%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT093_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 : n022.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 06:08:06 PM UTC 2025
% Result : Theorem 3.35s 1.91s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 21 ( 0 atm; 12 fun; 9 num; 0 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% 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_70,axiom,
length(nil) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f_87,axiom,
! [L: list] : ( append(nil,L) = L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(f_97,negated_conjecture,
~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum($sum(length(K),length(L)),1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(c_67,plain,
length(nil) = 0,
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_46,plain,
! [L_41: list] : ( append(nil,L_41) = L_41 ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_56,plain,
! [K_47: list,L_48: list] : ( length(append(K_47,L_48)) = $sum($sum(length(L_48),length(K_47)),1) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_57,plain,
! [K_47: list,L_48: list] : ( length(append(K_47,L_48)) = $sum(1,$sum(length(L_48),length(K_47))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_56]) ).
tff(c_132,plain,
! [K_63: list,L_64: list] : ( length(append(K_63,L_64)) = $sum(1,$sum(length(K_63),length(L_64))) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_57]) ).
tff(c_141,plain,
! [L_41: list] : ( $sum(1,$sum(length(nil),length(L_41))) = length(L_41) ),
inference(superposition,[status(thm),theory(equality)],[c_46,c_132]) ).
tff(c_146,plain,
! [L_41: list] : ( $sum(1,$sum(0,length(L_41))) = length(L_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_67,c_141]) ).
tff(c_149,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT093_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
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 18:18:21 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.35/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.35/1.91
% 3.35/1.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------