%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET018+4 : TPTP v9.0.0. Released v2.2.0.
% 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 : n022.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 : Wed Apr 9 08:37:31 PM UTC 2025
% Result : Theorem 5.83s 2.52s
% Output : CNFRefutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 18 ~; 21 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_119,negated_conjecture,
~ ! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> ( B = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50b) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_98,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_92,axiom,
! [X,A] :
( member(X,singleton(A))
<=> ( X = A ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
tff(c_60,plain,
'#skF_7' != '#skF_5',
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_62,plain,
equal_set(unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5')),unordered_pair(singleton('#skF_6'),unordered_pair('#skF_6','#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_10,plain,
! [B_7,A_6] :
( subset(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_46,plain,
! [X_22,B_24] : member(X_22,unordered_pair(X_22,B_24)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_146,plain,
! [X_75,B_76,A_77] :
( member(X_75,B_76)
| ~ member(X_75,A_77)
| ~ subset(A_77,B_76) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_188,plain,
! [X_86,B_87,B_88] :
( member(X_86,B_87)
| ~ subset(unordered_pair(X_86,B_88),B_87) ),
inference(resolution,[status(thm)],[c_46,c_146]) ).
tff(c_230,plain,
! [X_95,A_96,B_97] :
( member(X_95,A_96)
| ~ equal_set(A_96,unordered_pair(X_95,B_97)) ),
inference(resolution,[status(thm)],[c_10,c_188]) ).
tff(c_234,plain,
member(singleton('#skF_6'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_62,c_230]) ).
tff(c_514,plain,
! [X_123,B_124,A_125] :
( ( X_123 = B_124 )
| ( X_123 = A_125 )
| ~ member(X_123,unordered_pair(A_125,B_124)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_539,plain,
( ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_6') )
| ( singleton('#skF_6') = singleton('#skF_4') ) ),
inference(resolution,[status(thm)],[c_234,c_514]) ).
tff(c_741,plain,
singleton('#skF_6') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_539]) ).
tff(c_40,plain,
! [X_20] : member(X_20,singleton(X_20)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_763,plain,
member('#skF_6',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_741,c_40]) ).
tff(c_38,plain,
! [X_20,A_21] :
( ( X_20 = A_21 )
| ~ member(X_20,singleton(A_21)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_776,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_763,c_38]) ).
tff(c_12,plain,
! [A_6,B_7] :
( subset(A_6,B_7)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_44,plain,
! [X_22,A_23] : member(X_22,unordered_pair(A_23,X_22)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_205,plain,
! [X_89,B_90,A_91] :
( member(X_89,B_90)
| ~ subset(unordered_pair(A_91,X_89),B_90) ),
inference(resolution,[status(thm)],[c_44,c_146]) ).
tff(c_240,plain,
! [X_101,B_102,A_103] :
( member(X_101,B_102)
| ~ equal_set(unordered_pair(A_103,X_101),B_102) ),
inference(resolution,[status(thm)],[c_12,c_205]) ).
tff(c_244,plain,
member(unordered_pair('#skF_4','#skF_5'),unordered_pair(singleton('#skF_6'),unordered_pair('#skF_6','#skF_7'))),
inference(resolution,[status(thm)],[c_62,c_240]) ).
tff(c_42,plain,
! [X_22,B_24,A_23] :
( ( X_22 = B_24 )
| ( X_22 = A_23 )
| ~ member(X_22,unordered_pair(A_23,B_24)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_556,plain,
( ( unordered_pair('#skF_6','#skF_7') = unordered_pair('#skF_4','#skF_5') )
| ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_6') ) ),
inference(resolution,[status(thm)],[c_244,c_42]) ).
tff(c_1739,plain,
( ( unordered_pair('#skF_4','#skF_7') = unordered_pair('#skF_4','#skF_5') )
| ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_4') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_776,c_776,c_556]) ).
tff(c_1740,plain,
unordered_pair('#skF_4','#skF_5') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_1739]) ).
tff(c_1769,plain,
member('#skF_5',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_1740,c_44]) ).
tff(c_1789,plain,
'#skF_5' = '#skF_4',
inference(resolution,[status(thm)],[c_1769,c_38]) ).
tff(c_1792,plain,
'#skF_7' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_1789,c_60]) ).
tff(c_1791,plain,
unordered_pair('#skF_4','#skF_4') = singleton('#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_1789,c_1740]) ).
tff(c_235,plain,
! [X_98,A_99,A_100] :
( member(X_98,A_99)
| ~ equal_set(A_99,unordered_pair(A_100,X_98)) ),
inference(resolution,[status(thm)],[c_10,c_205]) ).
tff(c_239,plain,
member(unordered_pair('#skF_6','#skF_7'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_62,c_235]) ).
tff(c_538,plain,
( ( unordered_pair('#skF_6','#skF_7') = unordered_pair('#skF_4','#skF_5') )
| ( unordered_pair('#skF_6','#skF_7') = singleton('#skF_4') ) ),
inference(resolution,[status(thm)],[c_239,c_514]) ).
tff(c_1931,plain,
( ( unordered_pair('#skF_4','#skF_7') = singleton('#skF_4') )
| ( unordered_pair('#skF_4','#skF_7') = singleton('#skF_4') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_776,c_1791,c_1789,c_776,c_538]) ).
tff(c_1932,plain,
unordered_pair('#skF_4','#skF_7') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_1931]) ).
tff(c_1960,plain,
member('#skF_7',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_1932,c_44]) ).
tff(c_1976,plain,
'#skF_7' = '#skF_4',
inference(resolution,[status(thm)],[c_1960,c_38]) ).
tff(c_1983,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1792,c_1976]) ).
tff(c_1985,plain,
unordered_pair('#skF_4','#skF_7') != singleton('#skF_4'),
inference(splitRight,[status(thm)],[c_1931]) ).
tff(c_1984,plain,
unordered_pair('#skF_4','#skF_7') = singleton('#skF_4'),
inference(splitRight,[status(thm)],[c_1931]) ).
tff(c_1986,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1985,c_1984]) ).
tff(c_1987,plain,
unordered_pair('#skF_4','#skF_7') = unordered_pair('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_1739]) ).
tff(c_2065,plain,
member('#skF_7',unordered_pair('#skF_4','#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_1987,c_44]) ).
tff(c_2079,plain,
( ( '#skF_7' = '#skF_5' )
| ( '#skF_7' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_2065,c_42]) ).
tff(c_2086,plain,
'#skF_7' = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_60,c_2079]) ).
tff(c_2090,plain,
'#skF_5' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_2086,c_60]) ).
tff(c_2089,plain,
unordered_pair('#skF_4','#skF_5') = unordered_pair('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_2086,c_1987]) ).
tff(c_2124,plain,
member('#skF_5',unordered_pair('#skF_4','#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_2089,c_44]) ).
tff(c_2138,plain,
'#skF_5' = '#skF_4',
inference(resolution,[status(thm)],[c_2124,c_42]) ).
tff(c_2146,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2090,c_2090,c_2138]) ).
tff(c_2147,plain,
unordered_pair('#skF_4','#skF_5') = singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_539]) ).
tff(c_2250,plain,
member('#skF_4',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_2147,c_46]) ).
tff(c_2306,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_2250,c_38]) ).
tff(c_2148,plain,
singleton('#skF_6') != singleton('#skF_4'),
inference(splitRight,[status(thm)],[c_539]) ).
tff(c_2315,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2306,c_2148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET018+4 : TPTP v9.0.0. Released v2.2.0.
% 0.09/0.12 % 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
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 19:43:06 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.83/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.83/2.53
% 5.83/2.53 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------