TSTP Solution File: DAT100_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT100_1 : TPTP v8.1.2. 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 : 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 : Tue Aug 22 10:37:09 EDT 2023
% Result : Theorem 3.59s 2.14s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 24 unt; 11 typ; 0 def)
% Number of atoms : 80 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 59 ( 23 ~; 32 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 202 ( 17 atm; 0 fun; 168 num; 17 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 34 (; 32 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
%$ inRange > cons > #nlpp > tail > head > nil > #skF_1 > #skF_2
%Foreground sorts:
tff(list,type,
list: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
%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_31,axiom,
! [Ka: $int,L: list] : ( head(cons(Ka,L)) = Ka ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
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_58,negated_conjecture,
~ ~ inRange(4,cons(1,cons(5,cons(2,nil)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
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(c_35,plain,
! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
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_25,plain,
inRange(4,cons(1,cons(5,cons(2,nil)))),
inference(cnfTransformation,[status(thm)],[f_58]) ).
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_78,plain,
! [N_24a: $int,L_25: list] :
( ~ $less('#skF_1'(N_24a,L_25),0)
| ( nil = L_25 )
| ~ inRange(N_24a,L_25) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_14]) ).
tff(c_81,plain,
( ~ $less('#skF_1'(4,cons(1,cons(5,cons(2,nil)))),0)
| ( cons(1,cons(5,cons(2,nil))) = nil ) ),
inference(resolution,[status(thm)],[c_25,c_78]) ).
tff(c_88,plain,
~ $less('#skF_1'(4,cons(1,cons(5,cons(2,nil)))),0),
inference(negUnitSimplification,[status(thm)],[c_32,c_81]) ).
tff(c_120,plain,
'#skF_1'(4,cons(1,cons(5,cons(2,nil)))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_88]) ).
tff(c_130,plain,
! [N_30a: $int,L_31: list] :
( ( cons('#skF_1'(N_30a,L_31),'#skF_2'(N_30a,L_31)) = L_31 )
| ( nil = L_31 )
| ~ inRange(N_30a,L_31) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_136,plain,
( ( cons('#skF_1'(4,cons(1,cons(5,cons(2,nil)))),'#skF_2'(4,cons(1,cons(5,cons(2,nil))))) = cons(1,cons(5,cons(2,nil))) )
| ( cons(1,cons(5,cons(2,nil))) = nil ) ),
inference(resolution,[status(thm)],[c_25,c_130]) ).
tff(c_144,plain,
( ( cons('#skE_1','#skF_2'(4,cons(1,cons(5,cons(2,nil))))) = cons(1,cons(5,cons(2,nil))) )
| ( cons(1,cons(5,cons(2,nil))) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_120,c_136]) ).
tff(c_280,plain,
cons('#skE_1','#skF_2'(4,cons(1,cons(5,cons(2,nil))))) = cons(1,cons(5,cons(2,nil))),
inference(negUnitSimplification,[status(thm)],[c_32,c_144]) ).
tff(c_289,plain,
tail(cons(1,cons(5,cons(2,nil)))) = '#skF_2'(4,cons(1,cons(5,cons(2,nil)))),
inference(superposition,[status(thm),theory(equality)],[c_280,c_34]) ).
tff(c_305,plain,
'#skF_2'(4,cons(1,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_34,c_289]) ).
tff(c_92,plain,
! [N_26a: $int,L_27: list] :
( inRange(N_26a,'#skF_2'(N_26a,L_27))
| ( nil = L_27 )
| ~ inRange(N_26a,L_27) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_29,plain,
! [N_8a: $int,L_9: list] :
( ~ $less('#skF_1'(N_8a,L_9),0)
| ( nil = L_9 )
| ~ inRange(N_8a,L_9) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_14]) ).
tff(c_200,plain,
! [N_39a: $int,L_40: list] :
( ~ $less('#skF_1'(N_39a,'#skF_2'(N_39a,L_40)),0)
| ( nil = '#skF_2'(N_39a,L_40) )
| ( nil = L_40 )
| ~ inRange(N_39a,L_40) ),
inference(resolution,[status(thm)],[c_92,c_29]) ).
tff(c_209,plain,
( ~ $less('#skF_1'(4,'#skF_2'(4,cons(1,cons(5,cons(2,nil))))),0)
| ( '#skF_2'(4,cons(1,cons(5,cons(2,nil)))) = nil )
| ( cons(1,cons(5,cons(2,nil))) = nil ) ),
inference(resolution,[status(thm)],[c_25,c_200]) ).
tff(c_222,plain,
( ~ $less('#skF_1'(4,'#skF_2'(4,cons(1,cons(5,cons(2,nil))))),0)
| ( '#skF_2'(4,cons(1,cons(5,cons(2,nil)))) = nil ) ),
inference(negUnitSimplification,[status(thm)],[c_32,c_209]) ).
tff(c_421,plain,
( ~ $less('#skF_1'(4,cons(5,cons(2,nil))),0)
| ( cons(5,cons(2,nil)) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_305,c_305,c_222]) ).
tff(c_423,plain,
~ $less('#skF_1'(4,cons(5,cons(2,nil))),0),
inference(negUnitSimplification,[status(thm)],[c_32,c_421]) ).
tff(c_427,plain,
'#skF_1'(4,cons(5,cons(2,nil))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_423]) ).
tff(c_31,plain,
! [N_8a: $int,L_9: list] :
( inRange(N_8a,'#skF_2'(N_8a,L_9))
| ( nil = L_9 )
| ~ inRange(N_8a,L_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_361,plain,
( inRange(4,cons(5,cons(2,nil)))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ inRange(4,cons(1,cons(5,cons(2,nil)))) ),
inference(superposition,[status(thm),theory(equality)],[c_305,c_31]) ).
tff(c_365,plain,
( inRange(4,cons(5,cons(2,nil)))
| ( cons(1,cons(5,cons(2,nil))) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_25,c_361]) ).
tff(c_367,plain,
inRange(4,cons(5,cons(2,nil))),
inference(negUnitSimplification,[status(thm)],[c_32,c_365]) ).
tff(c_28,plain,
! [N_8a: $int,L_9: list] :
( ( cons('#skF_1'(N_8a,L_9),'#skF_2'(N_8a,L_9)) = L_9 )
| ( nil = L_9 )
| ~ inRange(N_8a,L_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_386,plain,
( ( cons('#skF_1'(4,cons(5,cons(2,nil))),'#skF_2'(4,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)) )
| ( cons(5,cons(2,nil)) = nil ) ),
inference(resolution,[status(thm)],[c_367,c_28]) ).
tff(c_412,plain,
cons('#skF_1'(4,cons(5,cons(2,nil))),'#skF_2'(4,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)),
inference(negUnitSimplification,[status(thm)],[c_32,c_386]) ).
tff(c_827,plain,
cons('#skE_2','#skF_2'(4,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_412]) ).
tff(c_868,plain,
head(cons(5,cons(2,nil))) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_827,c_35]) ).
tff(c_874,plain,
'#skE_2' = 5,
inference(demodulation,[status(thm),theory(equality)],[c_35,c_868]) ).
tff(c_30,plain,
! [N_8a: $int,L_9: list] :
( $less('#skF_1'(N_8a,L_9),N_8a)
| ( nil = L_9 )
| ~ inRange(N_8a,L_9) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_389,plain,
( $less('#skF_1'(4,cons(5,cons(2,nil))),4)
| ( cons(5,cons(2,nil)) = nil ) ),
inference(resolution,[status(thm)],[c_367,c_30]) ).
tff(c_416,plain,
$less('#skF_1'(4,cons(5,cons(2,nil))),4),
inference(negUnitSimplification,[status(thm)],[c_32,c_389]) ).
tff(c_437,plain,
$less('#skE_2',4),
inference(demodulation,[status(thm),theory(equality)],[c_427,c_416]) ).
tff(c_878,plain,
$less(5,4),
inference(demodulation,[status(thm),theory(equality)],[c_874,c_437]) ).
tff(c_887,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT100_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 13:28:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 3.59/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/2.15
% 3.59/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.59/2.18
% 3.59/2.18 Inference rules
% 3.59/2.18 ----------------------
% 3.59/2.18 #Ref : 0
% 3.59/2.18 #Sup : 146
% 3.59/2.18 #Fact : 0
% 3.59/2.18 #Define : 3
% 3.59/2.18 #Split : 1
% 3.59/2.18 #Chain : 0
% 3.59/2.18 #Close : 0
% 3.59/2.18
% 3.59/2.18 Ordering : LPO
% 3.59/2.18
% 3.59/2.18 Simplification rules
% 3.59/2.18 ----------------------
% 3.59/2.18 #Subsume : 17
% 3.59/2.18 #Demod : 84
% 3.59/2.18 #Tautology : 67
% 3.59/2.18 #SimpNegUnit : 45
% 3.59/2.18 #BackRed : 6
% 3.59/2.18
% 3.59/2.18 #Partial instantiations: 0
% 3.59/2.18 #Strategies tried : 1
% 3.59/2.18
% 3.59/2.18 Timing (in seconds)
% 3.59/2.18 ----------------------
% 3.59/2.18 Preprocessing : 0.54
% 3.59/2.18 Parsing : 0.29
% 3.59/2.18 CNF conversion : 0.03
% 3.59/2.18 Main loop : 0.56
% 3.59/2.18 Inferencing : 0.20
% 3.59/2.18 Reduction : 0.13
% 3.59/2.18 Demodulation : 0.09
% 3.59/2.18 BG Simplification : 0.06
% 3.59/2.18 Subsumption : 0.11
% 3.59/2.18 Abstraction : 0.03
% 3.59/2.18 MUC search : 0.00
% 3.59/2.18 Cooper : 0.03
% 3.59/2.18 Total : 1.15
% 3.59/2.18 Index Insertion : 0.00
% 3.59/2.18 Index Deletion : 0.00
% 3.59/2.18 Index Matching : 0.00
% 3.59/2.18 BG Taut test : 0.00
%------------------------------------------------------------------------------