%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT088_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 : n028.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 3.53s 1.92s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 5 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 36 ( 6 atm; 0 fun; 9 num; 21 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 : 14 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 34 !; 4 ?; 38 :)
% 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_41,axiom,
! [Ka: $int,L: list] : ( cons(Ka,L) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f_33,axiom,
! [Ka: $int,L: list] : ( tail(cons(Ka,L)) = L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
tff(f_100,negated_conjecture,
~ ~ ! [Na: $int,L: list] :
( ( L != nil )
=> ( count(Na,L) = count(Na,tail(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_78,plain,
! [K_6a: $int,L_7: list] : ( cons(K_6a,L_7) != nil ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_80,plain,
! [K_3a: $int,L_4: list] : ( tail(cons(K_3a,L_4)) = L_4 ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_130,plain,
! [N_63a: $int,L_64: list] :
( ( count(N_63a,tail(L_64)) = count(N_63a,L_64) )
| ( nil = L_64 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_139,plain,
! [N_63a: $int,K_3a: $int,L_4: list] :
( ( count(N_63a,cons(K_3a,L_4)) = count(N_63a,L_4) )
| ( cons(K_3a,L_4) = nil ) ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_130]) ).
tff(c_145,plain,
! [N_63a: $int,K_3a: $int,L_4: list] : ( count(N_63a,cons(K_3a,L_4)) = count(N_63a,L_4) ),
inference(negUnitSimplification,[status(thm)],[c_78,c_139]) ).
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_178,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_193,plain,
! [H_18a: $int,T_19: list] : $less(0,count(H_18a,cons(H_18a,T_19))),
inference(resolution,[status(thm)],[c_72,c_178]) ).
tff(c_222,plain,
! [H_79a: $int,T_80: list] : $less(0,count(H_79a,T_80)),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_193]) ).
tff(c_228,plain,
$less(0,0),
inference(superposition,[status(thm),theory(equality)],[c_63,c_222]) ).
tff(c_233,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT088_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
% 0.12/0.33 % Computer : n028.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 18:17:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.53/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.53/1.92
% 3.53/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------