%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU056+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/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 : n008.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 08:52:42 PM UTC 2025
% Result : Theorem 4.74s 2.27s
% Output : CNFRefutation 5.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 17 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 41 ( 17 ~; 13 |; 4 &)
% ( 1 <=>; 6 =>; 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 : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 25 ( 24 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > disjoint > relation_empty_yielding > relation > one_to_one > function > empty > set_intersection2 > relation_image > #nlpp > powerset > empty_set > #skF_4 > #skF_11 > #skF_1 > #skF_8 > #skF_7 > #skF_10 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_9 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(relation,type,
relation: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $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(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_153,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( ( disjoint(A,B)
& one_to_one(C) )
=> disjoint(relation_image(C,A),relation_image(C,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
tff(f_88,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_190,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_157,axiom,
! [A] :
( relation(A)
=> ( relation_image(A,empty_set) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
tff(f_57,axiom,
! [A,B] :
( disjoint(A,B)
<=> ( set_intersection2(A,B) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
tff(f_142,axiom,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( one_to_one(C)
=> ( relation_image(C,set_intersection2(A,B)) = set_intersection2(relation_image(C,A),relation_image(C,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
tff(c_94,plain,
relation('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_92,plain,
function('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_88,plain,
one_to_one('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_46,plain,
empty('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_124,plain,
! [A_51] :
( ( empty_set = A_51 )
| ~ empty(A_51) ),
inference(cnfTransformation,[status(thm)],[f_190]) ).
tff(c_144,plain,
empty_set = '#skF_3',
inference(resolution,[status(thm)],[c_46,c_124]) ).
tff(c_96,plain,
! [A_28] :
( ( relation_image(A_28,empty_set) = empty_set )
| ~ relation(A_28) ),
inference(cnfTransformation,[status(thm)],[f_157]) ).
tff(c_230,plain,
! [A_64] :
( ( relation_image(A_64,'#skF_3') = '#skF_3' )
| ~ relation(A_64) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_144,c_96]) ).
tff(c_258,plain,
relation_image('#skF_14','#skF_3') = '#skF_3',
inference(resolution,[status(thm)],[c_94,c_230]) ).
tff(c_90,plain,
disjoint('#skF_12','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_16,plain,
! [A_8,B_9] :
( ( set_intersection2(A_8,B_9) = empty_set )
| ~ disjoint(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_422,plain,
! [A_83,B_84] :
( ( set_intersection2(A_83,B_84) = '#skF_3' )
| ~ disjoint(A_83,B_84) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_16]) ).
tff(c_434,plain,
set_intersection2('#skF_12','#skF_13') = '#skF_3',
inference(resolution,[status(thm)],[c_90,c_422]) ).
tff(c_656,plain,
! [C_118,A_119,B_120] :
( ( set_intersection2(relation_image(C_118,A_119),relation_image(C_118,B_120)) = relation_image(C_118,set_intersection2(A_119,B_120)) )
| ~ one_to_one(C_118)
| ~ function(C_118)
| ~ relation(C_118) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_18,plain,
! [A_8,B_9] :
( disjoint(A_8,B_9)
| ( set_intersection2(A_8,B_9) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_397,plain,
! [A_77,B_78] :
( disjoint(A_77,B_78)
| ( set_intersection2(A_77,B_78) != '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_18]) ).
tff(c_86,plain,
~ disjoint(relation_image('#skF_14','#skF_12'),relation_image('#skF_14','#skF_13')),
inference(cnfTransformation,[status(thm)],[f_153]) ).
tff(c_404,plain,
set_intersection2(relation_image('#skF_14','#skF_12'),relation_image('#skF_14','#skF_13')) != '#skF_3',
inference(resolution,[status(thm)],[c_397,c_86]) ).
tff(c_664,plain,
( ( relation_image('#skF_14',set_intersection2('#skF_12','#skF_13')) != '#skF_3' )
| ~ one_to_one('#skF_14')
| ~ function('#skF_14')
| ~ relation('#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_656,c_404]) ).
tff(c_730,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_94,c_92,c_88,c_258,c_434,c_664]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU056+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 21:59:32 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.74/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.74/2.28
% 4.74/2.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------