TSTP Solution File: SET930+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n021.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 10:57:22 EDT 2023
% Result : Theorem 3.59s 1.91s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 41 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 54 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 15 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 31 (; 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_difference > #nlpp > singleton > empty_set > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_65,axiom,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set )
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
tff(f_36,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_79,negated_conjecture,
~ ! [A,B,C] :
~ ( ( set_difference(unordered_pair(A,B),C) != empty_set )
& ( set_difference(unordered_pair(A,B),C) != singleton(A) )
& ( set_difference(unordered_pair(A,B),C) != singleton(B) )
& ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
tff(f_46,axiom,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A) )
<=> ( ~ in(A,C)
& ( in(B,C)
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
tff(f_59,axiom,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
<=> ( ~ in(A,C)
& ~ in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
tff(c_170,plain,
! [A_45,B_46,C_47] :
( ( set_difference(unordered_pair(A_45,B_46),C_47) = empty_set )
| ~ in(B_46,C_47)
| ~ in(A_45,C_47) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_4,plain,
! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_38,plain,
set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != empty_set,
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_39,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_38]) ).
tff(c_224,plain,
( ~ in('#skF_3','#skF_5')
| ~ in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_170,c_39]) ).
tff(c_227,plain,
~ in('#skF_4','#skF_5'),
inference(splitLeft,[status(thm)],[c_224]) ).
tff(c_269,plain,
! [B_57,C_58,A_59] :
( ~ in(B_57,C_58)
| ( set_difference(unordered_pair(A_59,B_57),C_58) = singleton(A_59) )
| in(A_59,C_58) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_34,plain,
set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != singleton('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_41,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_34]) ).
tff(c_312,plain,
( ~ in('#skF_3','#skF_5')
| in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_269,c_41]) ).
tff(c_342,plain,
~ in('#skF_3','#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_227,c_312]) ).
tff(c_348,plain,
! [A_60,B_61,C_62] :
( ( set_difference(unordered_pair(A_60,B_61),C_62) = unordered_pair(A_60,B_61) )
| in(B_61,C_62)
| in(A_60,C_62) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_32,plain,
set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != unordered_pair('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_42,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != unordered_pair('#skF_4','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_32]) ).
tff(c_391,plain,
( in('#skF_3','#skF_5')
| in('#skF_4','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_348,c_42]) ).
tff(c_425,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_227,c_342,c_391]) ).
tff(c_426,plain,
~ in('#skF_3','#skF_5'),
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_427,plain,
in('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_474,plain,
! [B_72,C_73,A_74] :
( ~ in(B_72,C_73)
| ( set_difference(unordered_pair(A_74,B_72),C_73) = singleton(A_74) )
| in(A_74,C_73) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_570,plain,
! [A_78,C_79,B_80] :
( ~ in(A_78,C_79)
| ( set_difference(unordered_pair(A_78,B_80),C_79) = singleton(B_80) )
| in(B_80,C_79) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_474]) ).
tff(c_36,plain,
set_difference(unordered_pair('#skF_3','#skF_4'),'#skF_5') != singleton('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_40,plain,
set_difference(unordered_pair('#skF_4','#skF_3'),'#skF_5') != singleton('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_36]) ).
tff(c_622,plain,
( ~ in('#skF_4','#skF_5')
| in('#skF_3','#skF_5') ),
inference(superposition,[status(thm),theory(equality)],[c_570,c_40]) ).
tff(c_657,plain,
in('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_622]) ).
tff(c_659,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 3 16:13:51 EDT 2023
% 0.17/0.35 % CPUTime :
% 3.59/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.59/1.92
% 3.59/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/1.95
% 3.71/1.95 Inference rules
% 3.71/1.95 ----------------------
% 3.71/1.95 #Ref : 0
% 3.71/1.95 #Sup : 165
% 3.71/1.95 #Fact : 2
% 3.71/1.95 #Define : 0
% 3.71/1.95 #Split : 2
% 3.71/1.95 #Chain : 0
% 3.71/1.95 #Close : 0
% 3.71/1.95
% 3.71/1.95 Ordering : KBO
% 3.71/1.95
% 3.71/1.95 Simplification rules
% 3.71/1.95 ----------------------
% 3.71/1.95 #Subsume : 52
% 3.71/1.95 #Demod : 13
% 3.71/1.95 #Tautology : 64
% 3.71/1.95 #SimpNegUnit : 15
% 3.71/1.95 #BackRed : 0
% 3.71/1.95
% 3.71/1.95 #Partial instantiations: 0
% 3.71/1.95 #Strategies tried : 1
% 3.71/1.95
% 3.71/1.95 Timing (in seconds)
% 3.71/1.95 ----------------------
% 3.71/1.95 Preprocessing : 0.48
% 3.71/1.95 Parsing : 0.26
% 3.71/1.95 CNF conversion : 0.03
% 3.71/1.95 Main loop : 0.43
% 3.71/1.95 Inferencing : 0.15
% 3.71/1.95 Reduction : 0.13
% 3.71/1.95 Demodulation : 0.09
% 3.71/1.95 BG Simplification : 0.02
% 3.71/1.95 Subsumption : 0.09
% 3.71/1.95 Abstraction : 0.02
% 3.71/1.95 MUC search : 0.00
% 3.71/1.95 Cooper : 0.00
% 3.71/1.95 Total : 0.96
% 3.71/1.95 Index Insertion : 0.00
% 3.71/1.95 Index Deletion : 0.00
% 3.71/1.95 Index Matching : 0.00
% 3.71/1.95 BG Taut test : 0.00
%------------------------------------------------------------------------------