%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET985+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 : n002.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 08:39:43 PM UTC 2025
% Result : Theorem 3.76s 2.41s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 11 ~; 20 |; 1 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > cartesian_product2 > #nlpp > empty_set > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $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(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_59,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
| subset(cartesian_product2(B,A),cartesian_product2(D,C)) )
=> subset(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
tff(f_48,axiom,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( cartesian_product2(A,B) = empty_set )
| ( subset(A,C)
& subset(B,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] :
( ( cartesian_product2(A,B) = empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
tff(f_27,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
tff(f_61,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
tff(c_24,plain,
~ empty('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_22,plain,
( subset(cartesian_product2('#skF_4','#skF_3'),cartesian_product2('#skF_6','#skF_5'))
| subset(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_6')) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_51,plain,
subset(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_6')),
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_63,plain,
! [A_19,C_20,B_21,D_22] :
( subset(A_19,C_20)
| ( cartesian_product2(A_19,B_21) = empty_set )
| ~ subset(cartesian_product2(A_19,B_21),cartesian_product2(C_20,D_22)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_83,plain,
( subset('#skF_3','#skF_5')
| ( cartesian_product2('#skF_3','#skF_4') = empty_set ) ),
inference(resolution,[status(thm)],[c_51,c_63]) ).
tff(c_90,plain,
cartesian_product2('#skF_3','#skF_4') = empty_set,
inference(splitLeft,[status(thm)],[c_83]) ).
tff(c_10,plain,
! [B_4,A_3] :
( ( empty_set = B_4 )
| ( empty_set = A_3 )
| ( cartesian_product2(A_3,B_4) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_107,plain,
( ( empty_set = '#skF_4' )
| ( empty_set = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_90,c_10]) ).
tff(c_140,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_107]) ).
tff(c_2,plain,
empty(empty_set),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_148,plain,
empty('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_140,c_2]) ).
tff(c_150,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_148]) ).
tff(c_151,plain,
empty_set = '#skF_4',
inference(splitRight,[status(thm)],[c_107]) ).
tff(c_26,plain,
! [A_12] : subset(empty_set,A_12),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_177,plain,
! [A_12] : subset('#skF_4',A_12),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_26]) ).
tff(c_20,plain,
~ subset('#skF_4','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_185,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_177,c_20]) ).
tff(c_187,plain,
cartesian_product2('#skF_3','#skF_4') != empty_set,
inference(splitRight,[status(thm)],[c_83]) ).
tff(c_188,plain,
! [B_29,D_30,A_31,C_32] :
( subset(B_29,D_30)
| ( cartesian_product2(A_31,B_29) = empty_set )
| ~ subset(cartesian_product2(A_31,B_29),cartesian_product2(C_32,D_30)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_191,plain,
( subset('#skF_4','#skF_6')
| ( cartesian_product2('#skF_3','#skF_4') = empty_set ) ),
inference(resolution,[status(thm)],[c_51,c_188]) ).
tff(c_210,plain,
cartesian_product2('#skF_3','#skF_4') = empty_set,
inference(negUnitSimplification,[status(thm)],[c_20,c_191]) ).
tff(c_217,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_187,c_210]) ).
tff(c_218,plain,
subset(cartesian_product2('#skF_4','#skF_3'),cartesian_product2('#skF_6','#skF_5')),
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_231,plain,
! [B_35,D_36,A_37,C_38] :
( subset(B_35,D_36)
| ( cartesian_product2(A_37,B_35) = empty_set )
| ~ subset(cartesian_product2(A_37,B_35),cartesian_product2(C_38,D_36)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_251,plain,
( subset('#skF_3','#skF_5')
| ( cartesian_product2('#skF_4','#skF_3') = empty_set ) ),
inference(resolution,[status(thm)],[c_218,c_231]) ).
tff(c_258,plain,
cartesian_product2('#skF_4','#skF_3') = empty_set,
inference(splitLeft,[status(thm)],[c_251]) ).
tff(c_275,plain,
( ( empty_set = '#skF_3' )
| ( empty_set = '#skF_4' ) ),
inference(superposition,[status(thm),theory(equality)],[c_258,c_10]) ).
tff(c_277,plain,
empty_set = '#skF_4',
inference(splitLeft,[status(thm)],[c_275]) ).
tff(c_315,plain,
! [A_12] : subset('#skF_4',A_12),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_26]) ).
tff(c_323,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_315,c_20]) ).
tff(c_324,plain,
empty_set = '#skF_3',
inference(splitRight,[status(thm)],[c_275]) ).
tff(c_350,plain,
empty('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_324,c_2]) ).
tff(c_352,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_350]) ).
tff(c_354,plain,
cartesian_product2('#skF_4','#skF_3') != empty_set,
inference(splitRight,[status(thm)],[c_251]) ).
tff(c_366,plain,
! [A_47,C_48,B_49,D_50] :
( subset(A_47,C_48)
| ( cartesian_product2(A_47,B_49) = empty_set )
| ~ subset(cartesian_product2(A_47,B_49),cartesian_product2(C_48,D_50)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_369,plain,
( subset('#skF_4','#skF_6')
| ( cartesian_product2('#skF_4','#skF_3') = empty_set ) ),
inference(resolution,[status(thm)],[c_218,c_366]) ).
tff(c_389,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_354,c_20,c_369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET985+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.10 % 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
% 0.10/0.29 % Computer : n002.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Apr 8 21:54:17 EDT 2025
% 0.10/0.30 % CPUTime :
% 3.76/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/2.42
% 3.79/2.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------