%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET976+1 : TPTP v9.0.0. 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 : 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 : Wed Apr 9 08:39:42 PM UTC 2025
% Result : Theorem 4.62s 2.74s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 30 ~; 20 |; 2 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_63,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
tff(f_51,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(c_34,plain,
( ( '#skF_6' = '#skF_8' )
| ( '#skF_10' != '#skF_12' )
| ~ in('#skF_9','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_89,plain,
~ in('#skF_9','#skF_11'),
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_40,plain,
( ( '#skF_6' = '#skF_8' )
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_212,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_26,plain,
! [A_14,C_16,B_15,D_17] :
( in(A_14,C_16)
| ~ in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_215,plain,
in('#skF_9','#skF_11'),
inference(resolution,[status(thm)],[c_212,c_26]) ).
tff(c_221,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_89,c_215]) ).
tff(c_223,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_42,plain,
( in('#skF_5','#skF_7')
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_284,plain,
in('#skF_5','#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_223,c_42]) ).
tff(c_8,plain,
! [C_9] : in(C_9,singleton(C_9)),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_22,plain,
! [A_14,B_15,C_16,D_17] :
( in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17))
| ~ in(B_15,D_17)
| ~ in(A_14,C_16) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_222,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_38,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2('#skF_7',singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_439,plain,
( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2('#skF_7',singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_222,c_38]) ).
tff(c_440,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2('#skF_7',singleton('#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_223,c_439]) ).
tff(c_443,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5','#skF_7') ),
inference(resolution,[status(thm)],[c_22,c_440]) ).
tff(c_447,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_284,c_8,c_443]) ).
tff(c_449,plain,
in('#skF_9','#skF_11'),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_448,plain,
( ( '#skF_10' != '#skF_12' )
| ( '#skF_6' = '#skF_8' ) ),
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_453,plain,
'#skF_10' != '#skF_12',
inference(splitLeft,[status(thm)],[c_448]) ).
tff(c_578,plain,
in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_640,plain,
! [B_82,D_83,A_84,C_85] :
( in(B_82,D_83)
| ~ in(ordered_pair(A_84,B_82),cartesian_product2(C_85,D_83)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_644,plain,
in('#skF_10',singleton('#skF_12')),
inference(resolution,[status(thm)],[c_578,c_640]) ).
tff(c_6,plain,
! [C_9,A_5] :
( ( C_9 = A_5 )
| ~ in(C_9,singleton(A_5)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_649,plain,
'#skF_10' = '#skF_12',
inference(resolution,[status(thm)],[c_644,c_6]) ).
tff(c_654,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_453,c_649]) ).
tff(c_656,plain,
~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_661,plain,
in('#skF_5','#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_656,c_42]) ).
tff(c_655,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_766,plain,
( ~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2('#skF_7',singleton('#skF_8')))
| in(ordered_pair('#skF_9','#skF_10'),cartesian_product2('#skF_11',singleton('#skF_12'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_655,c_38]) ).
tff(c_767,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2('#skF_7',singleton('#skF_8'))),
inference(negUnitSimplification,[status(thm)],[c_656,c_766]) ).
tff(c_770,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5','#skF_7') ),
inference(resolution,[status(thm)],[c_22,c_767]) ).
tff(c_774,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_661,c_8,c_770]) ).
tff(c_776,plain,
'#skF_10' = '#skF_12',
inference(splitRight,[status(thm)],[c_448]) ).
tff(c_36,plain,
( in('#skF_5','#skF_7')
| ( '#skF_10' != '#skF_12' )
| ~ in('#skF_9','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_786,plain,
in('#skF_5','#skF_7'),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_776,c_36]) ).
tff(c_775,plain,
'#skF_6' = '#skF_8',
inference(splitRight,[status(thm)],[c_448]) ).
tff(c_32,plain,
( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2('#skF_7',singleton('#skF_8')))
| ( '#skF_10' != '#skF_12' )
| ~ in('#skF_9','#skF_11') ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_996,plain,
~ in(ordered_pair('#skF_5','#skF_8'),cartesian_product2('#skF_7',singleton('#skF_8'))),
inference(demodulation,[status(thm),theory(equality)],[c_449,c_776,c_775,c_32]) ).
tff(c_999,plain,
( ~ in('#skF_8',singleton('#skF_8'))
| ~ in('#skF_5','#skF_7') ),
inference(resolution,[status(thm)],[c_22,c_996]) ).
tff(c_1003,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_786,c_8,c_999]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : SET976+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.11 % 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
% 0.09/0.31 % Computer : n009.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue Apr 8 21:53:11 EDT 2025
% 0.09/0.31 % CPUTime :
% 4.62/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.05/2.75
% 5.05/2.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------