%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT087_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 : n023.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 3.56s 1.93s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 7 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 11 ( 4 ~; 3 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 30 ( 6 atm; 0 fun; 12 num; 12 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 19 !; 4 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > in > count > cons > append > #nlpp > tail > length > head > nil > #skF_4 > #skF_1 > #skF_2 > #skF_6 > #skF_3 > #skF_5
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
%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(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_75,axiom,
! [Ka: $int] : ( count(Ka,nil) = 0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f_97,negated_conjecture,
~ ~ ! [Na: $int,L: list] : ( count(Na,L) = count(Na,cons(1,L)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f_54,axiom,
! [Xa: $int,L: list] :
( in(Xa,L)
<=> ( ? [Ha: $int,T: list] :
( ( L = cons(Ha,T) )
& ( Xa = Ha ) )
| ? [Ha: $int,T: list] :
( ( L = cons(Ha,T) )
& in(Xa,T) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_conv) ).
tff(f_93,axiom,
! [Na: $int,L: list] :
( in(Na,L)
<=> $greater(count(Na,L),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_8) ).
tff(c_63,plain,
! [K_32a: $int] : ( count(K_32a,nil) = 0 ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_57,plain,
! [N_47a: $int,L_48: list] : ( count(N_47a,cons(1,L_48)) = count(N_47a,L_48) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_72,plain,
! [H_18a: $int,T_19: list] : in(H_18a,cons(H_18a,T_19)),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_50,plain,
! [N_45a: $int,L_46: list] :
( $greater(count(N_45a,L_46),0)
| ~ in(N_45a,L_46) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_173,plain,
! [N_70a: $int,L_71: list] :
( $less(0,count(N_70a,L_71))
| ~ in(N_70a,L_71) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_50]) ).
tff(c_189,plain,
! [H_72a: $int,T_73: list] : $less(0,count(H_72a,cons(H_72a,T_73))),
inference(resolution,[status(thm)],[c_72,c_173]) ).
tff(c_202,plain,
! [L_76: list] : $less(0,count(1,L_76)),
inference(superposition,[status(thm),theory(equality)],[c_57,c_189]) ).
tff(c_209,plain,
$less(0,0),
inference(superposition,[status(thm),theory(equality)],[c_63,c_202]) ).
tff(c_213,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT087_1 : TPTP v9.0.0. Released v6.1.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n023.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 18:17:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.56/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.93
% 3.56/1.93 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------