TSTP Solution File: SWC382-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC382-1 : 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 : n006.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 11:02:24 EDT 2023
% Result : Unsatisfiable 216.31s 194.21s
% Output : CNFRefutation 216.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 100
% Syntax : Number of formulae : 266 ( 98 unt; 72 typ; 0 def)
% Number of atoms : 411 ( 113 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 456 ( 239 ~; 217 |; 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 : 87 (; 87 !; 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_56,axiom,
ssList(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_961,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file(unknown,unknown) ).
tff(f_1653,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1711,axiom,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
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_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1703,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_624,axiom,
! [U,V] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(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(f_613,axiom,
! [U,V] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = 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_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_658,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
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(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_8743,plain,
! [U_883] :
( ( app(nil,U_883) = U_883 )
| ~ ssList(U_883) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_8863,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_8743]) ).
tff(c_12241,plain,
! [U_1162,V_1163] :
( frontsegP(app(U_1162,V_1163),U_1162)
| ~ ssList(app(U_1162,V_1163))
| ~ ssList(U_1162)
| ~ ssList(V_1163) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_12387,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_8863,c_12241]) ).
tff(c_12488,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_8863,c_12387]) ).
tff(c_11905,plain,
! [U_1155,V_1156] :
( rearsegP(app(U_1155,V_1156),V_1156)
| ~ ssList(app(U_1155,V_1156))
| ~ ssList(V_1156)
| ~ ssList(U_1155) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_12048,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_8863,c_11905]) ).
tff(c_12147,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_8863,c_12048]) ).
tff(c_473,plain,
! [U_392] :
( ( app(nil,U_392) = U_392 )
| ~ ssList(U_392) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_593,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_473]) ).
tff(c_3943,plain,
! [U_669,V_670] :
( frontsegP(app(U_669,V_670),U_669)
| ~ ssList(app(U_669,V_670))
| ~ ssList(U_669)
| ~ ssList(V_670) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_4089,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_593,c_3943]) ).
tff(c_4187,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_593,c_4089]) ).
tff(c_384,plain,
neq(sk2,nil),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_394,plain,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(cnfTransformation,[status(thm)],[f_1711]) ).
tff(c_399,plain,
( ~ neq(sk2,nil)
| ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).
tff(c_402,plain,
( ~ segmentP(sk2,sk1)
| ~ singletonP(sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_466,plain,
~ singletonP(sk1),
inference(splitLeft,[status(thm)],[c_402]) ).
tff(c_3612,plain,
! [U_662,V_663] :
( rearsegP(app(U_662,V_663),V_663)
| ~ ssList(app(U_662,V_663))
| ~ ssList(V_663)
| ~ ssList(U_662) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_3755,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_593,c_3612]) ).
tff(c_3851,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_593,c_3755]) ).
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_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
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_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_392,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_1703]) ).
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_392]) ).
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_8020,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_8023,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_8020]) ).
tff(c_8026,plain,
~ ssItem(hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_8023]) ).
tff(c_8029,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_8026]) ).
tff(c_8032,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_8029]) ).
tff(c_742,plain,
! [U_407] :
( ( app(U_407,nil) = U_407 )
| ~ ssList(U_407) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_860,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[c_405,c_742]) ).
tff(c_3746,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_860,c_3612]) ).
tff(c_3845,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_860,c_3746]) ).
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_3855,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_3845,c_256]) ).
tff(c_3858,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_3855]) ).
tff(c_7019,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_3858]) ).
tff(c_8035,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8032,c_7019]) ).
tff(c_8087,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3851,c_8035]) ).
tff(c_8088,plain,
( ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_8209,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_8088]) ).
tff(c_8212,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_8209]) ).
tff(c_8218,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_8212]) ).
tff(c_8223,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8218,c_7019]) ).
tff(c_8275,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3851,c_8223]) ).
tff(c_8276,plain,
( ~ ssItem(hd(sk2))
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_8088]) ).
tff(c_8327,plain,
~ ssItem(hd(sk2)),
inference(splitLeft,[status(thm)],[c_8276]) ).
tff(c_8330,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_8327]) ).
tff(c_8333,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_8330]) ).
tff(c_8338,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8333,c_7019]) ).
tff(c_8390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3851,c_8338]) ).
tff(c_8392,plain,
ssItem(hd(sk2)),
inference(splitRight,[status(thm)],[c_8276]) ).
tff(c_8391,plain,
cons(hd(sk2),nil) = sk1,
inference(splitRight,[status(thm)],[c_8276]) ).
tff(c_2197,plain,
! [U_553] :
( singletonP(cons(U_553,nil))
| ~ ssList(cons(U_553,nil))
| ~ ssItem(U_553) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_2204,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_2197]) ).
tff(c_2209,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2204]) ).
tff(c_8522,plain,
( singletonP(sk1)
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_8391,c_2209]) ).
tff(c_8579,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_8392,c_8522]) ).
tff(c_8581,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_466,c_8579]) ).
tff(c_8582,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_3858]) ).
tff(c_591,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[c_405,c_473]) ).
tff(c_4092,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_3943]) ).
tff(c_4189,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_591,c_4092]) ).
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_4250,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_4189,c_258]) ).
tff(c_4253,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_4250]) ).
tff(c_6972,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_4253]) ).
tff(c_8584,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8582,c_6972]) ).
tff(c_8635,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4187,c_8584]) ).
tff(c_8636,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_4253]) ).
tff(c_8683,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8636,c_384]) ).
tff(c_230,plain,
! [V_129] :
( ~ ssList(V_129)
| ~ neq(V_129,V_129) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_8729,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_8683,c_230]) ).
tff(c_8734,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_8729]) ).
tff(c_8735,plain,
~ segmentP(sk2,sk1),
inference(splitRight,[status(thm)],[c_402]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_15584,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_15587,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_15584]) ).
tff(c_15590,plain,
~ ssItem(hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_15587]) ).
tff(c_15593,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_15590]) ).
tff(c_15596,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_15593]) ).
tff(c_9011,plain,
! [U_897] :
( ( app(U_897,nil) = U_897 )
| ~ ssList(U_897) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_9129,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[c_405,c_9011]) ).
tff(c_12042,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_9129,c_11905]) ).
tff(c_12143,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_9129,c_12042]) ).
tff(c_12153,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_12143,c_256]) ).
tff(c_12156,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_12153]) ).
tff(c_15117,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_12156]) ).
tff(c_15599,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_15596,c_15117]) ).
tff(c_15652,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12147,c_15599]) ).
tff(c_15653,plain,
( ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_16004,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_15653]) ).
tff(c_16007,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_16004]) ).
tff(c_16013,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_16007]) ).
tff(c_16018,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16013,c_15117]) ).
tff(c_16071,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12147,c_16018]) ).
tff(c_16072,plain,
( ~ ssItem(hd(sk2))
| ( cons(hd(sk2),nil) = sk1 ) ),
inference(splitRight,[status(thm)],[c_15653]) ).
tff(c_16287,plain,
~ ssItem(hd(sk2)),
inference(splitLeft,[status(thm)],[c_16072]) ).
tff(c_16290,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_16287]) ).
tff(c_16293,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16290]) ).
tff(c_16298,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16293,c_15117]) ).
tff(c_16351,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12147,c_16298]) ).
tff(c_16353,plain,
ssItem(hd(sk2)),
inference(splitRight,[status(thm)],[c_16072]) ).
tff(c_16352,plain,
cons(hd(sk2),nil) = sk1,
inference(splitRight,[status(thm)],[c_16072]) ).
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_16461,plain,
( ( hd(sk2) = hd(sk1) )
| ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_16352,c_194]) ).
tff(c_16515,plain,
hd(sk2) = hd(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_16353,c_16,c_16461]) ).
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_16443,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_16352,c_240]) ).
tff(c_16501,plain,
! [V_139] :
( ( cons(hd(sk2),V_139) = app(sk1,V_139) )
| ~ ssList(V_139) ),
inference(demodulation,[status(thm),theory(equality)],[c_16353,c_16443]) ).
tff(c_23259,plain,
! [V_1880] :
( ( cons(hd(sk1),V_1880) = app(sk1,V_1880) )
| ~ ssList(V_1880) ),
inference(demodulation,[status(thm),theory(equality)],[c_16515,c_16501]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_11056,plain,
! [U_1065] :
( ( nil = U_1065 )
| ( cons(skaf83(U_1065),skaf82(U_1065)) = U_1065 )
| ~ ssList(U_1065) ),
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_11062,plain,
! [U_1065] :
( ( tl(U_1065) = skaf82(U_1065) )
| ~ ssList(skaf82(U_1065))
| ~ ssItem(skaf83(U_1065))
| ( nil = U_1065 )
| ~ ssList(U_1065) ),
inference(superposition,[status(thm),theory(equality)],[c_11056,c_192]) ).
tff(c_19693,plain,
! [U_1543] :
( ( tl(U_1543) = skaf82(U_1543) )
| ( nil = U_1543 )
| ~ ssList(U_1543) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_11062]) ).
tff(c_19823,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_19693]) ).
tff(c_20282,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_19823]) ).
tff(c_10553,plain,
! [V_1043,U_1044] :
( ( nil = V_1043 )
| ~ ssList(U_1044)
| ~ ssList(V_1043)
| ( app(U_1044,V_1043) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_19438,plain,
! [V_1513] :
( ( nil = V_1513 )
| ~ ssList(V_1513)
| ( app(sk2,V_1513) != nil ) ),
inference(resolution,[status(thm)],[c_405,c_10553]) ).
tff(c_19568,plain,
( ( sk2 = nil )
| ( app(sk2,sk2) != nil ) ),
inference(resolution,[status(thm)],[c_405,c_19438]) ).
tff(c_19575,plain,
app(sk2,sk2) != nil,
inference(splitLeft,[status(thm)],[c_19568]) ).
tff(c_20283,plain,
app(nil,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_20282,c_20282,c_19575]) ).
tff(c_20343,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8863,c_20283]) ).
tff(c_20345,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_19823]) ).
tff(c_20344,plain,
tl(sk2) = skaf82(sk2),
inference(splitRight,[status(thm)],[c_19823]) ).
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_20355,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_20344,c_208]) ).
tff(c_20368,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16515,c_20355]) ).
tff(c_20369,plain,
cons(hd(sk1),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_20345,c_20368]) ).
tff(c_23356,plain,
( ( app(sk1,skaf82(sk2)) = sk2 )
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_23259,c_20369]) ).
tff(c_23677,plain,
app(sk1,skaf82(sk2)) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_23356]) ).
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_8862,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_406,c_8743]) ).
tff(c_18064,plain,
! [U_1415,V_1416,W_1417] :
( segmentP(app(app(U_1415,V_1416),W_1417),V_1416)
| ~ ssList(app(app(U_1415,V_1416),W_1417))
| ~ ssList(V_1416)
| ~ ssList(U_1415)
| ~ ssList(W_1417) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_18270,plain,
! [W_1417] :
( segmentP(app(sk1,W_1417),sk1)
| ~ ssList(app(app(nil,sk1),W_1417))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(W_1417) ),
inference(superposition,[status(thm),theory(equality)],[c_8862,c_18064]) ).
tff(c_239727,plain,
! [W_7558] :
( segmentP(app(sk1,W_7558),sk1)
| ~ ssList(app(sk1,W_7558))
| ~ ssList(W_7558) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_8862,c_18270]) ).
tff(c_239752,plain,
( segmentP(sk2,sk1)
| ~ ssList(app(sk1,skaf82(sk2)))
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_23677,c_239727]) ).
tff(c_239777,plain,
segmentP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_405,c_23677,c_239752]) ).
tff(c_239779,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8735,c_239777]) ).
tff(c_239780,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_19568]) ).
tff(c_239788,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_239780,c_15117]) ).
tff(c_239844,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12147,c_239788]) ).
tff(c_239845,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_12156]) ).
tff(c_8861,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[c_405,c_8743]) ).
tff(c_12393,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_8861,c_12241]) ).
tff(c_12492,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_8861,c_12393]) ).
tff(c_12524,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_12492,c_258]) ).
tff(c_12527,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_12524]) ).
tff(c_15115,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_12527]) ).
tff(c_239947,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_239845,c_15115]) ).
tff(c_239999,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12488,c_239947]) ).
tff(c_240000,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_12527]) ).
tff(c_240048,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_240000,c_384]) ).
tff(c_240169,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_240048,c_230]) ).
tff(c_240174,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_240169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC382-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 21:31:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 216.31/194.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 216.40/194.24
% 216.40/194.24 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 216.60/194.28
% 216.60/194.28 Inference rules
% 216.60/194.28 ----------------------
% 216.60/194.28 #Ref : 33
% 216.60/194.28 #Sup : 56744
% 216.60/194.28 #Fact : 0
% 216.60/194.28 #Define : 0
% 216.60/194.28 #Split : 45
% 216.60/194.28 #Chain : 0
% 216.60/194.28 #Close : 0
% 216.60/194.28
% 216.60/194.28 Ordering : KBO
% 216.60/194.28
% 216.60/194.28 Simplification rules
% 216.60/194.28 ----------------------
% 216.60/194.28 #Subsume : 11991
% 216.60/194.28 #Demod : 56419
% 216.60/194.29 #Tautology : 7862
% 216.60/194.29 #SimpNegUnit : 1691
% 216.60/194.29 #BackRed : 679
% 216.60/194.29
% 216.60/194.29 #Partial instantiations: 0
% 216.60/194.29 #Strategies tried : 1
% 216.60/194.29
% 216.60/194.29 Timing (in seconds)
% 216.60/194.29 ----------------------
% 216.60/194.29 Preprocessing : 0.85
% 216.60/194.29 Parsing : 0.43
% 216.60/194.29 CNF conversion : 0.07
% 216.60/194.29 Main loop : 192.20
% 216.60/194.29 Inferencing : 19.30
% 216.60/194.29 Reduction : 92.22
% 216.60/194.29 Demodulation : 66.84
% 216.60/194.29 BG Simplification : 0.46
% 216.60/194.29 Subsumption : 66.39
% 216.60/194.29 Abstraction : 1.12
% 216.60/194.29 MUC search : 0.00
% 216.60/194.29 Cooper : 0.00
% 216.60/194.29 Total : 193.14
% 216.60/194.29 Index Insertion : 0.00
% 216.60/194.29 Index Deletion : 0.00
% 216.60/194.29 Index Matching : 0.00
% 216.60/194.29 BG Taut test : 0.00
%------------------------------------------------------------------------------