%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU245+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n023.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 08:53:22 PM UTC 2025
% Result : Theorem 6.77s 2.70s
% Output : CNFRefutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 24 |; 2 &)
% ( 3 <=>; 2 =>; 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 : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation > one_to_one > function > empty > set_intersection2 > relation_restriction > cartesian_product2 > #nlpp > empty_set > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_11 > #skF_9 > #skF_8 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(relation_restriction,type,
relation_restriction: ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_124,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
tff(f_115,axiom,
! [A] :
( relation(A)
=> ! [B] : ( relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
tff(f_133,axiom,
! [A,B,C] :
( ( C = set_intersection2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
tff(c_64,plain,
relation('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_76,plain,
( in('#skF_7',relation_restriction('#skF_9','#skF_8'))
| in('#skF_7','#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_95,plain,
in('#skF_7','#skF_9'),
inference(splitLeft,[status(thm)],[c_76]) ).
tff(c_72,plain,
( in('#skF_7',relation_restriction('#skF_9','#skF_8'))
| in('#skF_7',cartesian_product2('#skF_8','#skF_8')) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_137,plain,
in('#skF_7',cartesian_product2('#skF_8','#skF_8')),
inference(splitLeft,[status(thm)],[c_72]) ).
tff(c_62,plain,
! [A_23,B_25] :
( ( set_intersection2(A_23,cartesian_product2(B_25,B_25)) = relation_restriction(A_23,B_25) )
| ~ relation(A_23) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_525,plain,
! [D_69,A_70,B_71] :
( in(D_69,set_intersection2(A_70,B_71))
| ~ in(D_69,B_71)
| ~ in(D_69,A_70) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_3287,plain,
! [D_240,A_241,B_242] :
( in(D_240,relation_restriction(A_241,B_242))
| ~ in(D_240,cartesian_product2(B_242,B_242))
| ~ in(D_240,A_241)
| ~ relation(A_241) ),
inference(superposition,[status(thm),theory(equality)],[c_62,c_525]) ).
tff(c_3351,plain,
! [A_243] :
( in('#skF_7',relation_restriction(A_243,'#skF_8'))
| ~ in('#skF_7',A_243)
| ~ relation(A_243) ),
inference(resolution,[status(thm)],[c_137,c_3287]) ).
tff(c_66,plain,
( ~ in('#skF_7',cartesian_product2('#skF_8','#skF_8'))
| ~ in('#skF_7','#skF_9')
| ~ in('#skF_7',relation_restriction('#skF_9','#skF_8')) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_182,plain,
~ in('#skF_7',relation_restriction('#skF_9','#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_137,c_66]) ).
tff(c_3365,plain,
( ~ in('#skF_7','#skF_9')
| ~ relation('#skF_9') ),
inference(resolution,[status(thm)],[c_3351,c_182]) ).
tff(c_3383,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_64,c_95,c_3365]) ).
tff(c_3385,plain,
~ in('#skF_7',cartesian_product2('#skF_8','#skF_8')),
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_3406,plain,
( ~ in('#skF_7',cartesian_product2('#skF_8','#skF_8'))
| ~ in('#skF_7',relation_restriction('#skF_9','#skF_8')) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_66]) ).
tff(c_3407,plain,
~ in('#skF_7',relation_restriction('#skF_9','#skF_8')),
inference(splitLeft,[status(thm)],[c_3406]) ).
tff(c_3384,plain,
in('#skF_7',relation_restriction('#skF_9','#skF_8')),
inference(splitRight,[status(thm)],[c_72]) ).
tff(c_3421,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3407,c_3384]) ).
tff(c_3423,plain,
in('#skF_7',relation_restriction('#skF_9','#skF_8')),
inference(splitRight,[status(thm)],[c_3406]) ).
tff(c_3672,plain,
! [A_278,B_279] :
( ( set_intersection2(A_278,cartesian_product2(B_279,B_279)) = relation_restriction(A_278,B_279) )
| ~ relation(A_278) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_80,plain,
! [D_31,B_27,A_26] :
( in(D_31,B_27)
| ~ in(D_31,set_intersection2(A_26,B_27)) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_4129,plain,
! [D_312,B_313,A_314] :
( in(D_312,cartesian_product2(B_313,B_313))
| ~ in(D_312,relation_restriction(A_314,B_313))
| ~ relation(A_314) ),
inference(superposition,[status(thm),theory(equality)],[c_3672,c_80]) ).
tff(c_4151,plain,
( in('#skF_7',cartesian_product2('#skF_8','#skF_8'))
| ~ relation('#skF_9') ),
inference(resolution,[status(thm)],[c_3423,c_4129]) ).
tff(c_4162,plain,
in('#skF_7',cartesian_product2('#skF_8','#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_4151]) ).
tff(c_4164,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3385,c_4162]) ).
tff(c_4166,plain,
~ in('#skF_7','#skF_9'),
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_4165,plain,
in('#skF_7',relation_restriction('#skF_9','#skF_8')),
inference(splitRight,[status(thm)],[c_76]) ).
tff(c_4484,plain,
! [A_348,B_349] :
( ( set_intersection2(A_348,cartesian_product2(B_349,B_349)) = relation_restriction(A_348,B_349) )
| ~ relation(A_348) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_82,plain,
! [D_31,A_26,B_27] :
( in(D_31,A_26)
| ~ in(D_31,set_intersection2(A_26,B_27)) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_4648,plain,
! [D_356,A_357,B_358] :
( in(D_356,A_357)
| ~ in(D_356,relation_restriction(A_357,B_358))
| ~ relation(A_357) ),
inference(superposition,[status(thm),theory(equality)],[c_4484,c_82]) ).
tff(c_4658,plain,
( in('#skF_7','#skF_9')
| ~ relation('#skF_9') ),
inference(resolution,[status(thm)],[c_4165,c_4648]) ).
tff(c_4664,plain,
in('#skF_7','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_4658]) ).
tff(c_4666,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4166,c_4664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU245+1 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.12 % 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
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Apr 8 22:30:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 6.77/2.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.77/2.71
% 6.77/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------