%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT013_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 : n018.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 06:07:54 PM UTC 2025
% Result : Theorem 3.06s 1.80s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 2 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 7 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 47 ( 26 atm; 3 fun; 12 num; 6 var)
% Number of types : 2 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 7 con; 0-3 aty)
% Number of variables : 7 ( 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
%$ write > read > #nlpp > #skF_1
%Foreground sorts:
tff(array,type,
array: $tType ).
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
%Foreground operators:
tff(write,type,
write: ( array * $int * $int ) > array ).
tff('#skF_1',type,
'#skF_1': array ).
tff(read,type,
read: ( array * $int ) > $int ).
tff(f_80,negated_conjecture,
~ ! [U: array,Va: $int,Wa: $int] :
( ! [Xa: $int] :
( ( $lesseq(Va,Xa)
& $lesseq(Xa,Wa) )
=> $greater(read(U,Xa),0) )
=> ! [Ya: $int] :
( ( $lesseq($sum(Va,3),Ya)
& $lesseq(Ya,Wa) )
=> $greater(read(U,Ya),0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(c_7,plain,
$lesseq('#skF_4','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_15,plain,
~ $less('#skF_3','#skF_4'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_5,plain,
~ $greater(read('#skF_1','#skF_4'),0),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_19,plain,
~ $less(0,read('#skF_1','#skF_4')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_24,plain,
read('#skF_1','#skF_4') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_19]) ).
tff(c_23,plain,
~ $less(0,read('#skF_1','#skF_4')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_31,plain,
~ $less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_23]) ).
tff(c_30,plain,
read('#skF_1','#skF_4') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_19]) ).
tff(c_11,plain,
! [X_10a: $int] :
( $greater(read('#skF_1',X_10a),0)
| ~ $lesseq('#skF_2',X_10a)
| ~ $lesseq(X_10a,'#skF_3') ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_80,plain,
! [X_23a: $int] :
( $less(0,read('#skF_1',X_23a))
| $less(X_23a,'#skF_2')
| $less('#skF_3',X_23a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_83,plain,
( $less(0,'#skE_1')
| $less('#skF_4','#skF_2')
| $less('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_80]) ).
tff(c_87,plain,
( $less('#skF_4','#skF_2')
| $less('#skF_3','#skF_4') ),
inference(negUnitSimplification,[status(thm)],[c_31,c_83]) ).
tff(c_89,plain,
$less('#skF_4','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_15,c_87]) ).
tff(c_9,plain,
$lesseq($sum('#skF_2',3),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_14,plain,
~ $less('#skF_4',$sum(3,'#skF_2')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_90,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_89,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT013_1 : TPTP v9.0.0. Released v5.0.0.
% 0.11/0.12 % 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 : n018.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 18:15:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.06/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.06/1.80
% 3.06/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------