%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU055+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 : n012.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 11.71s 3.81s
% Output : CNFRefutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 51 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 91 ( 34 ~; 42 |; 5 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-2 aty)
% Number of variables : 53 ( 52 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > one_to_one > function > empty > set_difference > relation_image > apply > #nlpp > singleton > relation_dom > powerset > empty_set > #skF_5 > #skF_4 > #skF_11 > #skF_15 > #skF_8 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_3 > #skF_2 > #skF_12 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $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('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(relation_image,type,
relation_image: ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_179,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ! [B,C] : ( relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C)) )
=> one_to_one(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
tff(f_73,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( in(B,relation_dom(A))
& in(C,relation_dom(A))
& ( apply(A,B) = apply(A,C) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
tff(f_161,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_130,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_223,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_198,axiom,
! [A,B] :
( ( set_difference(A,B) = empty_set )
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
tff(f_188,axiom,
! [A,B] :
( ( set_difference(singleton(A),singleton(B)) = singleton(A) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
tff(f_200,axiom,
! [A] : ( set_difference(A,empty_set) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
tff(f_169,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( in(A,relation_dom(B))
=> ( relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
tff(c_106,plain,
~ one_to_one('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_110,plain,
function('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_112,plain,
relation('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_963,plain,
! [A_170] :
( ( '#skF_4'(A_170) != '#skF_3'(A_170) )
| one_to_one(A_170)
| ~ function(A_170)
| ~ relation(A_170) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_999,plain,
( ( '#skF_4'('#skF_16') != '#skF_3'('#skF_16') )
| one_to_one('#skF_16')
| ~ function('#skF_16') ),
inference(resolution,[status(thm)],[c_112,c_963]) ).
tff(c_1019,plain,
( ( '#skF_4'('#skF_16') != '#skF_3'('#skF_16') )
| one_to_one('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_999]) ).
tff(c_1020,plain,
'#skF_4'('#skF_16') != '#skF_3'('#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_106,c_1019]) ).
tff(c_102,plain,
! [A_30] : subset(A_30,A_30),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_74,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_130]) ).
tff(c_189,plain,
! [A_73] :
( ( empty_set = A_73 )
| ~ empty(A_73) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_208,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_74,c_189]) ).
tff(c_124,plain,
! [A_44,B_45] :
( ( set_difference(A_44,B_45) = empty_set )
| ~ subset(A_44,B_45) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_416,plain,
! [A_108,B_109] :
( ( set_difference(A_108,B_109) = '#skF_9' )
| ~ subset(A_108,B_109) ),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_124]) ).
tff(c_437,plain,
! [A_30] : ( set_difference(A_30,A_30) = '#skF_9' ),
inference(resolution,[status(thm)],[c_102,c_416]) ).
tff(c_116,plain,
! [B_41] : ( set_difference(singleton(B_41),singleton(B_41)) != singleton(B_41) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_439,plain,
! [B_41] : ( singleton(B_41) != '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_437,c_116]) ).
tff(c_126,plain,
! [A_46] : ( set_difference(A_46,empty_set) = A_46 ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_212,plain,
! [A_46] : ( set_difference(A_46,'#skF_9') = A_46 ),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_126]) ).
tff(c_440,plain,
! [A_111] : ( set_difference(A_111,A_111) = '#skF_9' ),
inference(resolution,[status(thm)],[c_102,c_416]) ).
tff(c_108,plain,
! [B_36,C_37] : ( set_difference(relation_image('#skF_16',B_36),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(B_36,C_37)) ),
inference(cnfTransformation,[status(thm)],[f_179]) ).
tff(c_453,plain,
! [B_36] : ( relation_image('#skF_16',set_difference(B_36,B_36)) = '#skF_9' ),
inference(superposition,[status(thm),theory(equality)],[c_440,c_108]) ).
tff(c_470,plain,
relation_image('#skF_16','#skF_9') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_437,c_453]) ).
tff(c_34,plain,
! [A_11] :
( in('#skF_3'(A_11),relation_dom(A_11))
| one_to_one(A_11)
| ~ function(A_11)
| ~ relation(A_11) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_2929,plain,
! [B_258,A_259] :
( ( relation_image(B_258,singleton(A_259)) = singleton(apply(B_258,A_259)) )
| ~ in(A_259,relation_dom(B_258))
| ~ function(B_258)
| ~ relation(B_258) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_8270,plain,
! [A_4532] :
( ( relation_image(A_4532,singleton('#skF_3'(A_4532))) = singleton(apply(A_4532,'#skF_3'(A_4532))) )
| one_to_one(A_4532)
| ~ function(A_4532)
| ~ relation(A_4532) ),
inference(resolution,[status(thm)],[c_34,c_2929]) ).
tff(c_8277,plain,
! [C_37] :
( ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),C_37)) )
| one_to_one('#skF_16')
| ~ function('#skF_16')
| ~ relation('#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_8270,c_108]) ).
tff(c_8389,plain,
! [C_37] :
( ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),C_37)) )
| one_to_one('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_112,c_110,c_8277]) ).
tff(c_10270,plain,
! [C_4925] : ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_4925)) = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),C_4925)) ),
inference(negUnitSimplification,[status(thm)],[c_106,c_8389]) ).
tff(c_10456,plain,
set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),'#skF_9') = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),'#skF_9')),
inference(superposition,[status(thm),theory(equality)],[c_470,c_10270]) ).
tff(c_10473,plain,
relation_image('#skF_16',singleton('#skF_3'('#skF_16'))) = singleton(apply('#skF_16','#skF_3'('#skF_16'))),
inference(demodulation,[status(thm),theory(equality)],[c_212,c_212,c_10456]) ).
tff(c_118,plain,
! [A_40,B_41] :
( ( set_difference(singleton(A_40),singleton(B_41)) = singleton(A_40) )
| ( B_41 = A_40 ) ),
inference(cnfTransformation,[status(thm)],[f_188]) ).
tff(c_8390,plain,
! [C_37] : ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),C_37)) ),
inference(negUnitSimplification,[status(thm)],[c_106,c_8389]) ).
tff(c_30,plain,
! [A_11] :
( ( apply(A_11,'#skF_4'(A_11)) = apply(A_11,'#skF_3'(A_11)) )
| one_to_one(A_11)
| ~ function(A_11)
| ~ relation(A_11) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_32,plain,
! [A_11] :
( in('#skF_4'(A_11),relation_dom(A_11))
| one_to_one(A_11)
| ~ function(A_11)
| ~ relation(A_11) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_7467,plain,
! [A_4378] :
( ( relation_image(A_4378,singleton('#skF_4'(A_4378))) = singleton(apply(A_4378,'#skF_4'(A_4378))) )
| one_to_one(A_4378)
| ~ function(A_4378)
| ~ relation(A_4378) ),
inference(resolution,[status(thm)],[c_32,c_2929]) ).
tff(c_7474,plain,
! [C_37] :
( ( set_difference(singleton(apply('#skF_16','#skF_4'('#skF_16'))),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_37)) )
| one_to_one('#skF_16')
| ~ function('#skF_16')
| ~ relation('#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_7467,c_108]) ).
tff(c_7586,plain,
! [C_37] :
( ( set_difference(singleton(apply('#skF_16','#skF_4'('#skF_16'))),relation_image('#skF_16',C_37)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_37)) )
| one_to_one('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_112,c_110,c_7474]) ).
tff(c_9010,plain,
! [C_4591] : ( set_difference(singleton(apply('#skF_16','#skF_4'('#skF_16'))),relation_image('#skF_16',C_4591)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_4591)) ),
inference(negUnitSimplification,[status(thm)],[c_106,c_7586]) ).
tff(c_9196,plain,
! [C_4591] :
( ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_4591)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_4591)) )
| one_to_one('#skF_16')
| ~ function('#skF_16')
| ~ relation('#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_9010]) ).
tff(c_9217,plain,
! [C_4591] :
( ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_4591)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_4591)) )
| one_to_one('#skF_16') ),
inference(demodulation,[status(thm),theory(equality)],[c_112,c_110,c_9196]) ).
tff(c_9218,plain,
! [C_4591] : ( set_difference(singleton(apply('#skF_16','#skF_3'('#skF_16'))),relation_image('#skF_16',C_4591)) = relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_4591)) ),
inference(negUnitSimplification,[status(thm)],[c_106,c_9217]) ).
tff(c_11381,plain,
! [C_5060] : ( relation_image('#skF_16',set_difference(singleton('#skF_4'('#skF_16')),C_5060)) = relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),C_5060)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8390,c_9218]) ).
tff(c_11569,plain,
relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),singleton('#skF_4'('#skF_16')))) = relation_image('#skF_16','#skF_9'),
inference(superposition,[status(thm),theory(equality)],[c_437,c_11381]) ).
tff(c_11609,plain,
relation_image('#skF_16',set_difference(singleton('#skF_3'('#skF_16')),singleton('#skF_4'('#skF_16')))) = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_470,c_11569]) ).
tff(c_11843,plain,
( ( relation_image('#skF_16',singleton('#skF_3'('#skF_16'))) = '#skF_9' )
| ( '#skF_4'('#skF_16') = '#skF_3'('#skF_16') ) ),
inference(superposition,[status(thm),theory(equality)],[c_118,c_11609]) ).
tff(c_11890,plain,
( ( singleton(apply('#skF_16','#skF_3'('#skF_16'))) = '#skF_9' )
| ( '#skF_4'('#skF_16') = '#skF_3'('#skF_16') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_10473,c_11843]) ).
tff(c_11892,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1020,c_439,c_11890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU055+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % 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
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 21:58:29 EDT 2025
% 0.12/0.33 % CPUTime :
% 11.71/3.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.71/3.82
% 11.71/3.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------