%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT103_1 : TPTP v9.0.0. Released v6.1.0.
% 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 : n027.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 06:08:07 PM UTC 2025
% Result : Theorem 3.31s 1.82s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 21 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 20 ( 6 ~; 8 |; 5 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 31 ( 13 atm; 5 fun; 6 num; 7 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 : 14 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 10 !; 4 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > cons > #nlpp > tail > head > nil > #skF_3 > #skF_1 > #skF_2
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
%Foreground operators:
tff('#skF_3',type,
'#skF_3': list ).
tff(inRange,type,
inRange: ( $int * list ) > $o ).
tff(tail,type,
tail: list > list ).
tff(nil,type,
nil: list ).
tff(head,type,
head: list > $int ).
tff(cons,type,
cons: ( $int * list ) > list ).
tff('#skF_1',type,
'#skF_1': ( $int * list ) > $int ).
tff('#skF_2',type,
'#skF_2': ( $int * list ) > list ).
tff(f_64,negated_conjecture,
~ ~ ? [L: list,Na: $int] :
( ( L != nil )
& inRange(Na,L)
& $less($difference(Na,head(L)),1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f_55,axiom,
! [Na: $int,L: list] :
( inRange(Na,L)
<=> ( ( L = nil )
| ? [Ka: $int,T: list] :
( ( L = cons(Ka,T) )
& $lesseq(0,Ka)
& $less(Ka,Na)
& inRange(Na,T) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f_31,axiom,
! [Ka: $int,L: list] : ( head(cons(Ka,L)) = Ka ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(c_24,plain,
$less($difference('#skF_4',head('#skF_3')),1),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_37,plain,
$less('#skF_4',$sum(1,head('#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_78,plain,
head('#skF_3') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_37]) ).
tff(c_29,plain,
nil != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_33,plain,
inRange('#skF_4','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_145,plain,
! [N_34a: $int,L_35: list] :
( $less('#skF_1'(N_34a,L_35),N_34a)
| ( nil = L_35 )
| ~ inRange(N_34a,L_35) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_151,plain,
( $less('#skF_1'('#skF_4','#skF_3'),'#skF_4')
| ( nil = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_33,c_145]) ).
tff(c_161,plain,
$less('#skF_1'('#skF_4','#skF_3'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_29,c_151]) ).
tff(c_176,plain,
'#skF_1'('#skF_4','#skF_3') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_161]) ).
tff(c_209,plain,
! [N_43a: $int,L_44: list] :
( ( cons('#skF_1'(N_43a,L_44),'#skF_2'(N_43a,L_44)) = L_44 )
| ( nil = L_44 )
| ~ inRange(N_43a,L_44) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_215,plain,
( ( cons('#skF_1'('#skF_4','#skF_3'),'#skF_2'('#skF_4','#skF_3')) = '#skF_3' )
| ( nil = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_33,c_209]) ).
tff(c_223,plain,
( ( cons('#skE_2','#skF_2'('#skF_4','#skF_3')) = '#skF_3' )
| ( nil = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_176,c_215]) ).
tff(c_233,plain,
cons('#skE_2','#skF_2'('#skF_4','#skF_3')) = '#skF_3',
inference(negUnitSimplification,[status(thm)],[c_29,c_223]) ).
tff(c_47,plain,
! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_252,plain,
head('#skF_3') = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_233,c_47]) ).
tff(c_261,plain,
'#skE_2' = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_78,c_252]) ).
tff(c_167,plain,
'#skF_1'('#skF_4','#skF_3') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_161]) ).
tff(c_166,plain,
$less('#skF_1'('#skF_4','#skF_3'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_29,c_151]) ).
tff(c_174,plain,
$less('#skE_2','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_167,c_166]) ).
tff(c_283,plain,
$less('#skE_1','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_261,c_174]) ).
tff(c_75,plain,
head('#skF_3') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_37]) ).
tff(c_49,plain,
$less('#skF_4',$sum(1,head('#skF_3'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_79,plain,
$less('#skF_4',$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_75,c_49]) ).
tff(c_284,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_283,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : DAT103_1 : TPTP v9.0.0. Released v6.1.0.
% 0.10/0.13 % 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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 18:18:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.31/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.31/1.83
% 3.31/1.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------