%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU212+3 : 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 08:53:13 PM UTC 2025
% Result : Theorem 7.19s 2.87s
% Output : CNFRefutation 7.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 21 |; 4 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 10 con; 0-3 aty)
% Number of variables : 18 ( 17 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > unordered_pair > ordered_pair > apply > #nlpp > singleton > relation_dom > powerset > empty_set > #skF_5 > #skF_15 > #skF_8 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_11 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
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(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_11',type,
'#skF_11': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_203,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( in(A,relation_dom(C))
& ( B = apply(C,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
tff(f_59,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( ( C = apply(A,B) )
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( ( C = apply(A,B) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
tff(f_70,axiom,
! [A] :
( relation(A)
=> ! [B] :
( ( B = relation_dom(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
tff(c_118,plain,
( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
| ( apply('#skF_16','#skF_14') = '#skF_15' ) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_130,plain,
apply('#skF_16','#skF_14') = '#skF_15',
inference(splitLeft,[status(thm)],[c_118]) ).
tff(c_122,plain,
( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
| in('#skF_14',relation_dom('#skF_16')) ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_126,plain,
in('#skF_14',relation_dom('#skF_16')),
inference(splitLeft,[status(thm)],[c_122]) ).
tff(c_112,plain,
( ( apply('#skF_16','#skF_14') != '#skF_15' )
| ~ in('#skF_14',relation_dom('#skF_16'))
| ~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_175,plain,
~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(splitLeft,[status(thm)],[c_112]) ).
tff(c_110,plain,
relation('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_108,plain,
function('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_203]) ).
tff(c_766,plain,
! [B_171,A_172] :
( in(ordered_pair(B_171,apply(A_172,B_171)),A_172)
| ~ in(B_171,relation_dom(A_172))
| ~ function(A_172)
| ~ relation(A_172) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_810,plain,
( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
| ~ in('#skF_14',relation_dom('#skF_16'))
| ~ function('#skF_16')
| ~ relation('#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_766]) ).
tff(c_831,plain,
in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_126,c_810]) ).
tff(c_833,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_175,c_831]) ).
tff(c_834,plain,
( ~ in('#skF_14',relation_dom('#skF_16'))
| ( apply('#skF_16','#skF_14') != '#skF_15' ) ),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_957,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_130,c_126,c_834]) ).
tff(c_959,plain,
apply('#skF_16','#skF_14') != '#skF_15',
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_958,plain,
in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_1004,plain,
~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(splitLeft,[status(thm)],[c_112]) ).
tff(c_1048,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_958,c_1004]) ).
tff(c_1050,plain,
in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(splitRight,[status(thm)],[c_112]) ).
tff(c_2489,plain,
! [A_348,B_349,C_350] :
( ( apply(A_348,B_349) = C_350 )
| ~ in(ordered_pair(B_349,C_350),A_348)
| ~ in(B_349,relation_dom(A_348))
| ~ function(A_348)
| ~ relation(A_348) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_2506,plain,
( ( apply('#skF_16','#skF_14') = '#skF_15' )
| ~ in('#skF_14',relation_dom('#skF_16'))
| ~ function('#skF_16')
| ~ relation('#skF_16') ),
inference(resolution,[status(thm)],[c_1050,c_2489]) ).
tff(c_2514,plain,
apply('#skF_16','#skF_14') = '#skF_15',
inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_126,c_2506]) ).
tff(c_2516,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_959,c_2514]) ).
tff(c_2518,plain,
~ in('#skF_14',relation_dom('#skF_16')),
inference(splitRight,[status(thm)],[c_122]) ).
tff(c_2517,plain,
in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
inference(splitRight,[status(thm)],[c_122]) ).
tff(c_2868,plain,
! [C_407,A_408,D_409] :
( in(C_407,relation_dom(A_408))
| ~ in(ordered_pair(C_407,D_409),A_408)
| ~ relation(A_408) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_2875,plain,
( in('#skF_14',relation_dom('#skF_16'))
| ~ relation('#skF_16') ),
inference(resolution,[status(thm)],[c_2517,c_2868]) ).
tff(c_2879,plain,
in('#skF_14',relation_dom('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_2875]) ).
tff(c_2881,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2518,c_2879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU212+3 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:21:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.19/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.54/2.88
% 7.54/2.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------