%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT085_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 : 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 3.98s 2.03s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 28 ( 0 atm; 6 fun; 6 num; 16 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 : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?; 37 :)
% 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_31,axiom,
! [Ka: $int,L: list] : ( head(cons(Ka,L)) = Ka ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
tff(f_72,axiom,
! [Ha: $int,T: list] : ( length(cons(Ha,T)) = $sum(1,length(T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1) ).
tff(f_99,negated_conjecture,
~ ~ ! [L1: list,L2: list] :
( ( length(L1) = length(L2) )
=> ( L1 = L2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(c_81,plain,
! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_64,plain,
! [H_30a: $int,T_31: list] : ( length(cons(H_30a,T_31)) = $sum(1,length(T_31)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_149,plain,
! [H_63a: $int,T_64: list] : ( length(cons(H_63a,T_64)) = $sum(1,length(T_64)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_57,plain,
! [L2_48: list,L1_47: list] :
( ( L2_48 = L1_47 )
| ( length(L2_48) != length(L1_47) ) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_229,plain,
! [H_74a: $int,T_75: list,L2_76: list] :
( ( cons(H_74a,T_75) = L2_76 )
| ( length(L2_76) != $sum(1,length(T_75)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_57]) ).
tff(c_231,plain,
! [H_74a: $int,T_75: list,H_30a: $int,T_31: list] :
( ( cons(H_74a,T_75) = cons(H_30a,T_31) )
| ( $sum(1,length(T_75)) != $sum(1,length(T_31)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_229]) ).
tff(c_411,plain,
! [H_102a: $int,T_103: list,H_100a: $int,T_101: list] :
( ( cons(H_102a,T_103) = cons(H_100a,T_101) )
| ( length(T_103) != length(T_101) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_231]) ).
tff(c_456,plain,
! [H_102a: $int,T_103: list,H_100a: $int,T_101: list] :
( ( head(cons(H_102a,T_103)) = H_100a )
| ( length(T_103) != length(T_101) ) ),
inference(superposition,[status(thm),theory(equality)],[c_411,c_81]) ).
tff(c_501,plain,
! [H_102a: $int,H_100a: $int,T_103: list,T_101: list] :
( ( H_102a = H_100a )
| ( length(T_103) != length(T_101) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_81,c_456]) ).
tff(c_511,plain,
! [T_103: list,T_101: list] : ( length(T_103) != length(T_101) ),
inference(splitLeft,[status(thm)],[c_501]) ).
tff(c_515,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_511]) ).
tff(c_517,plain,
! [H_102a: $int,H_100a: $int] : ( H_102a = H_100a ),
inference(splitRight,[status(thm)],[c_501]) ).
tff(c_519,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : DAT085_1 : TPTP v9.0.0. Released v6.1.0.
% 0.07/0.12 % 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
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 18:17:35 EDT 2025
% 0.13/0.33 % CPUTime :
% 3.98/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/2.04
% 3.98/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------