ).
tff(c_13004,plain,
! [X0_211,X1_212] : ( join(join(complement(X0_211),complement(X1_212)),meet(X0_211,X1_212)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_24]) ).
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_58]) ).
tff(c_78563,plain,
! [X0_490,X1_491] : ( join(complement(X0_490),join(complement(X1_491),meet(X0_490,X1_491))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_13004,c_4]) ).
tff(c_78751,plain,
! [X0_490,X1_491] : ( join(meet(X0_490,join(complement(X1_491),meet(X0_490,X1_491))),complement(top)) = X0_490 ),
inference(superposition,[status(thm),theory(equality)],[c_78563,c_37]) ).
tff(c_203480,plain,
! [X0_784,X1_785] : ( meet(X0_784,join(complement(X1_785),meet(X0_784,X1_785))) = X0_784 ),
inference(demodulation,[status(thm),theory(equality)],[c_3613,c_2,c_149,c_78751]) ).
tff(c_139,plain,
! [X1_44,X0_43] : ( complement(join(complement(X1_44),complement(X0_43))) = meet(X0_43,X1_44) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_112]) ).
tff(c_160217,plain,
! [X1_688,X0_689] : ( join(complement(X1_688),complement(X0_689)) = complement(meet(X0_689,X1_688)) ),
inference(superposition,[status(thm),theory(equality)],[c_139,c_3618]) ).
tff(c_160658,plain,
! [X1_118,X1_688] : ( complement(meet(complement(X1_118),X1_688)) = join(complement(X1_688),X1_118) ),
inference(superposition,[status(thm),theory(equality)],[c_3607,c_160217]) ).
tff(c_203569,plain,
! [X1_785,X1_118] : ( join(complement(join(complement(X1_785),meet(complement(X1_118),X1_785))),X1_118) = complement(complement(X1_118)) ),
inference(superposition,[status(thm),theory(equality)],[c_203480,c_160658]) ).
tff(c_213266,plain,
! [X1_804,X1_805] : ( join(X1_804,meet(X1_805,join(X1_804,complement(X1_805)))) = X1_804 ),
inference(demodulation,[status(thm),theory(equality)],[c_153050,c_2,c_3711,c_3607,c_203569]) ).
tff(c_213787,plain,
join(one,meet(composition(converse('#skF_1'),'#skF_1'),top)) = one,
inference(superposition,[status(thm),theory(equality)],[c_81552,c_213266]) ).
tff(c_214080,plain,
join(one,composition(converse('#skF_1'),'#skF_1')) = one,
inference(demodulation,[status(thm),theory(equality)],[c_3887,c_426,c_213787]) ).
tff(c_214082,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_214080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL042+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 15:33:13 EDT 2023
% 0.14/0.35 % CPUTime :
% 53.71/40.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.79/40.58
% 53.79/40.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 53.91/40.62
% 53.91/40.62 Inference rules
% 53.91/40.62 ----------------------
% 53.91/40.62 #Ref : 0
% 53.91/40.62 #Sup : 53677
% 53.91/40.62 #Fact : 0
% 53.91/40.62 #Define : 0
% 53.91/40.62 #Split : 0
% 53.91/40.62 #Chain : 0
% 53.91/40.62 #Close : 0
% 53.91/40.62
% 53.91/40.62 Ordering : KBO
% 53.91/40.62
% 53.91/40.62 Simplification rules
% 53.91/40.62 ----------------------
% 53.91/40.62 #Subsume : 709
% 53.91/40.62 #Demod : 107023
% 53.91/40.62 #Tautology : 30798
% 53.91/40.62 #SimpNegUnit : 1
% 53.91/40.62 #BackRed : 143
% 53.91/40.62
% 53.91/40.62 #Partial instantiations: 0
% 53.91/40.62 #Strategies tried : 1
% 53.91/40.62
% 53.91/40.62 Timing (in seconds)
% 53.91/40.62 ----------------------
% 53.91/40.62 Preprocessing : 0.52
% 53.91/40.62 Parsing : 0.28
% 53.91/40.62 CNF conversion : 0.03
% 53.91/40.62 Main loop : 38.94
% 53.91/40.62 Inferencing : 3.02
% 53.91/40.62 Reduction : 28.04
% 53.91/40.62 Demodulation : 26.54
% 53.91/40.62 BG Simplification : 0.36
% 53.91/40.62 Subsumption : 5.68
% 54.07/40.62 Abstraction : 0.78
% 54.07/40.62 MUC search : 0.00
% 54.07/40.62 Cooper : 0.00
% 54.07/40.62 Total : 39.53
% 54.07/40.62 Index Insertion : 0.00
% 54.07/40.62 Index Deletion : 0.00
% 54.07/40.62 Index Matching : 0.00
% 54.07/40.62 BG Taut test : 0.00
%------------------------------------------------------------------------------