%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEV421_1 : TPTP v9.0.0. Released v5.0.0.
% 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 : n019.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 09:11:05 PM UTC 2025
% Result : Theorem 3.59s 1.81s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 3 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 12 ( 0 atm; 0 fun; 11 num; 1 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > intersection > difference > #nlpp > singleton > complement > cardinality > empty_set > #skF_1 > #skF_2 > #skF_3 > #skF_4
%Foreground sorts:
tff(element,type,
element: $tType ).
tff(set,type,
set: $tType ).
%Background operators:
tff('#skF_5',type,
'#skF_5': $int ).
%Foreground operators:
tff(member,type,
member: ( element * set ) > $o ).
tff(intersection,type,
intersection: ( set * set ) > set ).
tff('#skF_1',type,
'#skF_1': set > element ).
tff('#skF_2',type,
'#skF_2': ( set * set ) > element ).
tff('#skF_3',type,
'#skF_3': element ).
tff(complement,type,
complement: set > set ).
tff(cardinality,type,
cardinality: set > $int ).
tff('#skF_4',type,
'#skF_4': set ).
tff(subset,type,
subset: ( set * set ) > $o ).
tff(singleton,type,
singleton: element > set ).
tff(union,type,
union: ( set * set ) > set ).
tff(empty_set,type,
empty_set: set ).
tff(difference,type,
difference: ( set * set ) > set ).
tff(f_102,negated_conjecture,
~ ! [X: element,C: set,Sizea: $int] :
( ( ~ member(X,C)
& ( Sizea = cardinality(C) ) )
=> ( ( Sizea = 0 )
<=> ( C = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc1) ).
tff(f_75,axiom,
! [S: set] :
( ( cardinality(S) = 0 )
<=> ( S = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_empty_set) ).
tff(c_70,plain,
( ( empty_set != '#skF_4' )
| ( '#skF_5' != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_96,plain,
'#skF_5' != 0,
inference(splitLeft,[status(thm)],[c_70]) ).
tff(c_68,plain,
( ( empty_set = '#skF_4' )
| ( '#skF_5' = 0 ) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_98,plain,
empty_set = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_96,c_68]) ).
tff(c_80,plain,
cardinality(empty_set) = 0,
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_102,plain,
cardinality('#skF_4') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_98,c_80]) ).
tff(c_71,plain,
cardinality('#skF_4') = '#skF_5',
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_115,plain,
'#skF_5' = 0,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_71]) ).
tff(c_117,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_96,c_115]) ).
tff(c_118,plain,
empty_set != '#skF_4',
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_120,plain,
'#skF_5' = 0,
inference(splitRight,[status(thm)],[c_70]) ).
tff(c_123,plain,
cardinality('#skF_4') = 0,
inference(demodulation,[status(thm),theory(equality)],[c_120,c_71]) ).
tff(c_133,plain,
! [S_37: set] :
( ( empty_set = S_37 )
| ( cardinality(S_37) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_136,plain,
empty_set = '#skF_4',
inference(superposition,[status(thm),theory(equality)],[c_123,c_133]) ).
tff(c_144,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_118,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV421_1 : TPTP v9.0.0. Released v5.0.0.
% 0.11/0.13 % 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
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Apr 9 00:43:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.59/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.59/1.81
% 3.59/1.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------