%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT105_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 : n015.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 3.40s 1.90s
% Output : CNFRefutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 54 ( 24 ~; 24 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 64 ( 21 atm; 7 fun; 14 num; 22 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 34 !; 2 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > cons > #nlpp > tail > head > nil > #skF_1 > #skF_2
%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(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_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/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(f_41,axiom,
! [Ka: $int,L: list] : ( cons(Ka,L) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
tff(f_31,axiom,
! [Ka: $int,L: list] : ( head(cons(Ka,L)) = Ka ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
tff(f_64,negated_conjecture,
~ ~ ! [L: list,Na: $int] :
( ( ( L != nil )
& inRange(Na,L) )
=> $greatereq($difference(Na,head(L)),2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(c_27,plain,
! [N_8a: $int] : inRange(N_8a,nil),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_33,plain,
! [K_6a: $int,L_7: list] : ( cons(K_6a,L_7) != nil ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_36,plain,
! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_19,plain,
! [N_8a: $int,T_15: list,K_14a: $int] :
( ~ inRange(N_8a,T_15)
| inRange(N_8a,cons(K_14a,T_15))
| ~ $lesseq(0,K_14a)
| ~ $less(K_14a,N_8a) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_140,plain,
! [N_38a: $int,T_39: list,K_40a: $int] :
( ~ inRange(N_38a,T_39)
| inRange(N_38a,cons(K_40a,T_39))
| $less(K_40a,0)
| ~ $less(K_40a,N_38a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_24,plain,
! [N_17a: $int,L_16: list] :
( $greatereq($difference(N_17a,head(L_16)),2)
| ~ inRange(N_17a,L_16)
| ( nil = L_16 ) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_26,plain,
! [N_17a: $int,L_16: list] :
( ~ $less(N_17a,$sum(2,head(L_16)))
| ~ inRange(N_17a,L_16)
| ( nil = L_16 ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).
tff(c_149,plain,
! [N_38a: $int,K_40a: $int,T_39: list] :
( ~ $less(N_38a,$sum(2,head(cons(K_40a,T_39))))
| ( cons(K_40a,T_39) = nil )
| ~ inRange(N_38a,T_39)
| $less(K_40a,0)
| ~ $less(K_40a,N_38a) ),
inference(resolution,[status(thm)],[c_140,c_26]) ).
tff(c_165,plain,
! [N_38a: $int,K_40a: $int,T_39: list] :
( ~ $less(N_38a,$sum(2,K_40a))
| ( cons(K_40a,T_39) = nil )
| ~ inRange(N_38a,T_39)
| $less(K_40a,0)
| ~ $less(K_40a,N_38a) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_149]) ).
tff(c_176,plain,
! [N_41a: $int,K_42a: $int,T_43: list] :
( ~ $less(N_41a,$sum(2,K_42a))
| ~ inRange(N_41a,T_43)
| $less(K_42a,0)
| ~ $less(K_42a,N_41a) ),
inference(negUnitSimplification,[status(thm)],[c_33,c_165]) ).
tff(c_189,plain,
! [N_8a: $int,K_42a: $int] :
( ~ $less(N_8a,$sum(2,K_42a))
| $less(K_42a,0)
| ~ $less(K_42a,N_8a) ),
inference(resolution,[status(thm)],[c_27,c_176]) ).
tff(c_191,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT105_1 : TPTP v9.0.0. Released v6.1.0.
% 0.07/0.13 % 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
% 0.13/0.34 % Computer : n015.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 18:17:51 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.40/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/1.90
% 3.40/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------