%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU295+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 08:53:32 PM UTC 2025
% Result : Theorem 5.10s 2.13s
% Output : CNFRefutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 1 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 17 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > set_intersection2 > #nlpp > powerset > empty_set > #skF_9 > #skF_7 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_1 > #skF_19 > #skF_10 > #skF_16 > #skF_15 > #skF_14 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_21 > #skF_8 > #skF_13 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $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(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $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('#skF_15',type,
'#skF_15': $i > $i ).
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_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_298,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
tff(f_115,axiom,
! [A,B] :
( finite(B)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
tff(f_107,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(c_214,plain,
finite('#skF_20'),
inference(cnfTransformation,[status(thm)],[f_298]) ).
tff(c_522,plain,
! [A_99,B_100] :
( finite(set_intersection2(A_99,B_100))
| ~ finite(B_100) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_44,plain,
! [B_18,A_17] : ( set_intersection2(B_18,A_17) = set_intersection2(A_17,B_18) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_212,plain,
~ finite(set_intersection2('#skF_20','#skF_21')),
inference(cnfTransformation,[status(thm)],[f_298]) ).
tff(c_243,plain,
~ finite(set_intersection2('#skF_21','#skF_20')),
inference(demodulation,[status(thm),theory(equality)],[c_44,c_212]) ).
tff(c_525,plain,
~ finite('#skF_20'),
inference(resolution,[status(thm)],[c_522,c_243]) ).
tff(c_535,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU295+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n020.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 22:42:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.10/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.10/2.13
% 5.10/2.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------