TSTP Solution File: SWC395-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC395-1 : 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 : n016.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 11:02:28 EDT 2023
% Result : Unsatisfiable 213.64s 190.73s
% Output : CNFRefutation 214.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 105
% Syntax : Number of formulae : 297 ( 92 unt; 73 typ; 0 def)
% Number of atoms : 548 ( 158 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 627 ( 303 ~; 324 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 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 : 54 ( 54 usr; 8 con; 0-2 aty)
% Number of variables : 154 (; 154 !; 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 > sk5 > 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(sk5,type,
sk5: $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_1654,axiom,
~ memberP(sk2,sk5),
file(unknown,unknown) ).
tff(f_1652,axiom,
memberP(sk1,sk5),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1658,axiom,
( ( nil = sk3 )
| ( nil != sk4 ) ),
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_240,axiom,
! [U,V] :
( ~ ssList(U)
| duplicatefreeP(U)
| ssItem(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_271,axiom,
! [U] :
( ~ ssList(U)
| ssList(tl(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_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(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_1693,axiom,
! [A,B,C,D] :
( ~ ssList(A)
| ( sk3 = A )
| ~ ssList(B)
| ~ ssList(C)
| ( tl(sk4) != B )
| ( app(B,C) != A )
| ~ ssItem(D)
| ( cons(D,nil) != C )
| ( hd(sk4) != D )
| ~ neq(nil,sk4)
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_1481,axiom,
! [W,U,X,Y,V] :
( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
| ~ ssList(X)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ duplicatefreeP(Y)
| ~ ssList(Y) ),
file(unknown,unknown) ).
tff(f_624,axiom,
! [U,V] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_1405,axiom,
! [U,V,W,X] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file(unknown,unknown) ).
tff(f_233,axiom,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file(unknown,unknown) ).
tff(f_464,axiom,
! [U] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file(unknown,unknown) ).
tff(f_1239,axiom,
! [U,V,W] :
( ~ memberP(cons(U,V),W)
| ~ ssList(V)
| ~ ssItem(U)
| ~ ssItem(W)
| memberP(V,W)
| ( W = U ) ),
file(unknown,unknown) ).
tff(f_1191,axiom,
! [U,V,W] :
( ~ memberP(app(U,V),W)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(W)
| memberP(V,W)
| memberP(U,W) ),
file(unknown,unknown) ).
tff(f_912,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| memberP(cons(W,U),V) ),
file(unknown,unknown) ).
tff(f_898,axiom,
! [U,V,W] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file(unknown,unknown) ).
tff(c_388,plain,
~ memberP(sk2,sk5),
inference(cnfTransformation,[status(thm)],[f_1654]) ).
tff(c_386,plain,
memberP(sk1,sk5),
inference(cnfTransformation,[status(thm)],[f_1652]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_390,plain,
( ( sk4 != nil )
| ( sk3 = nil ) ),
inference(cnfTransformation,[status(thm)],[f_1658]) ).
tff(c_393,plain,
( ( sk4 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).
tff(c_395,plain,
( ( sk2 != nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_393]) ).
tff(c_447,plain,
sk2 != nil,
inference(splitLeft,[status(thm)],[c_395]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_397,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_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_398,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_170,plain,
! [V_81,U_80] :
( ssList(app(V_81,U_80))
| ~ ssList(V_81)
| ~ ssList(U_80) ),
inference(cnfTransformation,[status(thm)],[f_334]) ).
tff(c_1539,plain,
! [V_474,U_475] :
( ssList(app(V_474,U_475))
| ~ ssList(V_474)
| ~ ssList(U_475) ),
inference(cnfTransformation,[status(thm)],[f_334]) ).
tff(c_144,plain,
! [V_67,U_66] :
( ssItem(V_67)
| duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
tff(c_729,plain,
! [U_66] :
( duplicatefreeP(U_66)
| ~ ssList(U_66) ),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_1658,plain,
! [V_474,U_475] :
( duplicatefreeP(app(V_474,U_475))
| ~ ssList(V_474)
| ~ ssList(U_475) ),
inference(resolution,[status(thm)],[c_1539,c_729]) ).
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_2338,plain,
! [U_567] :
( ( nil = U_567 )
| ( cons(skaf83(U_567),skaf82(U_567)) = U_567 )
| ~ ssList(U_567) ),
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_2344,plain,
! [U_567] :
( ( tl(U_567) = skaf82(U_567) )
| ~ ssList(skaf82(U_567))
| ~ ssItem(skaf83(U_567))
| ( nil = U_567 )
| ~ ssList(U_567) ),
inference(superposition,[status(thm),theory(equality)],[c_2338,c_192]) ).
tff(c_15212,plain,
! [U_1336] :
( ( tl(U_1336) = skaf82(U_1336) )
| ( nil = U_1336 )
| ~ ssList(U_1336) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2344]) ).
tff(c_15317,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_15212]) ).
tff(c_15357,plain,
tl(sk2) = skaf82(sk2),
inference(negUnitSimplification,[status(thm)],[c_447,c_15317]) ).
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_15389,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_15357,c_208]) ).
tff(c_15402,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_15389]) ).
tff(c_15403,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_447,c_15402]) ).
tff(c_154,plain,
! [U_72] :
( ( nil = U_72 )
| ssList(tl(U_72))
| ~ ssList(U_72) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
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_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_2347,plain,
! [U_567] :
( ( skaf83(U_567) = hd(U_567) )
| ~ ssList(skaf82(U_567))
| ~ ssItem(skaf83(U_567))
| ( nil = U_567 )
| ~ ssList(U_567) ),
inference(superposition,[status(thm),theory(equality)],[c_2338,c_194]) ).
tff(c_11548,plain,
! [U_1145] :
( ( skaf83(U_1145) = hd(U_1145) )
| ( nil = U_1145 )
| ~ ssList(U_1145) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2347]) ).
tff(c_11647,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_11548]) ).
tff(c_11683,plain,
skaf83(sk2) = hd(sk2),
inference(negUnitSimplification,[status(thm)],[c_447,c_11647]) ).
tff(c_11699,plain,
ssItem(hd(sk2)),
inference(superposition,[status(thm),theory(equality)],[c_11683,c_24]) ).
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_218,plain,
! [U_117] :
( ( nil = U_117 )
| ( cons(skaf83(U_117),skaf82(U_117)) = U_117 )
| ~ ssList(U_117) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_11689,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_11683,c_218]) ).
tff(c_11703,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_11689]) ).
tff(c_11704,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_447,c_11703]) ).
tff(c_12536,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_11704,c_192]) ).
tff(c_12601,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_11699,c_26,c_12536]) ).
tff(c_392,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(cnfTransformation,[status(thm)],[f_1693]) ).
tff(c_394,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ( app(tl(sk4),cons(hd(sk4),nil)) = sk1 )
| ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).
tff(c_396,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
| ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_394]) ).
tff(c_10087,plain,
~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
inference(splitLeft,[status(thm)],[c_396]) ).
tff(c_10224,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil)) ),
inference(resolution,[status(thm)],[c_170,c_10087]) ).
tff(c_13764,plain,
~ ssList(cons(hd(sk2),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_12601,c_10224]) ).
tff(c_13767,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_13764]) ).
tff(c_13771,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11699,c_16,c_13767]) ).
tff(c_13772,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ~ neq(sk2,nil)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_396]) ).
tff(c_14094,plain,
~ neq(sk2,nil),
inference(splitLeft,[status(thm)],[c_13772]) ).
tff(c_14097,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_200,c_14094]) ).
tff(c_14103,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_397,c_14097]) ).
tff(c_14105,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_14103]) ).
tff(c_14106,plain,
( ~ neq(nil,sk2)
| ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_13772]) ).
tff(c_14233,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_14106]) ).
tff(c_14236,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_14233]) ).
tff(c_14239,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_14236]) ).
tff(c_14241,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_14239]) ).
tff(c_14243,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_14106]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_14242,plain,
( ~ ssList(cons(hd(sk2),nil))
| ~ ssItem(hd(sk2))
| ~ neq(nil,sk2)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_14106]) ).
tff(c_14490,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_14242]) ).
tff(c_14493,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_14490]) ).
tff(c_14499,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_16,c_14493]) ).
tff(c_14501,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_14499]) ).
tff(c_14502,plain,
( ~ ssItem(hd(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_14242]) ).
tff(c_14524,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_14502]) ).
tff(c_14527,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[c_172,c_14524]) ).
tff(c_14530,plain,
~ ssItem(hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_14527]) ).
tff(c_14533,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_14530]) ).
tff(c_14536,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_14533]) ).
tff(c_14538,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_14536]) ).
tff(c_14539,plain,
( ~ ssItem(hd(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_14502]) ).
tff(c_14709,plain,
~ ssItem(hd(sk2)),
inference(splitLeft,[status(thm)],[c_14539]) ).
tff(c_14712,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_156,c_14709]) ).
tff(c_14715,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_14712]) ).
tff(c_14717,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_14715]) ).
tff(c_14719,plain,
ssItem(hd(sk2)),
inference(splitRight,[status(thm)],[c_14539]) ).
tff(c_14718,plain,
app(tl(sk2),cons(hd(sk2),nil)) = sk1,
inference(splitRight,[status(thm)],[c_14539]) ).
tff(c_358,plain,
! [U_288,V_291,W_287,X_289] :
( ~ ssList(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
| ~ duplicatefreeP(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
| ~ ssItem(V_291)
| ~ ssList(U_288)
| ~ ssList(W_287)
| ~ ssList(X_289) ),
inference(cnfTransformation,[status(thm)],[f_1481]) ).
tff(c_14762,plain,
! [X_289] :
( ~ ssList(app(sk1,cons(hd(sk2),X_289)))
| ~ duplicatefreeP(app(app(tl(sk2),cons(hd(sk2),nil)),cons(hd(sk2),X_289)))
| ~ ssItem(hd(sk2))
| ~ ssList(tl(sk2))
| ~ ssList(nil)
| ~ ssList(X_289) ),
inference(superposition,[status(thm),theory(equality)],[c_14718,c_358]) ).
tff(c_86147,plain,
! [X_4758] :
( ~ ssList(app(sk1,cons(hd(sk2),X_4758)))
| ~ duplicatefreeP(app(sk1,cons(hd(sk2),X_4758)))
| ~ ssList(X_4758) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_14243,c_14719,c_14718,c_14762]) ).
tff(c_86158,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,cons(hd(sk2),tl(sk2))))
| ~ ssList(tl(sk2))
| ( sk2 = nil )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_208,c_86147]) ).
tff(c_86167,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,sk2))
| ( sk2 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_26,c_15357,c_15403,c_15357,c_86158]) ).
tff(c_86168,plain,
( ~ ssList(app(sk1,sk2))
| ~ duplicatefreeP(app(sk1,sk2)) ),
inference(negUnitSimplification,[status(thm)],[c_447,c_86167]) ).
tff(c_86172,plain,
~ duplicatefreeP(app(sk1,sk2)),
inference(splitLeft,[status(thm)],[c_86168]) ).
tff(c_86175,plain,
( ~ ssList(sk1)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_1658,c_86172]) ).
tff(c_86179,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_86175]) ).
tff(c_86180,plain,
~ ssList(app(sk1,sk2)),
inference(splitRight,[status(thm)],[c_86168]) ).
tff(c_86185,plain,
( ~ ssList(sk1)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_170,c_86180]) ).
tff(c_86189,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_86185]) ).
tff(c_86190,plain,
! [V_67] : ssItem(V_67),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_86488,plain,
! [U_82,V_83] :
( ssList(cons(U_82,V_83))
| ~ ssList(V_83) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_172]) ).
tff(c_232,plain,
! [U_130] :
( singletonP(cons(U_130,nil))
| ~ ssList(cons(U_130,nil))
| ~ ssItem(U_130) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_87430,plain,
! [U_4951] :
( singletonP(cons(U_4951,nil))
| ~ ssList(cons(U_4951,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_232]) ).
tff(c_87437,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c_86488,c_87430]) ).
tff(c_87440,plain,
! [U_82] : singletonP(cons(U_82,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_87437]) ).
tff(c_204,plain,
! [V_105,U_104] :
( ( V_105 = U_104 )
| neq(V_105,U_104)
| ~ ssItem(V_105)
| ~ ssItem(U_104) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_87348,plain,
! [V_105,U_104] :
( ( V_105 = U_104 )
| neq(V_105,U_104) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_204]) ).
tff(c_88187,plain,
! [U_5000] :
( ( nil = U_5000 )
| ( cons(skaf83(U_5000),skaf82(U_5000)) = U_5000 )
| ~ ssList(U_5000) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_87293,plain,
! [U_95,V_96] :
( ( hd(cons(U_95,V_96)) = U_95 )
| ~ ssList(V_96) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_194]) ).
tff(c_88199,plain,
! [U_5000] :
( ( skaf83(U_5000) = hd(U_5000) )
| ~ ssList(skaf82(U_5000))
| ( nil = U_5000 )
| ~ ssList(U_5000) ),
inference(superposition,[status(thm),theory(equality)],[c_88187,c_87293]) ).
tff(c_97593,plain,
! [U_5541] :
( ( skaf83(U_5541) = hd(U_5541) )
| ( nil = U_5541 )
| ~ ssList(U_5541) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_88199]) ).
tff(c_97692,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_97593]) ).
tff(c_97730,plain,
skaf83(sk2) = hd(sk2),
inference(negUnitSimplification,[status(thm)],[c_447,c_97692]) ).
tff(c_97734,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_97730,c_218]) ).
tff(c_97738,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_97734]) ).
tff(c_97739,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_447,c_97738]) ).
tff(c_87362,plain,
! [U_93,V_94] :
( ( tl(cons(U_93,V_94)) = V_94 )
| ~ ssList(V_94) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_192]) ).
tff(c_97827,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_97739,c_87362]) ).
tff(c_97893,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_97827]) ).
tff(c_95292,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
| ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_396]) ).
tff(c_95293,plain,
~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
inference(splitLeft,[status(thm)],[c_95292]) ).
tff(c_95442,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil)) ),
inference(resolution,[status(thm)],[c_170,c_95293]) ).
tff(c_98502,plain,
~ ssList(cons(hd(sk2),nil)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_97893,c_95442]) ).
tff(c_98505,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86488,c_98502]) ).
tff(c_98509,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_98505]) ).
tff(c_98510,plain,
( ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ~ neq(sk2,nil)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_95292]) ).
tff(c_98729,plain,
~ neq(sk2,nil),
inference(splitLeft,[status(thm)],[c_98510]) ).
tff(c_98732,plain,
sk2 = nil,
inference(resolution,[status(thm)],[c_87348,c_98729]) ).
tff(c_98736,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_98732]) ).
tff(c_98737,plain,
( ~ neq(nil,sk2)
| ~ ssList(cons(hd(sk2),nil))
| ~ ssList(tl(sk2))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_98510]) ).
tff(c_98877,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_98737]) ).
tff(c_98880,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_98877]) ).
tff(c_98883,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_397,c_98880]) ).
tff(c_98885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_98883]) ).
tff(c_98886,plain,
( ~ ssList(cons(hd(sk2),nil))
| ~ neq(nil,sk2)
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_98737]) ).
tff(c_99195,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_98886]) ).
tff(c_99198,plain,
sk2 = nil,
inference(resolution,[status(thm)],[c_87348,c_99195]) ).
tff(c_99202,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_447,c_99198]) ).
tff(c_99203,plain,
( ~ ssList(cons(hd(sk2),nil))
| ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
inference(splitRight,[status(thm)],[c_98886]) ).
tff(c_99441,plain,
~ ssList(cons(hd(sk2),nil)),
inference(splitLeft,[status(thm)],[c_99203]) ).
tff(c_99444,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_86488,c_99441]) ).
tff(c_99448,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_99444]) ).
tff(c_99450,plain,
ssList(cons(hd(sk2),nil)),
inference(splitRight,[status(thm)],[c_99203]) ).
tff(c_148,plain,
! [U_69] :
( ( app(nil,U_69) = U_69 )
| ~ ssList(U_69) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_99534,plain,
app(nil,cons(hd(sk2),nil)) = cons(hd(sk2),nil),
inference(resolution,[status(thm)],[c_99450,c_148]) ).
tff(c_350,plain,
! [U_273,V_274,W_275] :
( memberP(app(U_273,cons(V_274,W_275)),V_274)
| ~ ssList(app(U_273,cons(V_274,W_275)))
| ~ ssItem(V_274)
| ~ ssList(U_273)
| ~ ssList(W_275) ),
inference(cnfTransformation,[status(thm)],[f_1405]) ).
tff(c_94757,plain,
! [U_273,V_274,W_275] :
( memberP(app(U_273,cons(V_274,W_275)),V_274)
| ~ ssList(app(U_273,cons(V_274,W_275)))
| ~ ssList(U_273)
| ~ ssList(W_275) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_350]) ).
tff(c_115638,plain,
( memberP(cons(hd(sk2),nil),hd(sk2))
| ~ ssList(app(nil,cons(hd(sk2),nil)))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_99534,c_94757]) ).
tff(c_115699,plain,
memberP(cons(hd(sk2),nil),hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_99450,c_99534,c_115638]) ).
tff(c_142,plain,
! [U_65] :
( ~ ssItem(U_65)
| ~ memberP(nil,U_65) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_86200,plain,
! [U_65] : ~ memberP(nil,U_65),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_142]) ).
tff(c_202,plain,
! [U_103] :
( ( cons(skaf44(U_103),nil) = U_103 )
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_322,plain,
! [W_242,U_240,V_241] :
( ( W_242 = U_240 )
| memberP(V_241,W_242)
| ~ ssItem(W_242)
| ~ ssItem(U_240)
| ~ ssList(V_241)
| ~ memberP(cons(U_240,V_241),W_242) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_92271,plain,
! [W_5232,U_5233,V_5234] :
( ( W_5232 = U_5233 )
| memberP(V_5234,W_5232)
| ~ ssList(V_5234)
| ~ memberP(cons(U_5233,V_5234),W_5232) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_322]) ).
tff(c_92283,plain,
! [U_103,W_5232] :
( ( skaf44(U_103) = W_5232 )
| memberP(nil,W_5232)
| ~ ssList(nil)
| ~ memberP(U_103,W_5232)
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_92271]) ).
tff(c_92291,plain,
! [U_103,W_5232] :
( ( skaf44(U_103) = W_5232 )
| memberP(nil,W_5232)
| ~ memberP(U_103,W_5232)
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_92283]) ).
tff(c_92292,plain,
! [U_103,W_5232] :
( ( skaf44(U_103) = W_5232 )
| ~ memberP(U_103,W_5232)
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(negUnitSimplification,[status(thm)],[c_86200,c_92291]) ).
tff(c_115745,plain,
( ( skaf44(cons(hd(sk2),nil)) = hd(sk2) )
| ~ ssList(cons(hd(sk2),nil))
| ~ singletonP(cons(hd(sk2),nil)) ),
inference(resolution,[status(thm)],[c_115699,c_92292]) ).
tff(c_115754,plain,
skaf44(cons(hd(sk2),nil)) = hd(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_87440,c_99450,c_115745]) ).
tff(c_88193,plain,
! [U_5000] :
( ( tl(U_5000) = skaf82(U_5000) )
| ~ ssList(skaf82(U_5000))
| ( nil = U_5000 )
| ~ ssList(U_5000) ),
inference(superposition,[status(thm),theory(equality)],[c_88187,c_87362]) ).
tff(c_101724,plain,
! [U_5742] :
( ( tl(U_5742) = skaf82(U_5742) )
| ( nil = U_5742 )
| ~ ssList(U_5742) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_88193]) ).
tff(c_101829,plain,
( ( tl(sk2) = skaf82(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_397,c_101724]) ).
tff(c_101873,plain,
tl(sk2) = skaf82(sk2),
inference(negUnitSimplification,[status(thm)],[c_447,c_101829]) ).
tff(c_98887,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_98737]) ).
tff(c_99449,plain,
app(tl(sk2),cons(hd(sk2),nil)) = sk1,
inference(splitRight,[status(thm)],[c_99203]) ).
tff(c_316,plain,
! [U_233,W_235,V_234] :
( memberP(U_233,W_235)
| memberP(V_234,W_235)
| ~ ssItem(W_235)
| ~ ssList(U_233)
| ~ ssList(V_234)
| ~ memberP(app(U_233,V_234),W_235) ),
inference(cnfTransformation,[status(thm)],[f_1191]) ).
tff(c_93224,plain,
! [U_233,W_235,V_234] :
( memberP(U_233,W_235)
| memberP(V_234,W_235)
| ~ ssList(U_233)
| ~ ssList(V_234)
| ~ memberP(app(U_233,V_234),W_235) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_316]) ).
tff(c_99733,plain,
! [W_235] :
( memberP(tl(sk2),W_235)
| memberP(cons(hd(sk2),nil),W_235)
| ~ ssList(tl(sk2))
| ~ ssList(cons(hd(sk2),nil))
| ~ memberP(sk1,W_235) ),
inference(superposition,[status(thm),theory(equality)],[c_99449,c_93224]) ).
tff(c_99791,plain,
! [W_235] :
( memberP(tl(sk2),W_235)
| memberP(cons(hd(sk2),nil),W_235)
| ~ memberP(sk1,W_235) ),
inference(demodulation,[status(thm),theory(equality)],[c_99450,c_98887,c_99733]) ).
tff(c_148650,plain,
! [W_8440] :
( memberP(skaf82(sk2),W_8440)
| memberP(cons(hd(sk2),nil),W_8440)
| ~ memberP(sk1,W_8440) ),
inference(demodulation,[status(thm),theory(equality)],[c_101873,c_99791]) ).
tff(c_148657,plain,
! [W_8440] :
( ( skaf44(cons(hd(sk2),nil)) = W_8440 )
| ~ ssList(cons(hd(sk2),nil))
| ~ singletonP(cons(hd(sk2),nil))
| memberP(skaf82(sk2),W_8440)
| ~ memberP(sk1,W_8440) ),
inference(resolution,[status(thm)],[c_148650,c_92292]) ).
tff(c_324150,plain,
! [W_11708] :
( ( hd(sk2) = W_11708 )
| memberP(skaf82(sk2),W_11708)
| ~ memberP(sk1,W_11708) ),
inference(demodulation,[status(thm),theory(equality)],[c_87440,c_99450,c_115754,c_148657]) ).
tff(c_278,plain,
! [W_181,U_179,V_180] :
( memberP(cons(W_181,U_179),V_180)
| ~ ssItem(V_180)
| ~ ssItem(W_181)
| ~ ssList(U_179)
| ~ memberP(U_179,V_180) ),
inference(cnfTransformation,[status(thm)],[f_912]) ).
tff(c_90044,plain,
! [W_5111,U_5112,V_5113] :
( memberP(cons(W_5111,U_5112),V_5113)
| ~ ssList(U_5112)
| ~ memberP(U_5112,V_5113) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_278]) ).
tff(c_90047,plain,
! [U_117,V_5113] :
( memberP(U_117,V_5113)
| ~ ssList(skaf82(U_117))
| ~ memberP(skaf82(U_117),V_5113)
| ( nil = U_117 )
| ~ ssList(U_117) ),
inference(superposition,[status(thm),theory(equality)],[c_218,c_90044]) ).
tff(c_90055,plain,
! [U_117,V_5113] :
( memberP(U_117,V_5113)
| ~ memberP(skaf82(U_117),V_5113)
| ( nil = U_117 )
| ~ ssList(U_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_90047]) ).
tff(c_324157,plain,
! [W_11708] :
( memberP(sk2,W_11708)
| ( sk2 = nil )
| ~ ssList(sk2)
| ( hd(sk2) = W_11708 )
| ~ memberP(sk1,W_11708) ),
inference(resolution,[status(thm)],[c_324150,c_90055]) ).
tff(c_324175,plain,
! [W_11708] :
( memberP(sk2,W_11708)
| ( sk2 = nil )
| ( hd(sk2) = W_11708 )
| ~ memberP(sk1,W_11708) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_324157]) ).
tff(c_324316,plain,
! [W_11711] :
( memberP(sk2,W_11711)
| ( hd(sk2) = W_11711 )
| ~ memberP(sk1,W_11711) ),
inference(negUnitSimplification,[status(thm)],[c_447,c_324175]) ).
tff(c_324329,plain,
( ( hd(sk2) = sk5 )
| ~ memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[c_324316,c_388]) ).
tff(c_324342,plain,
hd(sk2) = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_386,c_324329]) ).
tff(c_101908,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_101873,c_208]) ).
tff(c_101918,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_101908]) ).
tff(c_101919,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_447,c_101918]) ).
tff(c_276,plain,
! [V_177,W_178] :
( memberP(cons(V_177,W_178),V_177)
| ~ ssItem(V_177)
| ~ ssList(W_178) ),
inference(cnfTransformation,[status(thm)],[f_898]) ).
tff(c_87084,plain,
! [V_177,W_178] :
( memberP(cons(V_177,W_178),V_177)
| ~ ssList(W_178) ),
inference(demodulation,[status(thm),theory(equality)],[c_86190,c_276]) ).
tff(c_102205,plain,
( memberP(sk2,hd(sk2))
| ~ ssList(skaf82(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_101919,c_87084]) ).
tff(c_102271,plain,
memberP(sk2,hd(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_102205]) ).
tff(c_324403,plain,
memberP(sk2,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_324342,c_102271]) ).
tff(c_324409,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_388,c_324403]) ).
tff(c_324410,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_395]) ).
tff(c_324412,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_324410,c_386]) ).
tff(c_324411,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_395]) ).
tff(c_324420,plain,
~ memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_324411,c_388]) ).
tff(c_324437,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_324412,c_324420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC395-1 : 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
% 0.14/0.36 % Computer : n016.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 22:13:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 213.64/190.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 213.64/190.76
% 213.64/190.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 214.04/190.81
% 214.04/190.81 Inference rules
% 214.04/190.81 ----------------------
% 214.04/190.81 #Ref : 44
% 214.04/190.81 #Sup : 76533
% 214.04/190.81 #Fact : 0
% 214.04/190.81 #Define : 0
% 214.04/190.81 #Split : 88
% 214.04/190.81 #Chain : 0
% 214.04/190.81 #Close : 0
% 214.04/190.81
% 214.04/190.81 Ordering : KBO
% 214.04/190.81
% 214.04/190.81 Simplification rules
% 214.04/190.81 ----------------------
% 214.04/190.81 #Subsume : 15724
% 214.04/190.81 #Demod : 63631
% 214.04/190.81 #Tautology : 10488
% 214.04/190.81 #SimpNegUnit : 6412
% 214.04/190.81 #BackRed : 399
% 214.04/190.81
% 214.04/190.81 #Partial instantiations: 0
% 214.04/190.81 #Strategies tried : 1
% 214.04/190.81
% 214.04/190.81 Timing (in seconds)
% 214.04/190.81 ----------------------
% 214.04/190.82 Preprocessing : 0.90
% 214.04/190.82 Parsing : 0.46
% 214.04/190.82 CNF conversion : 0.07
% 214.04/190.82 Main loop : 188.74
% 214.04/190.82 Inferencing : 20.45
% 214.04/190.82 Reduction : 83.99
% 214.04/190.82 Demodulation : 62.92
% 214.04/190.82 BG Simplification : 0.55
% 214.04/190.82 Subsumption : 66.56
% 214.04/190.82 Abstraction : 1.40
% 214.04/190.82 MUC search : 0.00
% 214.04/190.82 Cooper : 0.00
% 214.04/190.82 Total : 189.73
% 214.04/190.82 Index Insertion : 0.00
% 214.04/190.82 Index Deletion : 0.00
% 214.04/190.82 Index Matching : 0.00
% 214.04/190.82 BG Taut test : 0.00
%------------------------------------------------------------------------------