%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU234+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 : n024.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 08:53:19 PM UTC 2025
% Result : Theorem 7.55s 2.74s
% Output : CNFRefutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 32 ~; 29 |; 8 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-1 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_4 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
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(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
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(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_95,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( in(B,A)
& in(C,A)
& ~ in(B,C)
& ( B != C )
& ~ in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
tff(f_240,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( ordinal(B)
& subset(B,A) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
tff(f_101,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
tff(f_78,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_224,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(A,B)
& ( A != B )
& ~ in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
tff(c_474,plain,
! [A_74] :
( ( '#skF_2'(A_74) != '#skF_3'(A_74) )
| epsilon_connected(A_74) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_360,plain,
! [A_65] :
( in('#skF_3'(A_65),A_65)
| epsilon_connected(A_65) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_164,plain,
! [B_33] :
( ordinal(B_33)
| ~ in(B_33,'#skF_18') ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_373,plain,
( ordinal('#skF_3'('#skF_18'))
| epsilon_connected('#skF_18') ),
inference(resolution,[status(thm)],[c_360,c_164]) ).
tff(c_381,plain,
epsilon_connected('#skF_18'),
inference(splitLeft,[status(thm)],[c_373]) ).
tff(c_412,plain,
! [A_70] :
( ordinal(A_70)
| ~ epsilon_connected(A_70)
| ~ epsilon_transitive(A_70) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_160,plain,
~ ordinal('#skF_18'),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_421,plain,
( ~ epsilon_connected('#skF_18')
| ~ epsilon_transitive('#skF_18') ),
inference(resolution,[status(thm)],[c_412,c_160]) ).
tff(c_426,plain,
~ epsilon_transitive('#skF_18'),
inference(demodulation,[status(thm),theory(equality)],[c_381,c_421]) ).
tff(c_439,plain,
! [A_73] :
( in('#skF_1'(A_73),A_73)
| epsilon_transitive(A_73) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_162,plain,
! [B_33] :
( subset(B_33,'#skF_18')
| ~ in(B_33,'#skF_18') ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_391,plain,
! [A_68] :
( ~ subset('#skF_1'(A_68),A_68)
| epsilon_transitive(A_68) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_396,plain,
( epsilon_transitive('#skF_18')
| ~ in('#skF_1'('#skF_18'),'#skF_18') ),
inference(resolution,[status(thm)],[c_162,c_391]) ).
tff(c_431,plain,
~ in('#skF_1'('#skF_18'),'#skF_18'),
inference(negUnitSimplification,[status(thm)],[c_426,c_396]) ).
tff(c_444,plain,
epsilon_transitive('#skF_18'),
inference(resolution,[status(thm)],[c_439,c_431]) ).
tff(c_459,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_426,c_444]) ).
tff(c_461,plain,
~ epsilon_connected('#skF_18'),
inference(splitRight,[status(thm)],[c_373]) ).
tff(c_478,plain,
'#skF_2'('#skF_18') != '#skF_3'('#skF_18'),
inference(resolution,[status(thm)],[c_474,c_461]) ).
tff(c_460,plain,
ordinal('#skF_3'('#skF_18')),
inference(splitRight,[status(thm)],[c_373]) ).
tff(c_493,plain,
! [A_77] :
( in('#skF_2'(A_77),A_77)
| epsilon_connected(A_77) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_503,plain,
( ordinal('#skF_2'('#skF_18'))
| epsilon_connected('#skF_18') ),
inference(resolution,[status(thm)],[c_493,c_164]) ).
tff(c_508,plain,
ordinal('#skF_2'('#skF_18')),
inference(negUnitSimplification,[status(thm)],[c_461,c_503]) ).
tff(c_866,plain,
! [B_121,A_122] :
( in(B_121,A_122)
| ( B_121 = A_122 )
| in(A_122,B_121)
| ~ ordinal(B_121)
| ~ ordinal(A_122) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_38,plain,
! [A_13] :
( ~ in('#skF_2'(A_13),'#skF_3'(A_13))
| epsilon_connected(A_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_2125,plain,
! [A_202] :
( epsilon_connected(A_202)
| in('#skF_3'(A_202),'#skF_2'(A_202))
| ( '#skF_2'(A_202) = '#skF_3'(A_202) )
| ~ ordinal('#skF_3'(A_202))
| ~ ordinal('#skF_2'(A_202)) ),
inference(resolution,[status(thm)],[c_866,c_38]) ).
tff(c_34,plain,
! [A_13] :
( ~ in('#skF_3'(A_13),'#skF_2'(A_13))
| epsilon_connected(A_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_3662,plain,
! [A_269] :
( epsilon_connected(A_269)
| ( '#skF_2'(A_269) = '#skF_3'(A_269) )
| ~ ordinal('#skF_3'(A_269))
| ~ ordinal('#skF_2'(A_269)) ),
inference(resolution,[status(thm)],[c_2125,c_34]) ).
tff(c_3674,plain,
( epsilon_connected('#skF_18')
| ( '#skF_2'('#skF_18') = '#skF_3'('#skF_18') )
| ~ ordinal('#skF_3'('#skF_18')) ),
inference(resolution,[status(thm)],[c_508,c_3662]) ).
tff(c_3683,plain,
( epsilon_connected('#skF_18')
| ( '#skF_2'('#skF_18') = '#skF_3'('#skF_18') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_460,c_3674]) ).
tff(c_3685,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_478,c_461,c_3683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU234+3 : TPTP v9.0.0. Released v3.2.0.
% 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
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 22:27:36 EDT 2025
% 0.14/0.34 % CPUTime :
% 7.55/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.55/2.74
% 7.55/2.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------