%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU115+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/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 : n010.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 08:52:47 PM UTC 2025
% Result : Theorem 3.57s 1.89s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 14 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 19 ( 6 ~; 2 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 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 : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-1 aty)
% Number of variables : 11 ( 9 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > #nlpp > singleton > powerset > finite_subsets > empty_set > #skF_7 > #skF_5 > #skF_4 > #skF_1 > #skF_8 > #skF_10 > #skF_2 > #skF_3 > #skF_9 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff(cup_closed,type,
cup_closed: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(finite_subsets,type,
finite_subsets: $i > $i ).
tff(singleton,type,
singleton: $i > $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(finite,type,
finite: $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_10',type,
'#skF_10': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(preboolean,type,
preboolean: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(diff_closed,type,
diff_closed: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(cap_closed,type,
cap_closed: $i > $o ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_210,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_217,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_224,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
tff(f_219,negated_conjecture,
finite_subsets(empty_set) != singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).
tff(f_165,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B)
& relation(B)
& function(B)
& one_to_one(B)
& epsilon_transitive(B)
& epsilon_connected(B)
& ordinal(B)
& natural(B)
& finite(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
tff(f_223,axiom,
! [A] :
( finite(A)
=> ( finite_subsets(A) = powerset(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).
tff(c_118,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_152,plain,
! [A_70] :
( ( empty_set = A_70 )
| ~ empty(A_70) ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_167,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_118,c_152]) ).
tff(c_128,plain,
singleton(empty_set) = powerset(empty_set),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_124,plain,
singleton(empty_set) != finite_subsets(empty_set),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_129,plain,
powerset(empty_set) != finite_subsets(empty_set),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_124]) ).
tff(c_171,plain,
powerset('#skF_9') != finite_subsets('#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_167,c_129]) ).
tff(c_88,plain,
! [A_35] : empty('#skF_4'(A_35)),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_165,plain,
! [A_35] : ( '#skF_4'(A_35) = empty_set ),
inference(resolution,[status(thm)],[c_88,c_152]) ).
tff(c_178,plain,
! [A_35] : ( '#skF_4'(A_35) = '#skF_9' ),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_165]) ).
tff(c_72,plain,
! [A_35] : finite('#skF_4'(A_35)),
inference(cnfTransformation,[status(thm)],[f_165]) ).
tff(c_179,plain,
finite('#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_178,c_72]) ).
tff(c_281,plain,
! [A_92] :
( ( powerset(A_92) = finite_subsets(A_92) )
| ~ finite(A_92) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_299,plain,
powerset('#skF_9') = finite_subsets('#skF_9'),
inference(resolution,[status(thm)],[c_179,c_281]) ).
tff(c_314,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_171,c_299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU115+1 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.13 % 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 : n010.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 22:04:48 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.57/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.57/1.89
% 3.57/1.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------