%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT084_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/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 : n010.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 06:08:05 PM UTC 2025
% Result : Theorem 3.43s 1.96s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 14 ( 0 atm; 4 fun; 8 num; 2 var)
% Number of types : 3 ( 1 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 : 18 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 4 !; 1 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > in > count > cons > append > #nlpp > tail > length > head > nil > #skF_4 > #skF_7 > #skF_1 > #skF_2 > #skF_6 > #skF_3 > #skF_5
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
%Foreground operators:
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(length,type,
length: list > $int ).
tff('#skF_4',type,
'#skF_4': ( $int * list ) > list ).
tff('#skF_7',type,
'#skF_7': list ).
tff(append,type,
append: ( list * list ) > list ).
tff(count,type,
count: ( $int * list ) > $int ).
tff(cons,type,
cons: ( $int * list ) > list ).
tff(in,type,
in: ( $int * list ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $int * list ) > $int ).
tff('#skF_2',type,
'#skF_2': ( $int * list ) > list ).
tff('#skF_6',type,
'#skF_6': ( $int * list ) > list ).
tff('#skF_3',type,
'#skF_3': ( $int * list ) > $int ).
tff('#skF_5',type,
'#skF_5': ( $int * list ) > $int ).
tff(f_97,negated_conjecture,
~ ~ ? [L: list] : ( length(L) = length(cons(1,L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(f_72,axiom,
! [Ha: $int,T: list] : ( length(cons(Ha,T)) = $sum(1,length(T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1) ).
tff(c_57,plain,
length(cons(1,'#skF_7')) = length('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_130,plain,
length('#skF_7') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_57]) ).
tff(c_129,plain,
length(cons(1,'#skF_7')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_57]) ).
tff(c_135,plain,
'#skE_2' = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_130,c_129,c_57]) ).
tff(c_134,plain,
length('#skF_7') = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_57]) ).
tff(c_137,plain,
length('#skF_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_135,c_134]) ).
tff(c_150,plain,
! [H_58a: $int,T_59: list] : ( length(cons(H_58a,T_59)) = $sum(1,length(T_59)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_133,plain,
length(cons(1,'#skF_7')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_57]) ).
tff(c_156,plain,
$sum(1,length('#skF_7')) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_150,c_133]) ).
tff(c_165,plain,
$sum(1,'#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_137,c_156]) ).
tff(c_168,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : DAT084_1 : TPTP v9.0.0. Released v6.1.0.
% 0.08/0.13 % 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
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 7 18:18:02 EDT 2025
% 0.13/0.35 % CPUTime :
% 3.43/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.43/1.97
% 3.43/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------