%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET955+1 : TPTP v9.0.0. Bugfixed 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 : n007.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 08:39:40 PM UTC 2025
% Result : Theorem 24.31s 8.88s
% Output : CNFRefutation 24.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 85 ( 37 ~; 40 |; 2 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 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 : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 63 ( 61 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_1 > #skF_11 > #skF_4 > #skF_7 > #skF_13 > #skF_10 > #skF_14 > #skF_2 > #skF_6 > #skF_9 > #skF_8 > #skF_5 > #skF_3 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
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_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_66,negated_conjecture,
~ ! [A,B,C,D] :
( ! [E,F] :
( in(ordered_pair(E,F),cartesian_product2(A,B))
<=> in(ordered_pair(E,F),cartesian_product2(C,D)) )
=> ( cartesian_product2(A,B) = cartesian_product2(C,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
tff(f_73,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
tff(f_48,axiom,
! [A,B,C] :
( ( C = cartesian_product2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& ( D = ordered_pair(E,F) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
tff(c_38,plain,
cartesian_product2('#skF_11','#skF_12') != cartesian_product2('#skF_9','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_50,plain,
! [A_47,B_48] :
( in('#skF_13'(A_47,B_48),B_48)
| in('#skF_14'(A_47,B_48),A_47)
| ( B_48 = A_47 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_12,plain,
! [A_5,B_6,D_32] :
( in('#skF_5'(A_5,B_6,cartesian_product2(A_5,B_6),D_32),A_5)
| ~ in(D_32,cartesian_product2(A_5,B_6)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_10,plain,
! [A_5,B_6,D_32] :
( in('#skF_6'(A_5,B_6,cartesian_product2(A_5,B_6),D_32),B_6)
| ~ in(D_32,cartesian_product2(A_5,B_6)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_6,plain,
! [E_37,F_38,A_5,B_6] :
( in(ordered_pair(E_37,F_38),cartesian_product2(A_5,B_6))
| ~ in(F_38,B_6)
| ~ in(E_37,A_5) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_2237,plain,
! [A_155,B_156,D_157] :
( ( ordered_pair('#skF_5'(A_155,B_156,cartesian_product2(A_155,B_156),D_157),'#skF_6'(A_155,B_156,cartesian_product2(A_155,B_156),D_157)) = D_157 )
| ~ in(D_157,cartesian_product2(A_155,B_156)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_40,plain,
! [E_45,F_46] :
( in(ordered_pair(E_45,F_46),cartesian_product2('#skF_11','#skF_12'))
| ~ in(ordered_pair(E_45,F_46),cartesian_product2('#skF_9','#skF_10')) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_4701,plain,
! [D_249,A_250,B_251] :
( in(D_249,cartesian_product2('#skF_11','#skF_12'))
| ~ in(ordered_pair('#skF_5'(A_250,B_251,cartesian_product2(A_250,B_251),D_249),'#skF_6'(A_250,B_251,cartesian_product2(A_250,B_251),D_249)),cartesian_product2('#skF_9','#skF_10'))
| ~ in(D_249,cartesian_product2(A_250,B_251)) ),
inference(superposition,[status(thm),theory(equality)],[c_2237,c_40]) ).
tff(c_14784,plain,
! [D_465,A_466,B_467] :
( in(D_465,cartesian_product2('#skF_11','#skF_12'))
| ~ in(D_465,cartesian_product2(A_466,B_467))
| ~ in('#skF_6'(A_466,B_467,cartesian_product2(A_466,B_467),D_465),'#skF_10')
| ~ in('#skF_5'(A_466,B_467,cartesian_product2(A_466,B_467),D_465),'#skF_9') ),
inference(resolution,[status(thm)],[c_6,c_4701]) ).
tff(c_14790,plain,
! [D_468,A_469] :
( in(D_468,cartesian_product2('#skF_11','#skF_12'))
| ~ in('#skF_5'(A_469,'#skF_10',cartesian_product2(A_469,'#skF_10'),D_468),'#skF_9')
| ~ in(D_468,cartesian_product2(A_469,'#skF_10')) ),
inference(resolution,[status(thm)],[c_10,c_14784]) ).
tff(c_14796,plain,
! [D_470] :
( in(D_470,cartesian_product2('#skF_11','#skF_12'))
| ~ in(D_470,cartesian_product2('#skF_9','#skF_10')) ),
inference(resolution,[status(thm)],[c_12,c_14790]) ).
tff(c_48,plain,
! [A_47,B_48] :
( ~ in('#skF_13'(A_47,B_48),A_47)
| in('#skF_14'(A_47,B_48),A_47)
| ( B_48 = A_47 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_36586,plain,
! [B_643] :
( in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),B_643),cartesian_product2('#skF_11','#skF_12'))
| ( cartesian_product2('#skF_11','#skF_12') = B_643 )
| ~ in('#skF_13'(cartesian_product2('#skF_11','#skF_12'),B_643),cartesian_product2('#skF_9','#skF_10')) ),
inference(resolution,[status(thm)],[c_14796,c_48]) ).
tff(c_36602,plain,
( in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_11','#skF_12'))
| ( cartesian_product2('#skF_11','#skF_12') = cartesian_product2('#skF_9','#skF_10') ) ),
inference(resolution,[status(thm)],[c_50,c_36586]) ).
tff(c_36617,plain,
in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_11','#skF_12')),
inference(negUnitSimplification,[status(thm)],[c_38,c_38,c_36602]) ).
tff(c_307,plain,
! [E_76,F_77,A_78,B_79] :
( in(ordered_pair(E_76,F_77),cartesian_product2(A_78,B_79))
| ~ in(F_77,B_79)
| ~ in(E_76,A_78) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_42,plain,
! [E_45,F_46] :
( in(ordered_pair(E_45,F_46),cartesian_product2('#skF_9','#skF_10'))
| ~ in(ordered_pair(E_45,F_46),cartesian_product2('#skF_11','#skF_12')) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_314,plain,
! [E_76,F_77] :
( in(ordered_pair(E_76,F_77),cartesian_product2('#skF_9','#skF_10'))
| ~ in(F_77,'#skF_12')
| ~ in(E_76,'#skF_11') ),
inference(resolution,[status(thm)],[c_307,c_42]) ).
tff(c_14623,plain,
! [D_459,A_460,B_461] :
( in(D_459,cartesian_product2('#skF_9','#skF_10'))
| ~ in('#skF_6'(A_460,B_461,cartesian_product2(A_460,B_461),D_459),'#skF_12')
| ~ in('#skF_5'(A_460,B_461,cartesian_product2(A_460,B_461),D_459),'#skF_11')
| ~ in(D_459,cartesian_product2(A_460,B_461)) ),
inference(superposition,[status(thm),theory(equality)],[c_2237,c_314]) ).
tff(c_14629,plain,
! [D_462,A_463] :
( in(D_462,cartesian_product2('#skF_9','#skF_10'))
| ~ in('#skF_5'(A_463,'#skF_12',cartesian_product2(A_463,'#skF_12'),D_462),'#skF_11')
| ~ in(D_462,cartesian_product2(A_463,'#skF_12')) ),
inference(resolution,[status(thm)],[c_10,c_14623]) ).
tff(c_14634,plain,
! [D_32] :
( in(D_32,cartesian_product2('#skF_9','#skF_10'))
| ~ in(D_32,cartesian_product2('#skF_11','#skF_12')) ),
inference(resolution,[status(thm)],[c_12,c_14629]) ).
tff(c_36628,plain,
in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_9','#skF_10')),
inference(resolution,[status(thm)],[c_36617,c_14634]) ).
tff(c_46,plain,
! [A_47,B_48] :
( in('#skF_13'(A_47,B_48),B_48)
| ~ in('#skF_14'(A_47,B_48),B_48)
| ( B_48 = A_47 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_44,plain,
! [A_47,B_48] :
( ~ in('#skF_13'(A_47,B_48),A_47)
| ~ in('#skF_14'(A_47,B_48),B_48)
| ( B_48 = A_47 ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_14870,plain,
! [B_48] :
( ~ in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),B_48),B_48)
| ( cartesian_product2('#skF_11','#skF_12') = B_48 )
| ~ in('#skF_13'(cartesian_product2('#skF_11','#skF_12'),B_48),cartesian_product2('#skF_9','#skF_10')) ),
inference(resolution,[status(thm)],[c_14796,c_44]) ).
tff(c_36632,plain,
( ( cartesian_product2('#skF_11','#skF_12') = cartesian_product2('#skF_9','#skF_10') )
| ~ in('#skF_13'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_9','#skF_10')) ),
inference(resolution,[status(thm)],[c_36628,c_14870]) ).
tff(c_36646,plain,
~ in('#skF_13'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_9','#skF_10')),
inference(negUnitSimplification,[status(thm)],[c_38,c_36632]) ).
tff(c_36666,plain,
( ~ in('#skF_14'(cartesian_product2('#skF_11','#skF_12'),cartesian_product2('#skF_9','#skF_10')),cartesian_product2('#skF_9','#skF_10'))
| ( cartesian_product2('#skF_11','#skF_12') = cartesian_product2('#skF_9','#skF_10') ) ),
inference(resolution,[status(thm)],[c_46,c_36646]) ).
tff(c_36677,plain,
cartesian_product2('#skF_11','#skF_12') = cartesian_product2('#skF_9','#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_36628,c_36666]) ).
tff(c_36679,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_36677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET955+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.03/0.13 % 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
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Apr 8 21:53:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 24.31/8.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.31/8.89
% 24.31/8.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------