TSTP Solution File: SWC079-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC079-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n023.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 11:01:04 EDT 2023
% Result : Unsatisfiable 221.35s 201.38s
% Output : CNFRefutation 221.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 99
% Syntax : Number of formulae : 221 ( 71 unt; 72 typ; 0 def)
% Number of atoms : 336 ( 89 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 388 ( 201 ~; 187 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 65 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 53 ( 53 usr; 7 con; 0-2 aty)
% Number of variables : 80 (; 80 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > skaf48 > skaf47 > skaf46 > skaf45 > skaf43 > skaf42 > cons > app > #nlpp > tl > skaf83 > skaf82 > skaf81 > skaf80 > skaf79 > skaf78 > skaf77 > skaf76 > skaf75 > skaf74 > skaf73 > skaf72 > skaf71 > skaf70 > skaf69 > skaf68 > skaf67 > skaf66 > skaf65 > skaf64 > skaf63 > skaf62 > skaf61 > skaf60 > skaf59 > skaf58 > skaf57 > skaf56 > skaf55 > skaf54 > skaf53 > skaf52 > skaf51 > skaf50 > skaf49 > skaf44 > hd > skac3 > skac2 > sk4 > sk3 > sk2 > sk1 > nil
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(skaf56,type,
skaf56: $i > $i ).
tff(segmentP,type,
segmentP: ( $i * $i ) > $o ).
tff(totalorderedP,type,
totalorderedP: $i > $o ).
tff(equalelemsP,type,
equalelemsP: $i > $o ).
tff(skaf74,type,
skaf74: $i > $i ).
tff(skaf61,type,
skaf61: $i > $i ).
tff(skaf51,type,
skaf51: $i > $i ).
tff(skaf83,type,
skaf83: $i > $i ).
tff(skac2,type,
skac2: $i ).
tff(skaf63,type,
skaf63: $i > $i ).
tff(skaf62,type,
skaf62: $i > $i ).
tff(sk2,type,
sk2: $i ).
tff(skaf52,type,
skaf52: $i > $i ).
tff(skaf50,type,
skaf50: $i > $i ).
tff(skaf42,type,
skaf42: ( $i * $i ) > $i ).
tff(skaf44,type,
skaf44: $i > $i ).
tff(singletonP,type,
singletonP: $i > $o ).
tff(skaf67,type,
skaf67: $i > $i ).
tff(skaf75,type,
skaf75: $i > $i ).
tff(sk1,type,
sk1: $i ).
tff(skaf58,type,
skaf58: $i > $i ).
tff(skaf46,type,
skaf46: ( $i * $i ) > $i ).
tff(frontsegP,type,
frontsegP: ( $i * $i ) > $o ).
tff(skaf70,type,
skaf70: $i > $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff(skaf82,type,
skaf82: $i > $i ).
tff(skaf47,type,
skaf47: ( $i * $i ) > $i ).
tff(skaf76,type,
skaf76: $i > $i ).
tff(skac3,type,
skac3: $i ).
tff(skaf80,type,
skaf80: $i > $i ).
tff(skaf59,type,
skaf59: $i > $i ).
tff(skaf53,type,
skaf53: $i > $i ).
tff(skaf45,type,
skaf45: ( $i * $i ) > $i ).
tff(hd,type,
hd: $i > $i ).
tff(app,type,
app: ( $i * $i ) > $i ).
tff(skaf72,type,
skaf72: $i > $i ).
tff(duplicatefreeP,type,
duplicatefreeP: $i > $o ).
tff(skaf64,type,
skaf64: $i > $i ).
tff(sk4,type,
sk4: $i ).
tff(gt,type,
gt: ( $i * $i ) > $o ).
tff(skaf71,type,
skaf71: $i > $i ).
tff(skaf78,type,
skaf78: $i > $i ).
tff(skaf79,type,
skaf79: $i > $i ).
tff(rearsegP,type,
rearsegP: ( $i * $i ) > $o ).
tff(memberP,type,
memberP: ( $i * $i ) > $o ).
tff(skaf73,type,
skaf73: $i > $i ).
tff(ssList,type,
ssList: $i > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(skaf54,type,
skaf54: $i > $i ).
tff(skaf77,type,
skaf77: $i > $i ).
tff(sk3,type,
sk3: $i ).
tff(skaf66,type,
skaf66: $i > $i ).
tff(strictorderP,type,
strictorderP: $i > $o ).
tff(skaf81,type,
skaf81: $i > $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff(skaf60,type,
skaf60: $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(lt,type,
lt: ( $i * $i ) > $o ).
tff(skaf69,type,
skaf69: $i > $i ).
tff(tl,type,
tl: $i > $i ).
tff(neq,type,
neq: ( $i * $i ) > $o ).
tff(skaf43,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf48,type,
skaf48: ( $i * $i ) > $i ).
tff(skaf65,type,
skaf65: $i > $i ).
tff(skaf57,type,
skaf57: $i > $i ).
tff(nil,type,
nil: $i ).
tff(skaf49,type,
skaf49: $i > $i ).
tff(skaf55,type,
skaf55: $i > $i ).
tff(skaf68,type,
skaf68: $i > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_156,axiom,
! [U] :
( ~ ssList(U)
| segmentP(U,nil) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_1653,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1705,axiom,
! [A] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_975,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_961,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_1725,axiom,
! [A,B] :
( ~ ssList(A)
| ( sk3 = A )
| ~ ssItem(B)
| ( cons(B,nil) != A )
| ( hd(sk4) != B )
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_770,axiom,
! [U,V] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file(unknown,unknown) ).
tff(f_446,axiom,
! [U,V] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file(unknown,unknown) ).
tff(f_1371,axiom,
! [U,V,W,X] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_62,axiom,
! [U] : ssItem(skaf83(U)),
file(unknown,unknown) ).
tff(f_543,axiom,
! [U] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_666,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file(unknown,unknown) ).
tff(f_784,axiom,
! [U,V] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_406,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_112,plain,
! [U_50] :
( segmentP(U_50,nil)
| ~ ssList(U_50) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_405,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_384,plain,
neq(sk2,nil),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_392,plain,
! [A_330] :
( ~ neq(sk4,nil)
| ~ segmentP(sk1,A_330)
| ~ segmentP(sk2,A_330)
| ~ neq(A_330,nil)
| ~ ssList(A_330) ),
inference(cnfTransformation,[status(thm)],[f_1705]) ).
tff(c_399,plain,
! [A_330] :
( ~ neq(sk2,nil)
| ~ segmentP(sk1,A_330)
| ~ segmentP(sk2,A_330)
| ~ neq(A_330,nil)
| ~ ssList(A_330) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_392]) ).
tff(c_8837,plain,
! [A_905] :
( ~ segmentP(sk1,A_905)
| ~ segmentP(sk2,A_905)
| ~ neq(A_905,nil)
| ~ ssList(A_905) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_8845,plain,
( ~ segmentP(sk1,nil)
| ~ neq(nil,nil)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_112,c_8837]) ).
tff(c_8851,plain,
( ~ segmentP(sk1,nil)
| ~ neq(nil,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_8845]) ).
tff(c_9361,plain,
~ neq(nil,nil),
inference(splitLeft,[status(thm)],[c_8851]) ).
tff(c_471,plain,
! [U_393] :
( ( app(nil,U_393) = U_393 )
| ~ ssList(U_393) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_591,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_471]) ).
tff(c_9817,plain,
! [U_971,V_972] :
( frontsegP(app(U_971,V_972),U_971)
| ~ ssList(app(U_971,V_972))
| ~ ssList(U_971)
| ~ ssList(V_972) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_9963,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_9817]) ).
tff(c_10064,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_9963]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_9493,plain,
! [U_964,V_965] :
( rearsegP(app(U_964,V_965),V_965)
| ~ ssList(app(U_964,V_965))
| ~ ssList(V_965)
| ~ ssList(U_964) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_9636,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_9493]) ).
tff(c_9735,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_9636]) ).
tff(c_200,plain,
! [V_102,U_101] :
( ( V_102 = U_101 )
| neq(V_102,U_101)
| ~ ssList(V_102)
| ~ ssList(U_101) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_172,plain,
! [U_82,V_83] :
( ssList(cons(U_82,V_83))
| ~ ssList(V_83)
| ~ ssItem(U_82) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_394,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) = sk3 )
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cnfTransformation,[status(thm)],[f_1725]) ).
tff(c_398,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) = sk1 )
| ~ ssList(cons(hd(sk4),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_394]) ).
tff(c_400,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ( cons(hd(sk2),nil) = sk1 )
| ~ ssList(cons(hd(sk2),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_398]) ).
tff(c_404,plain,
( ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ( cons(hd(sk2),nil) = sk1 )
| ~ ssList(cons(hd(sk2),nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_400]) ).
tff(c_12919,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_12922,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_12919]) ).
tff(c_12925,plain,
~ ssItem(hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_12922]) ).
tff(c_12928,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_12925]) ).
tff(c_12931,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_12928]) ).
tff(c_608,plain,
! [U_398] :
( ( app(U_398,nil) = U_398 )
| ~ ssList(U_398) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_726,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[c_405,c_608]) ).
tff(c_9633,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_726,c_9493]) ).
tff(c_9733,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_726,c_9633]) ).
tff(c_256,plain,
! [V_155,U_154] :
( ( V_155 = U_154 )
| ~ ssList(V_155)
| ~ ssList(U_154)
| ~ rearsegP(V_155,U_154)
| ~ rearsegP(U_154,V_155) ),
inference(cnfTransformation,[status(thm)],[f_770]) ).
tff(c_9746,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_9733,c_256]) ).
tff(c_9749,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_9746]) ).
tff(c_12917,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_9749]) ).
tff(c_13034,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_12931,c_12917]) ).
tff(c_13088,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9735,c_13034]) ).
tff(c_13089,plain,
( ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_13137,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_13089]) ).
tff(c_13140,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_13137]) ).
tff(c_13146,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_13140]) ).
tff(c_13151,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_13146,c_12917]) ).
tff(c_13205,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9735,c_13151]) ).
tff(c_13206,plain,
( ~ ssItem(hd(sk2))
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_13089]) ).
tff(c_13518,plain,
~ ssItem(hd(sk2)),
inference(splitLeft,[status(thm)],[c_13206]) ).
tff(c_13521,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_13518]) ).
tff(c_13524,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_13521]) ).
tff(c_13207,plain,
neq(nil,sk2),
inference(splitRight,[status(thm)],[c_13089]) ).
tff(c_13526,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_13524,c_13207]) ).
tff(c_13582,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9361,c_13526]) ).
tff(c_13584,plain,
ssItem(hd(sk2)),
inference(splitRight,[status(thm)],[c_13206]) ).
tff(c_13583,plain,
cons(hd(sk2),nil) = sk1,
inference(splitRight,[status(thm)],[c_13206]) ).
tff(c_194,plain,
! [U_95,V_96] :
( ( hd(cons(U_95,V_96)) = U_95 )
| ~ ssList(V_96)
| ~ ssItem(U_95) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_13692,plain,
( ( hd(sk2) = hd(sk1) )
| ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_13583,c_194]) ).
tff(c_13739,plain,
hd(sk2) = hd(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_13584,c_16,c_13692]) ).
tff(c_13879,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_13739,c_13583]) ).
tff(c_13880,plain,
ssItem(hd(sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_13739,c_13584]) ).
tff(c_1494,plain,
! [V_466,U_467] :
( ~ ssList(V_466)
| ~ ssItem(U_467)
| ( cons(U_467,V_466) != V_466 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_1593,plain,
! [U_467] :
( ~ ssItem(U_467)
| ( cons(U_467,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1494]) ).
tff(c_13955,plain,
cons(hd(sk1),nil) != nil,
inference(resolution,[status(thm)],[c_13880,c_1593]) ).
tff(c_14099,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_13879,c_13955]) ).
tff(c_727,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_406,c_608]) ).
tff(c_590,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_406,c_471]) ).
tff(c_15428,plain,
! [U_1209,V_1210,W_1211] :
( segmentP(app(app(U_1209,V_1210),W_1211),V_1210)
| ~ ssList(app(app(U_1209,V_1210),W_1211))
| ~ ssList(V_1210)
| ~ ssList(U_1209)
| ~ ssList(W_1211) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_15628,plain,
! [W_1211] :
( segmentP(app(sk1,W_1211),sk1)
| ~ ssList(app(app(nil,sk1),W_1211))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(W_1211) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_15428]) ).
tff(c_239775,plain,
! [W_7348] :
( segmentP(app(sk1,W_7348),sk1)
| ~ ssList(app(sk1,W_7348))
| ~ ssList(W_7348) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_590,c_15628]) ).
tff(c_239810,plain,
( segmentP(sk1,sk1)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_239775]) ).
tff(c_239834,plain,
segmentP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_727,c_239810]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_8203,plain,
! [U_840] :
( ( nil = U_840 )
| ( cons(skaf83(U_840),skaf82(U_840)) = U_840 )
| ~ ssList(U_840) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_192,plain,
! [U_93,V_94] :
( ( tl(cons(U_93,V_94)) = V_94 )
| ~ ssList(V_94)
| ~ ssItem(U_93) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_8209,plain,
! [U_840] :
( ( tl(U_840) = skaf82(U_840) )
| ~ ssList(skaf82(U_840))
| ~ ssItem(skaf83(U_840))
| ( nil = U_840 )
| ~ ssList(U_840) ),
inference(superposition,[status(thm),theory(equality)],[c_8203,c_192]) ).
tff(c_17172,plain,
! [U_1318] :
( ( tl(U_1318) = skaf82(U_1318) )
| ( nil = U_1318 )
| ~ ssList(U_1318) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_8209]) ).
tff(c_17302,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_17172]) ).
tff(c_17599,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_17302]) ).
tff(c_17605,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_17599,c_13207]) ).
tff(c_17662,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9361,c_17605]) ).
tff(c_17664,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_17302]) ).
tff(c_17663,plain,
tl(sk2) = skaf82(sk2),
inference(splitRight,[status(thm)],[c_17302]) ).
tff(c_208,plain,
! [U_108] :
( ( nil = U_108 )
| ( cons(hd(U_108),tl(U_108)) = U_108 )
| ~ ssList(U_108) ),
inference(cnfTransformation,[status(thm)],[f_492]) ).
tff(c_17674,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_17663,c_208]) ).
tff(c_17687,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_13739,c_17674]) ).
tff(c_17688,plain,
cons(hd(sk1),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_17664,c_17687]) ).
tff(c_240,plain,
! [U_138,V_139] :
( ( app(cons(U_138,nil),V_139) = cons(U_138,V_139) )
| ~ ssList(V_139)
| ~ ssItem(U_138) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_13677,plain,
! [V_139] :
( ( cons(hd(sk2),V_139) = app(sk1,V_139) )
| ~ ssList(V_139)
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_13583,c_240]) ).
tff(c_13727,plain,
! [V_139] :
( ( cons(hd(sk2),V_139) = app(sk1,V_139) )
| ~ ssList(V_139) ),
inference(demodulation,[status(thm),theory(equality)],[c_13584,c_13677]) ).
tff(c_20915,plain,
! [V_1699] :
( ( cons(hd(sk1),V_1699) = app(sk1,V_1699) )
| ~ ssList(V_1699) ),
inference(demodulation,[status(thm),theory(equality)],[c_13739,c_13727]) ).
tff(c_21273,plain,
( ( app(sk1,skaf82(sk2)) = sk2 )
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_17688,c_20915]) ).
tff(c_21481,plain,
app(sk1,skaf82(sk2)) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_21273]) ).
tff(c_239803,plain,
( segmentP(sk2,sk1)
| ~ ssList(app(sk1,skaf82(sk2)))
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_21481,c_239775]) ).
tff(c_239830,plain,
segmentP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_405,c_21481,c_239803]) ).
tff(c_402,plain,
! [A_330] :
( ~ segmentP(sk1,A_330)
| ~ segmentP(sk2,A_330)
| ~ neq(A_330,nil)
| ~ ssList(A_330) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_239866,plain,
( ~ segmentP(sk1,sk1)
| ~ neq(sk1,nil)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_239830,c_402]) ).
tff(c_239882,plain,
~ neq(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_239834,c_239866]) ).
tff(c_239885,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_200,c_239882]) ).
tff(c_239891,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_239885]) ).
tff(c_239893,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14099,c_239891]) ).
tff(c_239894,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_9749]) ).
tff(c_589,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[c_405,c_471]) ).
tff(c_9969,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_589,c_9817]) ).
tff(c_10068,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_589,c_9969]) ).
tff(c_258,plain,
! [V_157,U_156] :
( ( V_157 = U_156 )
| ~ ssList(V_157)
| ~ ssList(U_156)
| ~ frontsegP(V_157,U_156)
| ~ frontsegP(U_156,V_157) ),
inference(cnfTransformation,[status(thm)],[f_784]) ).
tff(c_10100,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_10068,c_258]) ).
tff(c_10103,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_10100]) ).
tff(c_12916,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_10103]) ).
tff(c_239896,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_239894,c_12916]) ).
tff(c_239949,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10064,c_239896]) ).
tff(c_239950,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_10103]) ).
tff(c_240000,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_239950,c_384]) ).
tff(c_240011,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9361,c_240000]) ).
tff(c_240012,plain,
~ segmentP(sk1,nil),
inference(splitRight,[status(thm)],[c_8851]) ).
tff(c_240016,plain,
~ ssList(sk1),
inference(resolution,[status(thm)],[c_112,c_240012]) ).
tff(c_240020,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_406,c_240016]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC079-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % 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
% 0.14/0.36 % Computer : n023.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 21:44:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 221.35/201.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 221.44/201.40
% 221.44/201.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 221.44/201.44
% 221.44/201.44 Inference rules
% 221.44/201.44 ----------------------
% 221.44/201.44 #Ref : 32
% 221.44/201.44 #Sup : 56794
% 221.44/201.44 #Fact : 0
% 221.44/201.44 #Define : 0
% 221.44/201.44 #Split : 45
% 221.44/201.44 #Chain : 0
% 221.44/201.44 #Close : 0
% 221.44/201.44
% 221.44/201.44 Ordering : KBO
% 221.44/201.44
% 221.44/201.44 Simplification rules
% 221.44/201.44 ----------------------
% 221.44/201.44 #Subsume : 11957
% 221.44/201.44 #Demod : 56769
% 221.44/201.44 #Tautology : 7807
% 221.44/201.44 #SimpNegUnit : 1696
% 221.44/201.44 #BackRed : 637
% 221.44/201.44
% 221.44/201.44 #Partial instantiations: 0
% 221.44/201.44 #Strategies tried : 1
% 221.44/201.44
% 221.44/201.44 Timing (in seconds)
% 221.44/201.44 ----------------------
% 221.44/201.44 Preprocessing : 0.99
% 221.44/201.44 Parsing : 0.52
% 221.44/201.44 CNF conversion : 0.07
% 221.44/201.44 Main loop : 199.33
% 221.44/201.44 Inferencing : 24.53
% 221.44/201.44 Reduction : 90.93
% 221.44/201.44 Demodulation : 66.83
% 221.44/201.44 BG Simplification : 0.48
% 221.44/201.44 Subsumption : 68.60
% 221.44/201.44 Abstraction : 1.13
% 221.44/201.44 MUC search : 0.00
% 221.44/201.44 Cooper : 0.00
% 221.44/201.44 Total : 200.40
% 221.44/201.44 Index Insertion : 0.00
% 221.44/201.44 Index Deletion : 0.00
% 221.44/201.45 Index Matching : 0.00
% 221.44/201.45 BG Taut test : 0.00
%------------------------------------------------------------------------------