%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT026_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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n009.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 06:07:56 PM UTC 2025
% Result : Theorem 3.41s 1.84s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 33 ( 13 ~; 12 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 53 ( 11 atm; 8 fun; 18 num; 16 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 : 11 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > empty > #skF_1 > #skF_2
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff('#skF_1',type,
'#skF_1': collection ).
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_95,negated_conjecture,
~ ! [U: collection,V: collection,Wa: $int] :
( ( ! [Xa: $int] :
( in(Xa,V)
=> $greater(Xa,0) )
& in(Wa,V)
& ( U = add($sum(Wa,2),remove(Wa,V)) ) )
=> ! [Ya: $int] :
( in(Ya,U)
=> $greater(Ya,0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f_78,axiom,
! [X3a: $int,X4: collection,X5a: $int] :
( ( in(X3a,X4)
& ( X3a != X5a ) )
<=> in(X3a,remove(X5a,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5) ).
tff(c_17,plain,
~ $greater('#skF_4',0),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_40,plain,
~ $less(0,'#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).
tff(c_39,plain,
in('#skF_4','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_35,plain,
add($sum(2,'#skF_3'),remove('#skF_3','#skF_2')) = '#skF_1',
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_111,plain,
! [Z_45a: $int,X1_46: collection,X2_47a: $int] :
( in(Z_45a,X1_46)
| ~ in(Z_45a,add(X2_47a,X1_46))
| ( Z_45a = X2_47a ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_140,plain,
! [Z_51a: $int] :
( in(Z_51a,remove('#skF_3','#skF_2'))
| ~ in(Z_51a,'#skF_1')
| ( Z_51a = $sum(2,'#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_35,c_111]) ).
tff(c_41,plain,
! [X3_9a: $int,X4_10: collection,X5_11a: $int] :
( in(X3_9a,X4_10)
| ~ in(X3_9a,remove(X5_11a,X4_10)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_183,plain,
! [Z_56a: $int] :
( in(Z_56a,'#skF_2')
| ~ in(Z_56a,'#skF_1')
| ( Z_56a = $sum(2,'#skF_3') ) ),
inference(resolution,[status(thm)],[c_140,c_41]) ).
tff(c_200,plain,
( in('#skF_4','#skF_2')
| ( '#skF_4' = $sum(2,'#skF_3') ) ),
inference(resolution,[status(thm)],[c_39,c_183]) ).
tff(c_203,plain,
'#skF_4' = $sum(2,'#skF_3'),
inference(splitLeft,[status(thm)],[c_200]) ).
tff(c_212,plain,
~ $less(0,$sum(2,'#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_203,c_40]) ).
tff(c_217,plain,
~ $less($uminus(2),'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_212]) ).
tff(c_31,plain,
in('#skF_3','#skF_2'),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_25,plain,
! [X_14a: $int] :
( ~ in(X_14a,'#skF_2')
| $greater(X_14a,0) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_62,plain,
! [X_30a: $int] :
( ~ in(X_30a,'#skF_2')
| $less(0,X_30a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_67,plain,
$less(0,'#skF_3'),
inference(resolution,[status(thm)],[c_31,c_62]) ).
tff(c_218,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_217,c_67]) ).
tff(c_227,plain,
in('#skF_4','#skF_2'),
inference(splitRight,[status(thm)],[c_200]) ).
tff(c_27,plain,
! [X_14a: $int] :
( ~ in(X_14a,'#skF_2')
| $less(0,X_14a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_232,plain,
$less(0,'#skF_4'),
inference(resolution,[status(thm)],[c_227,c_27]) ).
tff(c_233,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_40,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT026_1 : TPTP v9.0.0. Released v5.0.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33 % Computer : n009.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 : Mon Apr 7 18:15:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.41/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.41/1.84
% 3.41/1.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------