%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT102_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 : n008.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 3.19s 1.76s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 15 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 43 ( 11 atm; 0 fun; 6 num; 26 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 40 !; 2 ?; 42 :)
% 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/sandbox/benchmark/theBenchmark.p',inRange) ).
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_61,negated_conjecture,
~ ~ ! [L: list,Na: $int] :
( inRange(Na,tail(L))
=> inRange(Na,L) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(c_26,plain,
! [N_8a: $int] : inRange(N_8a,nil),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_32,plain,
! [K_6a: $int,L_7: list] : ( cons(K_6a,L_7) != nil ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_34,plain,
! [K_3a: $int,L_4: list] : ( tail(cons(K_3a,L_4)) = L_4 ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_58,plain,
! [N_25a: $int,L_26: list] :
( inRange(N_25a,L_26)
| ~ inRange(N_25a,tail(L_26)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_62,plain,
! [N_25a: $int,K_3a: $int,L_4: list] :
( inRange(N_25a,cons(K_3a,L_4))
| ~ inRange(N_25a,L_4) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_58]) ).
tff(c_121,plain,
! [N_40a: $int,L_41: list] :
( $less('#skF_1'(N_40a,L_41),N_40a)
| ( nil = L_41 )
| ~ inRange(N_40a,L_41) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_127,plain,
! [N_25a: $int,K_3a: $int,L_4: list] :
( $less('#skF_1'(N_25a,cons(K_3a,L_4)),N_25a)
| ( cons(K_3a,L_4) = nil )
| ~ inRange(N_25a,L_4) ),
inference(resolution,[status(thm)],[c_62,c_121]) ).
tff(c_140,plain,
! [N_42a: $int,K_43a: $int,L_44: list] :
( $less('#skF_1'(N_42a,cons(K_43a,L_44)),N_42a)
| ~ inRange(N_42a,L_44) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_127]) ).
tff(c_156,plain,
! [N_45a: $int,K_46a: $int] : $less('#skF_1'(N_45a,cons(K_46a,nil)),N_45a),
inference(resolution,[status(thm)],[c_26,c_140]) ).
tff(c_14,plain,
! [N_8a: $int,L_9: list] :
( $lesseq(0,'#skF_1'(N_8a,L_9))
| ( nil = L_9 )
| ~ inRange(N_8a,L_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_84,plain,
! [N_31a: $int,L_32: list] :
( ~ $less('#skF_1'(N_31a,L_32),0)
| ( nil = L_32 )
| ~ inRange(N_31a,L_32) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_14]) ).
tff(c_87,plain,
! [N_25a: $int,K_3a: $int,L_4: list] :
( ~ $less('#skF_1'(N_25a,cons(K_3a,L_4)),0)
| ( cons(K_3a,L_4) = nil )
| ~ inRange(N_25a,L_4) ),
inference(resolution,[status(thm)],[c_62,c_84]) ).
tff(c_104,plain,
! [N_35a: $int,K_36a: $int,L_37: list] :
( ~ $less('#skF_1'(N_35a,cons(K_36a,L_37)),0)
| ~ inRange(N_35a,L_37) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_87]) ).
tff(c_119,plain,
! [N_8a: $int,K_36a: $int] : ~ $less('#skF_1'(N_8a,cons(K_36a,nil)),0),
inference(resolution,[status(thm)],[c_26,c_104]) ).
tff(c_161,plain,
$false,
inference(resolution,[status(thm)],[c_156,c_119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT102_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/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 : n008.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 18:18:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.19/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.19/1.76
% 3.19/1.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------