%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT029_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 : n007.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 06:07:57 PM UTC 2025
% Result : Theorem 3.42s 1.94s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 2 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 6 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 57 ( 13 atm; 14 fun; 21 num; 9 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 11 ( 10 !; 1 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > empty > #skF_1 > #skF_3 > #skF_2
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff('#skF_1',type,
'#skF_1': collection ).
tff('#skF_3',type,
'#skF_3': $int > $int ).
tff('#skF_2',type,
'#skF_2': collection ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_98,negated_conjecture,
~ ! [U: collection,V: collection] :
( ( ! [Wa: $int] :
( in(Wa,V)
=> $greater(Wa,0) )
& ! [Xa: $int] :
( in(Xa,U)
=> ? [Ya: $int] :
( in(Ya,V)
& $greater($difference($product(2,Xa),$product(5,Ya)),0) ) ) )
=> ! [Za: $int] :
( in(Za,U)
=> $greater(Za,2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(c_37,plain,
in('#skF_4','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_24,plain,
! [X_18a: $int] :
( $greater($difference($product(2,X_18a),$product(5,'#skF_3'(X_18a))),0)
| ~ in(X_18a,'#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_61,plain,
! [X_38a: $int] :
( $less($product(5,'#skF_3'(X_38a)),$product(2,X_38a))
| ~ in(X_38a,'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_67,plain,
$less($product(5,'#skF_3'('#skF_4')),$product(2,'#skF_4')),
inference(resolution,[status(thm)],[c_37,c_61]) ).
tff(c_95,plain,
'#skF_3'('#skF_4') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_67]) ).
tff(c_94,plain,
$less($product(5,'#skF_3'('#skF_4')),$product(2,'#skF_4')),
inference(resolution,[status(thm)],[c_37,c_61]) ).
tff(c_102,plain,
$less($product(5,'#skE_1'),$product(2,'#skF_4')),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_94]) ).
tff(c_51,plain,
in('#skF_4','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_105,plain,
'#skF_3'('#skF_4') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_67]) ).
tff(c_28,plain,
! [X_18a: $int] :
( in('#skF_3'(X_18a),'#skF_2')
| ~ in(X_18a,'#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_112,plain,
( in('#skE_1','#skF_2')
| ~ in('#skF_4','#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_105,c_28]) ).
tff(c_131,plain,
in('#skE_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_51,c_112]) ).
tff(c_21,plain,
! [W_17a: $int] :
( ~ in(W_17a,'#skF_2')
| $greater(W_17a,0) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_33,plain,
! [W_17a: $int] :
( ~ in(W_17a,'#skF_2')
| $less(0,W_17a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).
tff(c_136,plain,
$less(0,'#skE_1'),
inference(resolution,[status(thm)],[c_131,c_33]) ).
tff(c_17,plain,
~ $greater('#skF_4',2),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_38,plain,
~ $less(2,'#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).
tff(c_137,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_102,c_136,c_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT029_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
% 0.13/0.34 % Computer : n007.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 : Mon Apr 7 18:16:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.42/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.42/1.94
% 3.42/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------