%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU234+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 : n020.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 10.37s 3.48s
% Output : CNFRefutation 10.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 44 ~; 50 |; 8 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-1 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_4 > #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_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
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_78,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_235,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_219,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_36,plain,
! [A_13] :
( ( '#skF_2'(A_13) != '#skF_3'(A_13) )
| epsilon_connected(A_13) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_398,plain,
! [A_67] :
( in('#skF_1'(A_67),A_67)
| epsilon_transitive(A_67) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_162,plain,
! [B_33] :
( subset(B_33,'#skF_17')
| ~ in(B_33,'#skF_17') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_299,plain,
! [A_61] :
( ~ subset('#skF_1'(A_61),A_61)
| epsilon_transitive(A_61) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_304,plain,
( epsilon_transitive('#skF_17')
| ~ in('#skF_1'('#skF_17'),'#skF_17') ),
inference(resolution,[status(thm)],[c_162,c_299]) ).
tff(c_337,plain,
~ in('#skF_1'('#skF_17'),'#skF_17'),
inference(splitLeft,[status(thm)],[c_304]) ).
tff(c_412,plain,
epsilon_transitive('#skF_17'),
inference(resolution,[status(thm)],[c_398,c_337]) ).
tff(c_433,plain,
! [A_71] :
( ordinal(A_71)
| ~ epsilon_connected(A_71)
| ~ epsilon_transitive(A_71) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_160,plain,
~ ordinal('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_442,plain,
( ~ epsilon_connected('#skF_17')
| ~ epsilon_transitive('#skF_17') ),
inference(resolution,[status(thm)],[c_433,c_160]) ).
tff(c_447,plain,
~ epsilon_connected('#skF_17'),
inference(demodulation,[status(thm),theory(equality)],[c_412,c_442]) ).
tff(c_454,plain,
'#skF_2'('#skF_17') != '#skF_3'('#skF_17'),
inference(resolution,[status(thm)],[c_36,c_447]) ).
tff(c_483,plain,
! [A_73] :
( in('#skF_3'(A_73),A_73)
| epsilon_connected(A_73) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_164,plain,
! [B_33] :
( ordinal(B_33)
| ~ in(B_33,'#skF_17') ),
inference(cnfTransformation,[status(thm)],[f_235]) ).
tff(c_495,plain,
( ordinal('#skF_3'('#skF_17'))
| epsilon_connected('#skF_17') ),
inference(resolution,[status(thm)],[c_483,c_164]) ).
tff(c_501,plain,
ordinal('#skF_3'('#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_447,c_495]) ).
tff(c_456,plain,
! [A_72] :
( in('#skF_2'(A_72),A_72)
| epsilon_connected(A_72) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_468,plain,
( ordinal('#skF_2'('#skF_17'))
| epsilon_connected('#skF_17') ),
inference(resolution,[status(thm)],[c_456,c_164]) ).
tff(c_474,plain,
ordinal('#skF_2'('#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_447,c_468]) ).
tff(c_770,plain,
! [B_107,A_108] :
( in(B_107,A_108)
| ( B_107 = A_108 )
| in(A_108,B_107)
| ~ ordinal(B_107)
| ~ ordinal(A_108) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
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_2323,plain,
! [A_203] :
( epsilon_connected(A_203)
| in('#skF_3'(A_203),'#skF_2'(A_203))
| ( '#skF_2'(A_203) = '#skF_3'(A_203) )
| ~ ordinal('#skF_3'(A_203))
| ~ ordinal('#skF_2'(A_203)) ),
inference(resolution,[status(thm)],[c_770,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_3854,plain,
! [A_262] :
( epsilon_connected(A_262)
| ( '#skF_2'(A_262) = '#skF_3'(A_262) )
| ~ ordinal('#skF_3'(A_262))
| ~ ordinal('#skF_2'(A_262)) ),
inference(resolution,[status(thm)],[c_2323,c_34]) ).
tff(c_3863,plain,
( epsilon_connected('#skF_17')
| ( '#skF_2'('#skF_17') = '#skF_3'('#skF_17') )
| ~ ordinal('#skF_3'('#skF_17')) ),
inference(resolution,[status(thm)],[c_474,c_3854]) ).
tff(c_3874,plain,
( epsilon_connected('#skF_17')
| ( '#skF_2'('#skF_17') = '#skF_3'('#skF_17') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_501,c_3863]) ).
tff(c_3876,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_454,c_447,c_3874]) ).
tff(c_3877,plain,
epsilon_transitive('#skF_17'),
inference(splitRight,[status(thm)],[c_304]) ).
tff(c_3948,plain,
! [A_266] :
( in('#skF_3'(A_266),A_266)
| epsilon_connected(A_266) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_3961,plain,
( ordinal('#skF_3'('#skF_17'))
| epsilon_connected('#skF_17') ),
inference(resolution,[status(thm)],[c_3948,c_164]) ).
tff(c_3965,plain,
epsilon_connected('#skF_17'),
inference(splitLeft,[status(thm)],[c_3961]) ).
tff(c_4018,plain,
! [A_272] :
( ordinal(A_272)
| ~ epsilon_connected(A_272)
| ~ epsilon_transitive(A_272) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_4027,plain,
( ~ epsilon_connected('#skF_17')
| ~ epsilon_transitive('#skF_17') ),
inference(resolution,[status(thm)],[c_4018,c_160]) ).
tff(c_4033,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3877,c_3965,c_4027]) ).
tff(c_4035,plain,
~ epsilon_connected('#skF_17'),
inference(splitRight,[status(thm)],[c_3961]) ).
tff(c_4042,plain,
'#skF_2'('#skF_17') != '#skF_3'('#skF_17'),
inference(resolution,[status(thm)],[c_36,c_4035]) ).
tff(c_4034,plain,
ordinal('#skF_3'('#skF_17')),
inference(splitRight,[status(thm)],[c_3961]) ).
tff(c_4086,plain,
! [A_277] :
( in('#skF_2'(A_277),A_277)
| epsilon_connected(A_277) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_4098,plain,
( ordinal('#skF_2'('#skF_17'))
| epsilon_connected('#skF_17') ),
inference(resolution,[status(thm)],[c_4086,c_164]) ).
tff(c_4104,plain,
ordinal('#skF_2'('#skF_17')),
inference(negUnitSimplification,[status(thm)],[c_4035,c_4098]) ).
tff(c_4480,plain,
! [B_321,A_322] :
( in(B_321,A_322)
| ( B_321 = A_322 )
| in(A_322,B_321)
| ~ ordinal(B_321)
| ~ ordinal(A_322) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_5694,plain,
! [A_397] :
( epsilon_connected(A_397)
| in('#skF_3'(A_397),'#skF_2'(A_397))
| ( '#skF_2'(A_397) = '#skF_3'(A_397) )
| ~ ordinal('#skF_3'(A_397))
| ~ ordinal('#skF_2'(A_397)) ),
inference(resolution,[status(thm)],[c_4480,c_38]) ).
tff(c_7703,plain,
! [A_476] :
( epsilon_connected(A_476)
| ( '#skF_2'(A_476) = '#skF_3'(A_476) )
| ~ ordinal('#skF_3'(A_476))
| ~ ordinal('#skF_2'(A_476)) ),
inference(resolution,[status(thm)],[c_5694,c_34]) ).
tff(c_7715,plain,
( epsilon_connected('#skF_17')
| ( '#skF_2'('#skF_17') = '#skF_3'('#skF_17') )
| ~ ordinal('#skF_3'('#skF_17')) ),
inference(resolution,[status(thm)],[c_4104,c_7703]) ).
tff(c_7724,plain,
( epsilon_connected('#skF_17')
| ( '#skF_2'('#skF_17') = '#skF_3'('#skF_17') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4034,c_7715]) ).
tff(c_7726,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4042,c_4035,c_7724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU234+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.14 % 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
% 0.12/0.35 % Computer : n020.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Apr 8 22:26:49 EDT 2025
% 0.12/0.35 % CPUTime :
% 10.37/3.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.37/3.49
% 10.37/3.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------