%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT080_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 : n017.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 06:08:04 PM UTC 2025
% Result : Theorem 3.75s 1.92s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 5 ~; 7 |; 0 &)
% ( 1 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 66 ( 6 atm; 0 fun; 50 num; 10 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 : 19 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% 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:
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(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_96,negated_conjecture,
~ ~ in(4,cons(1,cons(2,cons(3,nil)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
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(f_80,axiom,
! [Ka: $int,Ha: $int,T: list,Na: $int] :
( ( count(Ka,cons(Ha,T)) = count(Ka,T) )
<= ( Ka != Ha ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(c_63,plain,
! [K_32a: $int] : ( count(K_32a,nil) = 0 ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_57,plain,
in(4,cons(1,cons(2,cons(3,nil)))),
inference(cnfTransformation,[status(thm)],[f_96]) ).
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_162,plain,
! [N_66a: $int,L_67: list] :
( $less(0,count(N_66a,L_67))
| ~ in(N_66a,L_67) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_50]) ).
tff(c_178,plain,
$less(0,count(4,cons(1,cons(2,cons(3,nil))))),
inference(resolution,[status(thm)],[c_57,c_162]) ).
tff(c_244,plain,
count(4,cons(1,cons(2,cons(3,nil)))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_178]) ).
tff(c_62,plain,
! [K_33a: $int,H_34a: $int,T_35: list] :
( ( count(K_33a,cons(H_34a,T_35)) = count(K_33a,T_35) )
| ( K_33a = H_34a ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_275,plain,
( ( count(4,cons(2,cons(3,nil))) = '#skE_1' )
| ( 4 = 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_244,c_62]) ).
tff(c_283,plain,
count(4,cons(2,cons(3,nil))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_275]) ).
tff(c_371,plain,
( ( count(4,cons(3,nil)) = '#skE_1' )
| ( 4 = 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_283,c_62]) ).
tff(c_379,plain,
count(4,cons(3,nil)) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_371]) ).
tff(c_389,plain,
( ( count(4,nil) = '#skE_1' )
| ( 4 = 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_379,c_62]) ).
tff(c_396,plain,
( ( '#skE_1' = 0 )
| ( 4 = 3 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_63,c_389]) ).
tff(c_398,plain,
'#skE_1' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_396]) ).
tff(c_241,plain,
count(4,cons(1,cons(2,cons(3,nil)))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_178]) ).
tff(c_245,plain,
$less(0,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_241,c_178]) ).
tff(c_410,plain,
$less(0,0),
inference(demodulation,[status(thm),theory(equality)],[c_398,c_245]) ).
tff(c_416,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT080_1 : TPTP v9.0.0. Released v6.1.0.
% 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
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 18:17:10 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.75/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/1.92
% 3.75/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------