TSTP Solution File: REL002+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL002+1 : 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 : n014.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 10:54:23 EDT 2023
% Result : Theorem 5.47s 2.36s
% Output : CNFRefutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of formulae : 90 ( 81 unt; 9 typ; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 84 (; 84 !; 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_53,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_80,axiom,
! [X0] : ( zero = meet(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
tff(f_78,axiom,
! [X0] : ( top = join(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
tff(f_59,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_57,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_55,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_85,negated_conjecture,
~ ! [X0] : ( join(X0,top) = top ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_2,plain,
! [X1_2,X0_1] : ( join(X1_2,X0_1) = join(X0_1,X1_2) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_26,plain,
! [X0_25] : ( meet(X0_25,complement(X0_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_24,plain,
! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_145,plain,
! [X0_36,X1_37] : ( complement(join(complement(X0_36),complement(X1_37))) = meet(X0_36,X1_37) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_179,plain,
! [X0_36] : ( meet(X0_36,complement(X0_36)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_145]) ).
tff(c_182,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_179]) ).
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_59]) ).
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_57]) ).
tff(c_560,plain,
! [X0_53,X1_54] : ( join(meet(X0_53,X1_54),complement(join(complement(X0_53),X1_54))) = X0_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_614,plain,
! [X0_53] : ( join(meet(X0_53,complement(complement(X0_53))),complement(top)) = X0_53 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_560]) ).
tff(c_625,plain,
! [X0_53] : ( join(zero,meet(X0_53,complement(complement(X0_53)))) = X0_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_182,c_614]) ).
tff(c_225,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_182,c_24]) ).
tff(c_317,plain,
! [X0_44,X1_45,X2_46] : ( join(join(X0_44,X1_45),X2_46) = join(X0_44,join(X1_45,X2_46)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_525,plain,
! [X2_52] : ( join(top,join(zero,X2_52)) = join(top,X2_52) ),
inference(superposition,[status(thm),theory(equality)],[c_225,c_317]) ).
tff(c_546,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_525]) ).
tff(c_222,plain,
! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_8]) ).
tff(c_390,plain,
! [X0_47] : ( complement(join(zero,complement(X0_47))) = meet(X0_47,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_222]) ).
tff(c_439,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_390]) ).
tff(c_443,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_182,c_439]) ).
tff(c_581,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_443,c_560]) ).
tff(c_623,plain,
join(zero,complement(join(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_546,c_2,c_581]) ).
tff(c_342,plain,
! [X2_46] : ( join(top,join(zero,X2_46)) = join(top,X2_46) ),
inference(superposition,[status(thm),theory(equality)],[c_225,c_317]) ).
tff(c_646,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm),theory(equality)],[c_623,c_342]) ).
tff(c_658,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_225,c_646]) ).
tff(c_231,plain,
! [X0_8] : ( complement(join(zero,complement(X0_8))) = meet(X0_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_222]) ).
tff(c_649,plain,
meet(join(top,top),top) = complement(zero),
inference(superposition,[status(thm),theory(equality)],[c_623,c_231]) ).
tff(c_29,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_738,plain,
join(complement(zero),complement(join(complement(join(top,top)),top))) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_649,c_29]) ).
tff(c_747,plain,
join(top,top) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_182,c_2,c_658,c_2,c_738]) ).
tff(c_754,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_747,c_623]) ).
tff(c_757,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_182,c_754]) ).
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_55]) ).
tff(c_1188,plain,
! [X2_67] : ( join(zero,join(zero,X2_67)) = join(zero,X2_67) ),
inference(superposition,[status(thm),theory(equality)],[c_757,c_4]) ).
tff(c_1212,plain,
! [X0_53] : ( join(zero,meet(X0_53,complement(complement(X0_53)))) = join(zero,X0_53) ),
inference(superposition,[status(thm),theory(equality)],[c_625,c_1188]) ).
tff(c_1247,plain,
! [X0_68] : ( join(zero,X0_68) = X0_68 ),
inference(demodulation,[status(thm),theory(equality)],[c_625,c_1212]) ).
tff(c_1276,plain,
complement(zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_1247,c_24]) ).
tff(c_1238,plain,
! [X0_53] : ( join(zero,X0_53) = X0_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_625,c_1212]) ).
tff(c_1332,plain,
! [X1_9] : ( complement(join(top,complement(X1_9))) = meet(zero,X1_9) ),
inference(superposition,[status(thm),theory(equality)],[c_1276,c_8]) ).
tff(c_761,plain,
! [X2_5] : ( join(top,join(top,X2_5)) = join(top,X2_5) ),
inference(superposition,[status(thm),theory(equality)],[c_747,c_4]) ).
tff(c_891,plain,
! [X1_60,X0_61] : ( complement(join(complement(X1_60),complement(X0_61))) = meet(X0_61,X1_60) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_145]) ).
tff(c_927,plain,
! [X1_60,X0_61] : ( meet(X1_60,X0_61) = meet(X0_61,X1_60) ),
inference(superposition,[status(thm),theory(equality)],[c_891,c_8]) ).
tff(c_362,plain,
! [X0_24,X2_46] : ( join(X0_24,join(complement(X0_24),X2_46)) = join(top,X2_46) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_317]) ).
tff(c_219,plain,
! [X1_9] : ( complement(join(zero,complement(X1_9))) = meet(top,X1_9) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_8]) ).
tff(c_1246,plain,
! [X1_9] : ( complement(complement(X1_9)) = meet(top,X1_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_1238,c_219]) ).
tff(c_1260,plain,
! [X0_53] : ( meet(X0_53,complement(complement(X0_53))) = X0_53 ),
inference(superposition,[status(thm),theory(equality)],[c_1247,c_625]) ).
tff(c_1883,plain,
! [X0_53] : ( meet(X0_53,meet(top,X0_53)) = X0_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_1246,c_1260]) ).
tff(c_1688,plain,
! [X1_75] : ( complement(complement(X1_75)) = meet(top,X1_75) ),
inference(demodulation,[status(thm),theory(equality)],[c_1238,c_219]) ).
tff(c_979,plain,
! [X1_60] : ( meet(complement(X1_60),X1_60) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_891]) ).
tff(c_987,plain,
! [X1_60] : ( meet(complement(X1_60),X1_60) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_979]) ).
tff(c_2127,plain,
! [X1_82] : ( meet(meet(top,X1_82),complement(X1_82)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_1688,c_987]) ).
tff(c_2138,plain,
! [X1_82] : ( join(zero,complement(join(complement(meet(top,X1_82)),complement(X1_82)))) = meet(top,X1_82) ),
inference(superposition,[status(thm),theory(equality)],[c_2127,c_29]) ).
tff(c_2195,plain,
! [X1_82] : ( meet(top,X1_82) = X1_82 ),
inference(demodulation,[status(thm),theory(equality)],[c_1883,c_1238,c_8,c_2,c_2138]) ).
tff(c_2210,plain,
! [X1_9] : ( complement(complement(X1_9)) = X1_9 ),
inference(demodulation,[status(thm),theory(equality)],[c_2195,c_1246]) ).
tff(c_1245,plain,
! [X0_8] : ( complement(complement(X0_8)) = meet(X0_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_1238,c_231]) ).
tff(c_2282,plain,
! [X0_8] : ( meet(X0_8,top) = X0_8 ),
inference(demodulation,[status(thm),theory(equality)],[c_2210,c_1245]) ).
tff(c_2713,plain,
! [X0_91,X1_92] : ( join(meet(X0_91,complement(X1_92)),meet(X0_91,X1_92)) = X0_91 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_560]) ).
tff(c_2760,plain,
! [X0_91] : ( join(meet(X0_91,top),meet(X0_91,zero)) = X0_91 ),
inference(superposition,[status(thm),theory(equality)],[c_1276,c_2713]) ).
tff(c_2817,plain,
! [X0_93] : ( join(X0_93,meet(X0_93,zero)) = X0_93 ),
inference(demodulation,[status(thm),theory(equality)],[c_2282,c_2760]) ).
tff(c_366,plain,
! [X0_44,X1_45] : ( join(X0_44,join(X1_45,complement(join(X0_44,X1_45)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_317]) ).
tff(c_2827,plain,
! [X0_93] : ( join(X0_93,join(meet(X0_93,zero),complement(X0_93))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_2817,c_366]) ).
tff(c_2892,plain,
! [X0_94] : ( join(top,meet(X0_94,zero)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_362,c_2,c_2827]) ).
tff(c_2925,plain,
! [X0_61] : ( join(top,meet(zero,X0_61)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_927,c_2892]) ).
tff(c_3721,plain,
! [X1_106] : ( complement(join(top,complement(X1_106))) = meet(zero,X1_106) ),
inference(superposition,[status(thm),theory(equality)],[c_1276,c_8]) ).
tff(c_3724,plain,
! [X1_106] : ( meet(zero,join(top,complement(X1_106))) = complement(join(top,meet(zero,X1_106))) ),
inference(superposition,[status(thm),theory(equality)],[c_3721,c_1332]) ).
tff(c_3803,plain,
! [X1_107] : ( meet(zero,join(top,complement(X1_107))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_2925,c_3724]) ).
tff(c_3821,plain,
! [X1_107] : ( join(zero,complement(join(complement(zero),join(top,complement(X1_107))))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_3803,c_29]) ).
tff(c_3861,plain,
! [X1_108] : ( meet(zero,X1_108) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_1332,c_1238,c_761,c_1276,c_3821]) ).
tff(c_3901,plain,
! [X1_108] : ( join(zero,complement(join(complement(zero),X1_108))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_3861,c_29]) ).
tff(c_4022,plain,
! [X1_110] : ( complement(join(top,X1_110)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_1238,c_1276,c_3901]) ).
tff(c_4033,plain,
! [X1_110] : ( join(top,X1_110) = complement(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_4022,c_2210]) ).
tff(c_4123,plain,
! [X1_111] : ( join(top,X1_111) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_1276,c_4033]) ).
tff(c_4153,plain,
! [X1_111] : ( join(X1_111,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_4123,c_2]) ).
tff(c_28,plain,
join('#skF_1',top) != top,
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_4193,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4153,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL002+1 : 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
% 0.14/0.34 % Computer : n014.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 15:27:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.47/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/2.37
% 5.67/2.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.67/2.41
% 5.67/2.41 Inference rules
% 5.67/2.41 ----------------------
% 5.67/2.41 #Ref : 0
% 5.67/2.41 #Sup : 1050
% 5.67/2.41 #Fact : 0
% 5.67/2.41 #Define : 0
% 5.67/2.41 #Split : 0
% 5.67/2.41 #Chain : 0
% 5.67/2.41 #Close : 0
% 5.67/2.41
% 5.67/2.41 Ordering : KBO
% 5.67/2.41
% 5.67/2.41 Simplification rules
% 5.67/2.41 ----------------------
% 5.67/2.41 #Subsume : 16
% 5.67/2.41 #Demod : 933
% 5.67/2.41 #Tautology : 682
% 5.67/2.41 #SimpNegUnit : 0
% 5.67/2.41 #BackRed : 35
% 5.67/2.41
% 5.67/2.41 #Partial instantiations: 0
% 5.67/2.41 #Strategies tried : 1
% 5.67/2.41
% 5.67/2.41 Timing (in seconds)
% 5.67/2.41 ----------------------
% 5.67/2.41 Preprocessing : 0.46
% 5.67/2.41 Parsing : 0.25
% 5.67/2.41 CNF conversion : 0.03
% 5.67/2.41 Main loop : 0.89
% 5.67/2.41 Inferencing : 0.28
% 5.67/2.41 Reduction : 0.38
% 5.67/2.41 Demodulation : 0.32
% 5.67/2.41 BG Simplification : 0.04
% 5.67/2.41 Subsumption : 0.14
% 5.67/2.41 Abstraction : 0.04
% 5.67/2.41 MUC search : 0.00
% 5.67/2.41 Cooper : 0.00
% 5.67/2.41 Total : 1.42
% 5.67/2.41 Index Insertion : 0.00
% 5.67/2.41 Index Deletion : 0.00
% 5.67/2.41 Index Matching : 0.00
% 5.67/2.41 BG Taut test : 0.00
%------------------------------------------------------------------------------