%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT089_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 06:08:05 PM UTC 2025
% Result : Theorem 3.64s 1.96s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 9 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 49 ( 8 atm; 4 fun; 13 num; 24 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 : 16 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?; 32 :)
% 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_80,axiom,
! [Ka: $int,Ha: $int,T: list,Na: $int] :
( ( count(Ka,cons(Ha,T)) = count(Ka,T) )
<= ( Ka != Ha ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(f_70,axiom,
length(nil) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(f_72,axiom,
! [Ha: $int,T: list] : ( length(cons(Ha,T)) = $sum(1,length(T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(f_97,negated_conjecture,
~ ~ ! [Na: $int,L: list] : $greatereq(count(Na,L),length(L)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(c_64,plain,
! [K_32a: $int] : ( count(K_32a,nil) = 0 ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_63,plain,
! [K_33a: $int,H_34a: $int,T_35: list] :
( ( count(K_33a,cons(H_34a,T_35)) = count(K_33a,T_35) )
| ( K_33a = H_34a ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_66,plain,
length(nil) = 0,
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_144,plain,
! [H_65a: $int,T_66: list] : ( length(cons(H_65a,T_66)) = $sum(1,length(T_66)) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_56,plain,
! [N_47a: $int,L_48: list] : $greatereq(count(N_47a,L_48),length(L_48)),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_58,plain,
! [N_47a: $int,L_48: list] : ~ $less(count(N_47a,L_48),length(L_48)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_56]) ).
tff(c_244,plain,
! [N_83a: $int,H_84a: $int,T_85: list] : ~ $less(count(N_83a,cons(H_84a,T_85)),$sum(1,length(T_85))),
inference(superposition,[status(thm),theory(equality)],[c_144,c_58]) ).
tff(c_258,plain,
! [N_83a: $int,H_84a: $int] : ~ $less(count(N_83a,cons(H_84a,nil)),$sum(1,0)),
inference(superposition,[status(thm),theory(equality)],[c_66,c_244]) ).
tff(c_261,plain,
! [N_87a: $int,H_88a: $int] : ~ $less(count(N_87a,cons(H_88a,nil)),1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_258]) ).
tff(c_265,plain,
! [K_33a: $int,H_34a: $int] :
( ~ $less(count(K_33a,nil),1)
| ( K_33a = H_34a ) ),
inference(superposition,[status(thm),theory(equality)],[c_63,c_261]) ).
tff(c_266,plain,
! [K_33a: $int,H_34a: $int] :
( ~ $less(0,1)
| ( K_33a = H_34a ) ),
inference(demodulation,[status(thm),theory(equality)],[c_64,c_265]) ).
tff(c_268,plain,
! [K_33a: $int,H_34a: $int] : ( K_33a = H_34a ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_266]) ).
tff(c_270,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT089_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
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Apr 7 18:17:36 EDT 2025
% 0.12/0.32 % CPUTime :
% 3.64/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/1.96
% 3.64/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------