TSTP Solution File: SWC184-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC184-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : 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 11:01:31 EDT 2023
% Result : Unsatisfiable 146.83s 126.95s
% Output : CNFRefutation 147.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 130
% Syntax : Number of formulae : 711 ( 294 unt; 76 typ; 0 def)
% Number of atoms : 1394 ( 398 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1553 ( 794 ~; 759 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 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 : 57 ( 57 usr; 11 con; 0-2 aty)
% Number of variables : 289 (; 289 !; 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 > sk8 > sk7 > sk6 > 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(sk6,type,
sk6: $i ).
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(sk8,type,
sk8: $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(sk7,type,
sk7: $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_1651,axiom,
ssItem(sk5),
file(unknown,unknown) ).
tff(f_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_437,axiom,
! [U,V] :
( ( cons(U,V) != nil )
| ~ ssItem(U)
| ~ ssList(V) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file(unknown,unknown) ).
tff(f_1652,axiom,
ssList(sk6),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = 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_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_1653,axiom,
ssList(sk7),
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_770,axiom,
! [U,V] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1660,axiom,
( ssItem(sk8)
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_1685,axiom,
( ( cons(sk8,nil) = sk3 )
| ( nil = sk3 ) ),
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_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
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(f_1422,axiom,
! [U,V,W,X] :
( ~ frontsegP(cons(U,V),cons(W,X))
| ~ ssList(X)
| ~ ssList(V)
| ~ ssItem(W)
| ~ ssItem(U)
| ( U = W ) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_1654,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
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_1051,axiom,
! [U,V,W] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file(unknown,unknown) ).
tff(f_1460,axiom,
! [U,V,W,X] :
( ~ frontsegP(U,V)
| ( W != X )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(W)
| frontsegP(cons(W,U),cons(X,V)) ),
file(unknown,unknown) ).
tff(f_926,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,W),V) ),
file(unknown,unknown) ).
tff(f_1666,axiom,
( ( cons(sk8,nil) = sk3 )
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_446,axiom,
! [U,V] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
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_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_233,axiom,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file(unknown,unknown) ).
tff(f_756,axiom,
! [U,V] :
( ~ segmentP(U,V)
| ~ segmentP(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_647,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
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_132,axiom,
! [U] : ssItem(skaf44(U)),
file(unknown,unknown) ).
tff(f_464,axiom,
! [U] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file(unknown,unknown) ).
tff(f_197,axiom,
! [U] :
( ~ ssItem(U)
| equalelemsP(cons(U,nil)) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [U] :
( ~ ssItem(U)
| strictorderedP(cons(U,nil)) ),
file(unknown,unknown) ).
tff(f_715,axiom,
! [U,V] :
( ~ strictorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| strictorderedP(V)
| ( nil = V ) ),
file(unknown,unknown) ).
tff(f_624,axiom,
! [U,V] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file(unknown,unknown) ).
tff(f_1657,axiom,
( memberP(sk6,sk5)
| memberP(sk7,sk5) ),
file(unknown,unknown) ).
tff(f_702,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(V) ) ),
file(unknown,unknown) ).
tff(f_1669,axiom,
( memberP(sk4,sk8)
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_940,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file(unknown,unknown) ).
tff(f_1688,axiom,
( memberP(sk4,sk8)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(f_294,axiom,
! [U] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_1663,axiom,
( ssItem(sk8)
| ( nil = sk3 ) ),
file(unknown,unknown) ).
tff(c_384,plain,
ssItem(sk5),
inference(cnfTransformation,[status(thm)],[f_1651]) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_244761,plain,
! [V_9979,U_9980] :
( ~ ssList(V_9979)
| ~ ssItem(U_9980)
| ( cons(U_9980,V_9979) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_245272,plain,
! [U_10026] :
( ~ ssItem(U_10026)
| ( cons(U_10026,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_244761]) ).
tff(c_245348,plain,
cons(sk5,nil) != nil,
inference(resolution,[status(thm)],[c_384,c_245272]) ).
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_386,plain,
ssList(sk6),
inference(cnfTransformation,[status(thm)],[f_1652]) ).
tff(c_243833,plain,
! [U_9909] :
( ( app(U_9909,nil) = U_9909 )
| ~ ssList(U_9909) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_243951,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_243833]) ).
tff(c_247087,plain,
! [U_10198,V_10199] :
( frontsegP(app(U_10198,V_10199),U_10198)
| ~ ssList(app(U_10198,V_10199))
| ~ ssList(U_10198)
| ~ ssList(V_10199) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_247242,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_243951,c_247087]) ).
tff(c_247343,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_243951,c_247242]) ).
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_388,plain,
ssList(sk7),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_243953,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_243833]) ).
tff(c_247360,plain,
! [U_10200,V_10201] :
( rearsegP(app(U_10200,V_10201),V_10201)
| ~ ssList(app(U_10200,V_10201))
| ~ ssList(V_10201)
| ~ ssList(U_10200) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_247512,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_243953,c_247360]) ).
tff(c_247614,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_243953,c_247512]) ).
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_247908,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_247614,c_256]) ).
tff(c_247911,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_247908]) ).
tff(c_250869,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_247911]) ).
tff(c_210110,plain,
! [V_7861,U_7862] :
( ~ ssList(V_7861)
| ~ ssItem(U_7862)
| ( cons(U_7862,V_7861) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_210555,plain,
! [U_7931] :
( ~ ssItem(U_7931)
| ( cons(U_7931,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_210110]) ).
tff(c_210635,plain,
cons(sk5,nil) != nil,
inference(resolution,[status(thm)],[c_384,c_210555]) ).
tff(c_209115,plain,
! [U_7783] :
( ( app(U_7783,nil) = U_7783 )
| ~ ssList(U_7783) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_209236,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_209115]) ).
tff(c_212083,plain,
! [U_8059,V_8060] :
( rearsegP(app(U_8059,V_8060),V_8060)
| ~ ssList(app(U_8059,V_8060))
| ~ ssList(V_8060)
| ~ ssList(U_8059) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_212226,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_209236,c_212083]) ).
tff(c_212328,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_209236,c_212226]) ).
tff(c_212341,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_212328,c_256]) ).
tff(c_212344,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_212341]) ).
tff(c_215285,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_212344]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_394,plain,
( ( sk4 = nil )
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1660]) ).
tff(c_417,plain,
( ( sk2 = nil )
| ssItem(sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).
tff(c_469,plain,
ssItem(sk8),
inference(splitLeft,[status(thm)],[c_417]) ).
tff(c_622,plain,
! [U_391] :
( ( app(U_391,nil) = U_391 )
| ~ ssList(U_391) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_746,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_622]) ).
tff(c_127599,plain,
! [U_4842,V_4843] :
( rearsegP(app(U_4842,V_4843),V_4843)
| ~ ssList(app(U_4842,V_4843))
| ~ ssList(V_4843)
| ~ ssList(U_4842) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_127742,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_127599]) ).
tff(c_127835,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_746,c_127742]) ).
tff(c_127925,plain,
! [U_4846,V_4847] :
( frontsegP(app(U_4846,V_4847),U_4846)
| ~ ssList(app(U_4846,V_4847))
| ~ ssList(U_4846)
| ~ ssList(V_4847) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_128071,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_127925]) ).
tff(c_128166,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_746,c_128071]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
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_421,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_404,plain,
( ( sk3 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1685]) ).
tff(c_410,plain,
( ( sk1 = nil )
| ( cons(sk8,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_404]) ).
tff(c_124452,plain,
cons(sk8,nil) = sk1,
inference(splitLeft,[status(thm)],[c_410]) ).
tff(c_126790,plain,
! [U_4789,V_4790] :
( ( app(cons(U_4789,nil),V_4790) = cons(U_4789,V_4790) )
| ~ ssList(V_4790)
| ~ ssItem(U_4789) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_126805,plain,
! [V_4790] :
( ( cons(sk8,V_4790) = app(sk1,V_4790) )
| ~ ssList(V_4790)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_126790]) ).
tff(c_139973,plain,
! [V_5579] :
( ( cons(sk8,V_5579) = app(sk1,V_5579) )
| ~ ssList(V_5579) ),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_126805]) ).
tff(c_140105,plain,
! [U_2] : ( cons(sk8,skaf82(U_2)) = app(sk1,skaf82(U_2)) ),
inference(resolution,[status(thm)],[c_26,c_139973]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_126338,plain,
! [U_4736] :
( ( nil = U_4736 )
| ( cons(skaf83(U_4736),skaf82(U_4736)) = U_4736 )
| ~ ssList(U_4736) ),
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_126344,plain,
! [U_4736] :
( ( tl(U_4736) = skaf82(U_4736) )
| ~ ssList(skaf82(U_4736))
| ~ ssItem(skaf83(U_4736))
| ( nil = U_4736 )
| ~ ssList(U_4736) ),
inference(superposition,[status(thm),theory(equality)],[c_126338,c_192]) ).
tff(c_137091,plain,
! [U_5486] :
( ( tl(U_5486) = skaf82(U_5486) )
| ( nil = U_5486 )
| ~ ssList(U_5486) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_126344]) ).
tff(c_137235,plain,
( ( tl(sk6) = skaf82(sk6) )
| ( sk6 = nil ) ),
inference(resolution,[status(thm)],[c_386,c_137091]) ).
tff(c_137380,plain,
sk6 = nil,
inference(splitLeft,[status(thm)],[c_137235]) ).
tff(c_126408,plain,
! [V_4760,U_4761] :
( ( nil = V_4760 )
| ~ ssList(U_4761)
| ~ ssList(V_4760)
| ( app(U_4761,V_4760) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_135346,plain,
! [V_5269] :
( ( nil = V_5269 )
| ~ ssList(V_5269)
| ( app(sk6,V_5269) != nil ) ),
inference(resolution,[status(thm)],[c_386,c_126408]) ).
tff(c_135491,plain,
( ( sk6 = nil )
| ( app(sk6,sk6) != nil ) ),
inference(resolution,[status(thm)],[c_386,c_135346]) ).
tff(c_135493,plain,
app(sk6,sk6) != nil,
inference(splitLeft,[status(thm)],[c_135491]) ).
tff(c_137384,plain,
app(nil,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_137380,c_137380,c_135493]) ).
tff(c_137448,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_746,c_137384]) ).
tff(c_137450,plain,
sk6 != nil,
inference(splitRight,[status(thm)],[c_137235]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_137449,plain,
tl(sk6) = skaf82(sk6),
inference(splitRight,[status(thm)],[c_137235]) ).
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_137460,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_137449,c_208]) ).
tff(c_137473,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_137460]) ).
tff(c_137474,plain,
cons(hd(sk6),skaf82(sk6)) = sk6,
inference(negUnitSimplification,[status(thm)],[c_137450,c_137473]) ).
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_137940,plain,
( memberP(sk6,hd(sk6))
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6)) ),
inference(superposition,[status(thm),theory(equality)],[c_137474,c_276]) ).
tff(c_138000,plain,
( memberP(sk6,hd(sk6))
| ~ ssItem(hd(sk6)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_137940]) ).
tff(c_138961,plain,
~ ssItem(hd(sk6)),
inference(splitLeft,[status(thm)],[c_138000]) ).
tff(c_138964,plain,
( ( sk6 = nil )
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[c_156,c_138961]) ).
tff(c_138967,plain,
sk6 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_386,c_138964]) ).
tff(c_138969,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_137450,c_138967]) ).
tff(c_138971,plain,
ssItem(hd(sk6)),
inference(splitRight,[status(thm)],[c_138000]) ).
tff(c_131970,plain,
! [W_5029,U_5030,V_5031,X_5032] :
( ( W_5029 = U_5030 )
| ~ ssItem(U_5030)
| ~ ssItem(W_5029)
| ~ ssList(V_5031)
| ~ ssList(X_5032)
| ~ frontsegP(cons(U_5030,V_5031),cons(W_5029,X_5032)) ),
inference(cnfTransformation,[status(thm)],[f_1422]) ).
tff(c_132003,plain,
! [U_5030,V_5031] :
( ( sk8 = U_5030 )
| ~ ssItem(U_5030)
| ~ ssItem(sk8)
| ~ ssList(V_5031)
| ~ ssList(nil)
| ~ frontsegP(cons(U_5030,V_5031),sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_131970]) ).
tff(c_162165,plain,
! [U_6326,V_6327] :
( ( sk8 = U_6326 )
| ~ ssItem(U_6326)
| ~ ssList(V_6327)
| ~ frontsegP(cons(U_6326,V_6327),sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_132003]) ).
tff(c_162249,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk6,sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_137474,c_162165]) ).
tff(c_162350,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk6,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_138971,c_162249]) ).
tff(c_162564,plain,
~ frontsegP(sk6,sk1),
inference(splitLeft,[status(thm)],[c_162350]) ).
tff(c_759,plain,
! [U_400] :
( ( app(nil,U_400) = U_400 )
| ~ ssList(U_400) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_879,plain,
! [U_2] : ( app(nil,skaf82(U_2)) = skaf82(U_2) ),
inference(resolution,[status(thm)],[c_26,c_759]) ).
tff(c_127963,plain,
! [U_2] :
( frontsegP(skaf82(U_2),nil)
| ~ ssList(app(nil,skaf82(U_2)))
| ~ ssList(nil)
| ~ ssList(skaf82(U_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_879,c_127925]) ).
tff(c_128094,plain,
! [U_2] : frontsegP(skaf82(U_2),nil),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_16,c_26,c_879,c_127963]) ).
tff(c_132000,plain,
! [W_5029,X_5032] :
( ( sk8 = W_5029 )
| ~ ssItem(sk8)
| ~ ssItem(W_5029)
| ~ ssList(nil)
| ~ ssList(X_5032)
| ~ frontsegP(sk1,cons(W_5029,X_5032)) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_131970]) ).
tff(c_162782,plain,
! [W_6344,X_6345] :
( ( sk8 = W_6344 )
| ~ ssItem(W_6344)
| ~ ssList(X_6345)
| ~ frontsegP(sk1,cons(W_6344,X_6345)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_132000]) ).
tff(c_162869,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_137474,c_162782]) ).
tff(c_162970,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_138971,c_162869]) ).
tff(c_162987,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_162970]) ).
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_390,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(cnfTransformation,[status(thm)],[f_1654]) ).
tff(c_133697,plain,
! [U_5085,V_5086,W_5087] :
( segmentP(app(app(U_5085,V_5086),W_5087),V_5086)
| ~ ssList(app(app(U_5085,V_5086),W_5087))
| ~ ssList(V_5086)
| ~ ssList(U_5085)
| ~ ssList(W_5087) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_133825,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_133697]) ).
tff(c_133986,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_421,c_390,c_133825]) ).
tff(c_140772,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_133986]) ).
tff(c_140775,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_140772]) ).
tff(c_140779,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_140775]) ).
tff(c_140781,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_133986]) ).
tff(c_131027,plain,
! [W_4990,V_4991,U_4992] :
( ( app(app(W_4990,V_4991),U_4992) = app(W_4990,app(V_4991,U_4992)) )
| ~ ssList(W_4990)
| ~ ssList(V_4991)
| ~ ssList(U_4992) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_131137,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_131027]) ).
tff(c_131274,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_131137]) ).
tff(c_168384,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_140781,c_131274]) ).
tff(c_168437,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_168384]) ).
tff(c_168473,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_168437]) ).
tff(c_288,plain,
! [U_192,V_193] :
( frontsegP(app(U_192,V_193),U_192)
| ~ ssList(app(U_192,V_193))
| ~ ssList(U_192)
| ~ ssList(V_193) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_168534,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_168473,c_288]) ).
tff(c_168583,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_421,c_168473,c_168534]) ).
tff(c_168584,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_162987,c_168583]) ).
tff(c_168601,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_168584]) ).
tff(c_168605,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_168601]) ).
tff(c_168606,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_162970]) ).
tff(c_168680,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_168606,c_137474]) ).
tff(c_131525,plain,
! [X_4998,U_4999,V_5000] :
( frontsegP(cons(X_4998,U_4999),cons(X_4998,V_5000))
| ~ ssItem(X_4998)
| ~ ssList(U_4999)
| ~ ssList(V_5000)
| ~ frontsegP(U_4999,V_5000) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_131559,plain,
! [U_4999] :
( frontsegP(cons(sk8,U_4999),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_4999)
| ~ ssList(nil)
| ~ frontsegP(U_4999,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_131525]) ).
tff(c_131573,plain,
! [U_4999] :
( frontsegP(cons(sk8,U_4999),sk1)
| ~ ssList(U_4999)
| ~ frontsegP(U_4999,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_131559]) ).
tff(c_169118,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_168680,c_131573]) ).
tff(c_169230,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_128094,c_26,c_169118]) ).
tff(c_169232,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_162564,c_169230]) ).
tff(c_169233,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_162350]) ).
tff(c_169247,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_169233,c_137474]) ).
tff(c_169545,plain,
app(sk1,skaf82(sk6)) = sk6,
inference(superposition,[status(thm),theory(equality)],[c_140105,c_169247]) ).
tff(c_280,plain,
! [U_182,W_184,V_183] :
( memberP(app(U_182,W_184),V_183)
| ~ ssItem(V_183)
| ~ ssList(U_182)
| ~ ssList(W_184)
| ~ memberP(U_182,V_183) ),
inference(cnfTransformation,[status(thm)],[f_926]) ).
tff(c_169886,plain,
! [V_183] :
( memberP(sk6,V_183)
| ~ ssItem(V_183)
| ~ ssList(sk1)
| ~ ssList(skaf82(sk6))
| ~ memberP(sk1,V_183) ),
inference(superposition,[status(thm),theory(equality)],[c_169545,c_280]) ).
tff(c_170674,plain,
! [V_6441] :
( memberP(sk6,V_6441)
| ~ ssItem(V_6441)
| ~ memberP(sk1,V_6441) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_421,c_169886]) ).
tff(c_398,plain,
( ( sk4 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1666]) ).
tff(c_412,plain,
( ( sk4 = nil )
| ( cons(sk8,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_398]) ).
tff(c_415,plain,
( ( sk2 = nil )
| ( cons(sk8,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_412]) ).
tff(c_952,plain,
cons(sk8,nil) = sk1,
inference(splitLeft,[status(thm)],[c_415]) ).
tff(c_80140,plain,
! [U_3009,V_3010] :
( ( app(cons(U_3009,nil),V_3010) = cons(U_3009,V_3010) )
| ~ ssList(V_3010)
| ~ ssItem(U_3009) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_80155,plain,
! [V_3010] :
( ( cons(sk8,V_3010) = app(sk1,V_3010) )
| ~ ssList(V_3010)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_80140]) ).
tff(c_93718,plain,
! [V_3789] :
( ( cons(sk8,V_3789) = app(sk1,V_3789) )
| ~ ssList(V_3789) ),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_80155]) ).
tff(c_93857,plain,
cons(sk8,sk1) = app(sk1,sk1),
inference(resolution,[status(thm)],[c_421,c_93718]) ).
tff(c_1443,plain,
! [V_465,U_466] :
( ~ ssList(V_465)
| ~ ssItem(U_466)
| ( cons(U_466,V_465) != V_465 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_2204,plain,
! [U_519] :
( ~ ssItem(U_519)
| ( cons(U_519,sk1) != sk1 ) ),
inference(resolution,[status(thm)],[c_421,c_1443]) ).
tff(c_2266,plain,
cons(sk8,sk1) != sk1,
inference(resolution,[status(thm)],[c_469,c_2204]) ).
tff(c_94929,plain,
app(sk1,sk1) != sk1,
inference(demodulation,[status(thm),theory(equality)],[c_93857,c_2266]) ).
tff(c_95017,plain,
( ssList(app(sk1,sk1))
| ~ ssList(sk1)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_93857,c_172]) ).
tff(c_95079,plain,
ssList(app(sk1,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_421,c_95017]) ).
tff(c_885,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_421,c_759]) ).
tff(c_81035,plain,
! [U_3049,V_3050] :
( frontsegP(app(U_3049,V_3050),U_3049)
| ~ ssList(app(U_3049,V_3050))
| ~ ssList(U_3049)
| ~ ssList(V_3050) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_81175,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_885,c_81035]) ).
tff(c_81272,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_16,c_421,c_885,c_81175]) ).
tff(c_86414,plain,
! [U_3280,V_3281,W_3282] :
( segmentP(app(app(U_3280,V_3281),W_3282),V_3281)
| ~ ssList(app(app(U_3280,V_3281),W_3282))
| ~ ssList(V_3281)
| ~ ssList(U_3280)
| ~ ssList(W_3282) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_86542,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_86414]) ).
tff(c_86692,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_421,c_390,c_86542]) ).
tff(c_101089,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_86692]) ).
tff(c_101092,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_101089]) ).
tff(c_101096,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_101092]) ).
tff(c_101098,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_86692]) ).
tff(c_83569,plain,
! [W_3171,V_3172,U_3173] :
( ( app(app(W_3171,V_3172),U_3173) = app(W_3171,app(V_3172,U_3173)) )
| ~ ssList(W_3171)
| ~ ssList(V_3172)
| ~ ssList(U_3173) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_83606,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_83569,c_390]) ).
tff(c_83777,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_83606]) ).
tff(c_117880,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_101098,c_83777]) ).
tff(c_117930,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_117880]) ).
tff(c_117963,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_117930]) ).
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_117991,plain,
( memberP(sk1,sk5)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_117963,c_350]) ).
tff(c_118048,plain,
memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_384,c_421,c_117963,c_117991]) ).
tff(c_84759,plain,
! [W_3215,U_3216,V_3217] :
( ( W_3215 = U_3216 )
| memberP(V_3217,W_3215)
| ~ ssItem(W_3215)
| ~ ssItem(U_3216)
| ~ ssList(V_3217)
| ~ memberP(cons(U_3216,V_3217),W_3215) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_84780,plain,
! [W_3215] :
( ( sk8 = W_3215 )
| memberP(nil,W_3215)
| ~ ssItem(W_3215)
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ memberP(sk1,W_3215) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_84759]) ).
tff(c_84789,plain,
! [W_3215] :
( ( sk8 = W_3215 )
| memberP(nil,W_3215)
| ~ ssItem(W_3215)
| ~ memberP(sk1,W_3215) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_84780]) ).
tff(c_118079,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_118048,c_84789]) ).
tff(c_118082,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_118079]) ).
tff(c_118083,plain,
memberP(nil,sk5),
inference(splitLeft,[status(thm)],[c_118082]) ).
tff(c_142,plain,
! [U_65] :
( ~ ssItem(U_65)
| ~ memberP(nil,U_65) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_118087,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_118083,c_142]) ).
tff(c_118091,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_118087]) ).
tff(c_118092,plain,
sk8 = sk5,
inference(splitRight,[status(thm)],[c_118082]) ).
tff(c_118188,plain,
cons(sk5,nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_118092,c_952]) ).
tff(c_101097,plain,
segmentP(sk1,cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_86692]) ).
tff(c_118409,plain,
segmentP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_118188,c_101097]) ).
tff(c_254,plain,
! [V_153,U_152] :
( ( V_153 = U_152 )
| ~ ssList(V_153)
| ~ ssList(U_152)
| ~ segmentP(V_153,U_152)
| ~ segmentP(U_152,V_153) ),
inference(cnfTransformation,[status(thm)],[f_756]) ).
tff(c_101214,plain,
( ( cons(sk5,nil) = sk1 )
| ~ ssList(sk1)
| ~ ssList(cons(sk5,nil))
| ~ segmentP(cons(sk5,nil),sk1) ),
inference(resolution,[status(thm)],[c_101097,c_254]) ).
tff(c_101220,plain,
( ( cons(sk5,nil) = sk1 )
| ~ segmentP(cons(sk5,nil),sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_101098,c_421,c_101214]) ).
tff(c_113024,plain,
~ segmentP(cons(sk5,nil),sk1),
inference(splitLeft,[status(thm)],[c_101220]) ).
tff(c_118370,plain,
~ segmentP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_118188,c_113024]) ).
tff(c_118654,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_118409,c_118370]) ).
tff(c_118655,plain,
cons(sk5,nil) = sk1,
inference(splitRight,[status(thm)],[c_101220]) ).
tff(c_4368,plain,
! [U_654,V_655] :
( frontsegP(app(U_654,V_655),U_654)
| ~ ssList(app(U_654,V_655))
| ~ ssList(U_654)
| ~ ssList(V_655) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_4517,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_4368]) ).
tff(c_4623,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_746,c_4517]) ).
tff(c_4079,plain,
! [U_652,V_653] :
( rearsegP(app(U_652,V_653),V_653)
| ~ ssList(app(U_652,V_653))
| ~ ssList(V_653)
| ~ ssList(U_652) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_4228,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_4079]) ).
tff(c_4334,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_746,c_4228]) ).
tff(c_2304,plain,
! [U_528,V_529] :
( ( tl(cons(U_528,V_529)) = V_529 )
| ~ ssList(V_529)
| ~ ssItem(U_528) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_2319,plain,
( ( tl(sk1) = nil )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_2304]) ).
tff(c_2325,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_16,c_2319]) ).
tff(c_2929,plain,
! [U_560] :
( ~ ssItem(U_560)
| ( cons(U_560,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1443]) ).
tff(c_2935,plain,
cons(sk8,nil) != nil,
inference(resolution,[status(thm)],[c_469,c_2929]) ).
tff(c_2992,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_952,c_2935]) ).
tff(c_2108,plain,
! [U_505,V_506] :
( ( hd(cons(U_505,V_506)) = U_505 )
| ~ ssList(V_506)
| ~ ssItem(U_505) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_2120,plain,
( ( hd(sk1) = sk8 )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_2108]) ).
tff(c_2124,plain,
hd(sk1) = sk8,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_16,c_2120]) ).
tff(c_3065,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_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_3074,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_3065,c_194]) ).
tff(c_12971,plain,
! [U_1231] :
( ( skaf83(U_1231) = hd(U_1231) )
| ( nil = U_1231 )
| ~ ssList(U_1231) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_3074]) ).
tff(c_13070,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_421,c_12971]) ).
tff(c_13111,plain,
( ( skaf83(sk1) = sk8 )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2124,c_13070]) ).
tff(c_13112,plain,
skaf83(sk1) = sk8,
inference(negUnitSimplification,[status(thm)],[c_2992,c_13111]) ).
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_13132,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_13112,c_218]) ).
tff(c_13145,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_13132]) ).
tff(c_13146,plain,
cons(sk8,skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_2992,c_13145]) ).
tff(c_13707,plain,
( ( tl(sk1) = skaf82(sk1) )
| ~ ssList(skaf82(sk1))
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_13146,c_192]) ).
tff(c_13772,plain,
skaf82(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_26,c_2325,c_13707]) ).
tff(c_749,plain,
app(sk6,nil) = sk6,
inference(resolution,[status(thm)],[c_386,c_622]) ).
tff(c_2365,plain,
! [U_546,V_547] :
( ( nil = U_546 )
| ~ ssList(U_546)
| ~ ssList(V_547)
| ( app(U_546,V_547) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_2470,plain,
! [V_547] :
( ( sk6 = nil )
| ~ ssList(V_547)
| ( app(sk6,V_547) != nil ) ),
inference(resolution,[status(thm)],[c_386,c_2365]) ).
tff(c_11577,plain,
! [V_1066] :
( ~ ssList(V_1066)
| ( app(sk6,V_1066) != nil ) ),
inference(splitLeft,[status(thm)],[c_2470]) ).
tff(c_11670,plain,
app(sk6,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_11577]) ).
tff(c_11714,plain,
sk6 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_749,c_11670]) ).
tff(c_13073,plain,
( ( skaf83(sk6) = hd(sk6) )
| ( sk6 = nil ) ),
inference(resolution,[status(thm)],[c_386,c_12971]) ).
tff(c_13115,plain,
skaf83(sk6) = hd(sk6),
inference(negUnitSimplification,[status(thm)],[c_11714,c_13073]) ).
tff(c_13172,plain,
ssItem(hd(sk6)),
inference(superposition,[status(thm),theory(equality)],[c_13115,c_24]) ).
tff(c_13164,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13115,c_218]) ).
tff(c_13176,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_13164]) ).
tff(c_13177,plain,
cons(hd(sk6),skaf82(sk6)) = sk6,
inference(negUnitSimplification,[status(thm)],[c_11714,c_13176]) ).
tff(c_8817,plain,
! [W_839,U_840,V_841,X_842] :
( ( W_839 = U_840 )
| ~ ssItem(U_840)
| ~ ssItem(W_839)
| ~ ssList(V_841)
| ~ ssList(X_842)
| ~ frontsegP(cons(U_840,V_841),cons(W_839,X_842)) ),
inference(cnfTransformation,[status(thm)],[f_1422]) ).
tff(c_8850,plain,
! [U_840,V_841] :
( ( sk8 = U_840 )
| ~ ssItem(U_840)
| ~ ssItem(sk8)
| ~ ssList(V_841)
| ~ ssList(nil)
| ~ frontsegP(cons(U_840,V_841),sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_8817]) ).
tff(c_56645,plain,
! [U_2470,V_2471] :
( ( sk8 = U_2470 )
| ~ ssItem(U_2470)
| ~ ssList(V_2471)
| ~ frontsegP(cons(U_2470,V_2471),sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_8850]) ).
tff(c_56732,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk6,sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_13177,c_56645]) ).
tff(c_56832,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk6,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13172,c_56732]) ).
tff(c_57017,plain,
~ frontsegP(sk6,sk1),
inference(splitLeft,[status(thm)],[c_56832]) ).
tff(c_4454,plain,
! [U_2] :
( frontsegP(skaf82(U_2),nil)
| ~ ssList(app(nil,skaf82(U_2)))
| ~ ssList(nil)
| ~ ssList(skaf82(U_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_879,c_4368]) ).
tff(c_4581,plain,
! [U_2] : frontsegP(skaf82(U_2),nil),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_16,c_26,c_879,c_4454]) ).
tff(c_8847,plain,
! [W_839,X_842] :
( ( sk8 = W_839 )
| ~ ssItem(sk8)
| ~ ssItem(W_839)
| ~ ssList(nil)
| ~ ssList(X_842)
| ~ frontsegP(sk1,cons(W_839,X_842)) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_8817]) ).
tff(c_57100,plain,
! [W_2475,X_2476] :
( ( sk8 = W_2475 )
| ~ ssItem(W_2475)
| ~ ssList(X_2476)
| ~ frontsegP(sk1,cons(W_2475,X_2476)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_8847]) ).
tff(c_57190,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13177,c_57100]) ).
tff(c_57290,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13172,c_57190]) ).
tff(c_57351,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_57290]) ).
tff(c_9783,plain,
! [U_889,V_890,W_891] :
( segmentP(app(app(U_889,V_890),W_891),V_890)
| ~ ssList(app(app(U_889,V_890),W_891))
| ~ ssList(V_890)
| ~ ssList(U_889)
| ~ ssList(W_891) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_9917,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_9783]) ).
tff(c_10069,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_421,c_390,c_9917]) ).
tff(c_17996,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_10069]) ).
tff(c_17999,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_17996]) ).
tff(c_18003,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_17999]) ).
tff(c_18005,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_10069]) ).
tff(c_8039,plain,
! [W_830,V_831,U_832] :
( ( app(app(W_830,V_831),U_832) = app(W_830,app(V_831,U_832)) )
| ~ ssList(W_830)
| ~ ssList(V_831)
| ~ ssList(U_832) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_8079,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_8039,c_390]) ).
tff(c_8265,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_8079]) ).
tff(c_66039,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_18005,c_8265]) ).
tff(c_66098,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_66039]) ).
tff(c_66138,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_66098]) ).
tff(c_66205,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_66138,c_288]) ).
tff(c_66258,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_421,c_66138,c_66205]) ).
tff(c_66259,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_57351,c_66258]) ).
tff(c_66276,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_66259]) ).
tff(c_66280,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_66276]) ).
tff(c_66281,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_57290]) ).
tff(c_66336,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_66281,c_13177]) ).
tff(c_7053,plain,
! [X_777,U_778,V_779] :
( frontsegP(cons(X_777,U_778),cons(X_777,V_779))
| ~ ssItem(X_777)
| ~ ssList(U_778)
| ~ ssList(V_779)
| ~ frontsegP(U_778,V_779) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_7081,plain,
! [U_778] :
( frontsegP(cons(sk8,U_778),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_778)
| ~ ssList(nil)
| ~ frontsegP(U_778,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_7053]) ).
tff(c_7095,plain,
! [U_778] :
( frontsegP(cons(sk8,U_778),sk1)
| ~ ssList(U_778)
| ~ frontsegP(U_778,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_7081]) ).
tff(c_66481,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_66336,c_7095]) ).
tff(c_66591,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_4581,c_26,c_66481]) ).
tff(c_66593,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_57017,c_66591]) ).
tff(c_66595,plain,
frontsegP(sk6,sk1),
inference(splitRight,[status(thm)],[c_56832]) ).
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_66887,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_66595,c_258]) ).
tff(c_66896,plain,
( ( sk6 = sk1 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_386,c_66887]) ).
tff(c_67171,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_66896]) ).
tff(c_78466,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_18005,c_8265]) ).
tff(c_78525,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_78466]) ).
tff(c_78565,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_78525]) ).
tff(c_78632,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_78565,c_288]) ).
tff(c_78685,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_421,c_78565,c_78632]) ).
tff(c_78686,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_67171,c_78685]) ).
tff(c_78703,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_78686]) ).
tff(c_78707,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_78703]) ).
tff(c_78708,plain,
sk6 = sk1,
inference(splitRight,[status(thm)],[c_66896]) ).
tff(c_94,plain,
! [U_36] : ssItem(skaf44(U_36)),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_2142,plain,
! [U_515] :
( ( cons(skaf44(U_515),nil) = U_515 )
| ~ ssList(U_515)
| ~ singletonP(U_515) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_128,plain,
! [U_58] :
( equalelemsP(cons(U_58,nil))
| ~ ssItem(U_58) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_2169,plain,
! [U_515] :
( equalelemsP(U_515)
| ~ ssItem(skaf44(U_515))
| ~ ssList(U_515)
| ~ singletonP(U_515) ),
inference(superposition,[status(thm),theory(equality)],[c_2142,c_128]) ).
tff(c_2472,plain,
! [U_548] :
( equalelemsP(U_548)
| ~ ssList(U_548)
| ~ singletonP(U_548) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_2169]) ).
tff(c_2613,plain,
( equalelemsP(sk6)
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_2472]) ).
tff(c_2722,plain,
~ singletonP(sk6),
inference(splitLeft,[status(thm)],[c_2613]) ).
tff(c_132,plain,
! [U_60] :
( strictorderedP(cons(U_60,nil))
| ~ ssItem(U_60) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_974,plain,
( strictorderedP(sk1)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_132]) ).
tff(c_990,plain,
strictorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_974]) ).
tff(c_38459,plain,
! [W_2123,X_2124] :
( ( sk8 = W_2123 )
| ~ ssItem(W_2123)
| ~ ssList(X_2124)
| ~ frontsegP(sk1,cons(W_2123,X_2124)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_8847]) ).
tff(c_38549,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13177,c_38459]) ).
tff(c_38649,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13172,c_38549]) ).
tff(c_38749,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_38649]) ).
tff(c_46191,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_18005,c_8265]) ).
tff(c_46244,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_46191]) ).
tff(c_46280,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_46244]) ).
tff(c_46341,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_46280,c_288]) ).
tff(c_46390,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_421,c_46280,c_46341]) ).
tff(c_46391,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_38749,c_46390]) ).
tff(c_46408,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_46391]) ).
tff(c_46412,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_46408]) ).
tff(c_46414,plain,
frontsegP(sk1,sk6),
inference(splitRight,[status(thm)],[c_38649]) ).
tff(c_46413,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_38649]) ).
tff(c_46432,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_46413,c_13177]) ).
tff(c_46571,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_46432,c_7095]) ).
tff(c_46680,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_4581,c_26,c_46571]) ).
tff(c_46948,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_46680,c_258]) ).
tff(c_46957,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_46414,c_421,c_386,c_46948]) ).
tff(c_248,plain,
! [V_147,U_146] :
( ( nil = V_147 )
| strictorderedP(V_147)
| ~ ssItem(U_146)
| ~ ssList(V_147)
| ~ strictorderedP(cons(U_146,V_147)) ),
inference(cnfTransformation,[status(thm)],[f_715]) ).
tff(c_14823,plain,
( ( skaf82(sk6) = nil )
| strictorderedP(skaf82(sk6))
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ strictorderedP(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13177,c_248]) ).
tff(c_14890,plain,
( ( skaf82(sk6) = nil )
| strictorderedP(skaf82(sk6))
| ~ strictorderedP(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13172,c_14823]) ).
tff(c_28752,plain,
~ strictorderedP(sk6),
inference(splitLeft,[status(thm)],[c_14890]) ).
tff(c_46981,plain,
~ strictorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_46957,c_28752]) ).
tff(c_47153,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_990,c_46981]) ).
tff(c_47154,plain,
( strictorderedP(skaf82(sk6))
| ( skaf82(sk6) = nil ) ),
inference(splitRight,[status(thm)],[c_14890]) ).
tff(c_47163,plain,
skaf82(sk6) = nil,
inference(splitLeft,[status(thm)],[c_47154]) ).
tff(c_47165,plain,
cons(hd(sk6),nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_47163,c_13177]) ).
tff(c_3011,plain,
! [U_561] :
( singletonP(cons(U_561,nil))
| ~ ssList(cons(U_561,nil))
| ~ ssItem(U_561) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_3018,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_3011]) ).
tff(c_3026,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3018]) ).
tff(c_47428,plain,
( singletonP(sk6)
| ~ ssItem(hd(sk6)) ),
inference(superposition,[status(thm),theory(equality)],[c_47165,c_3026]) ).
tff(c_47520,plain,
singletonP(sk6),
inference(demodulation,[status(thm),theory(equality)],[c_13172,c_47428]) ).
tff(c_47522,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2722,c_47520]) ).
tff(c_47524,plain,
skaf82(sk6) != nil,
inference(splitRight,[status(thm)],[c_47154]) ).
tff(c_78769,plain,
skaf82(sk1) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_78708,c_47524]) ).
tff(c_78943,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13772,c_78769]) ).
tff(c_78944,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_2470]) ).
tff(c_4216,plain,
( rearsegP(sk6,nil)
| ~ ssList(app(sk6,nil))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_749,c_4079]) ).
tff(c_4326,plain,
rearsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_749,c_4216]) ).
tff(c_4348,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ rearsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_4326,c_256]) ).
tff(c_4351,plain,
( ( sk6 = nil )
| ~ rearsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_4348]) ).
tff(c_8379,plain,
~ rearsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_4351]) ).
tff(c_78945,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_78944,c_8379]) ).
tff(c_79001,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4334,c_78945]) ).
tff(c_79002,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_4351]) ).
tff(c_886,plain,
app(nil,sk6) = sk6,
inference(resolution,[status(thm)],[c_386,c_759]) ).
tff(c_4523,plain,
( frontsegP(sk6,nil)
| ~ ssList(app(nil,sk6))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_886,c_4368]) ).
tff(c_4627,plain,
frontsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_886,c_4523]) ).
tff(c_4690,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_4627,c_258]) ).
tff(c_4693,plain,
( ( sk6 = nil )
| ~ frontsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_4690]) ).
tff(c_8038,plain,
~ frontsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_4693]) ).
tff(c_79004,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_79002,c_8038]) ).
tff(c_79059,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4623,c_79004]) ).
tff(c_79060,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_4693]) ).
tff(c_392,plain,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnfTransformation,[status(thm)],[f_1657]) ).
tff(c_897,plain,
memberP(sk6,sk5),
inference(splitLeft,[status(thm)],[c_392]) ).
tff(c_79111,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_79060,c_897]) ).
tff(c_79446,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_79111,c_142]) ).
tff(c_79450,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_79446]) ).
tff(c_79452,plain,
singletonP(sk6),
inference(splitRight,[status(thm)],[c_2613]) ).
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_79933,plain,
! [U_2990] :
( ~ ssItem(U_2990)
| ( cons(U_2990,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1443]) ).
tff(c_80057,plain,
! [U_2995] : ( cons(skaf44(U_2995),nil) != nil ),
inference(resolution,[status(thm)],[c_94,c_79933]) ).
tff(c_87976,plain,
! [U_3376] :
( ( nil != U_3376 )
| ~ ssList(U_3376)
| ~ singletonP(U_3376) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_80057]) ).
tff(c_88078,plain,
( ( sk6 != nil )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_87976]) ).
tff(c_88119,plain,
sk6 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_79452,c_88078]) ).
tff(c_93859,plain,
cons(sk8,sk7) = app(sk1,sk7),
inference(resolution,[status(thm)],[c_388,c_93718]) ).
tff(c_94249,plain,
( ssList(app(sk1,sk7))
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_93859,c_172]) ).
tff(c_94311,plain,
ssList(app(sk1,sk7)),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_388,c_94249]) ).
tff(c_118817,plain,
( ( hd(sk1) = sk5 )
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_118655,c_194]) ).
tff(c_118906,plain,
sk8 = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_2124,c_118817]) ).
tff(c_119011,plain,
hd(sk1) = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_118906,c_2124]) ).
tff(c_298,plain,
! [W_208,V_207,U_206] :
( ( app(app(W_208,V_207),U_206) = app(W_208,app(V_207,U_206)) )
| ~ ssList(W_208)
| ~ ssList(V_207)
| ~ ssList(U_206) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_118703,plain,
app(app(sk6,sk1),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_118655,c_390]) ).
tff(c_119154,plain,
( ( app(sk6,app(sk1,sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_298,c_118703]) ).
tff(c_119193,plain,
app(sk6,app(sk1,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_388,c_421,c_386,c_119154]) ).
tff(c_246,plain,
! [V_145,U_144] :
( ( hd(app(V_145,U_144)) = hd(V_145) )
| ( nil = V_145 )
| ~ ssList(V_145)
| ~ ssList(U_144) ),
inference(cnfTransformation,[status(thm)],[f_702]) ).
tff(c_120364,plain,
( ( hd(sk6) = hd(sk1) )
| ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(app(sk1,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_119193,c_246]) ).
tff(c_120397,plain,
( ( hd(sk6) = sk5 )
| ( sk6 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_94311,c_386,c_119011,c_120364]) ).
tff(c_120398,plain,
hd(sk6) = sk5,
inference(negUnitSimplification,[status(thm)],[c_88119,c_120397]) ).
tff(c_2316,plain,
! [U_103] :
( ( tl(U_103) = nil )
| ~ ssList(nil)
| ~ ssItem(skaf44(U_103))
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_2304]) ).
tff(c_88147,plain,
! [U_3408] :
( ( tl(U_3408) = nil )
| ~ ssList(U_3408)
| ~ singletonP(U_3408) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_2316]) ).
tff(c_88249,plain,
( ( tl(sk6) = nil )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_88147]) ).
tff(c_88290,plain,
tl(sk6) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_79452,c_88249]) ).
tff(c_88299,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),nil) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_88290,c_208]) ).
tff(c_88309,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),nil) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_88299]) ).
tff(c_88310,plain,
cons(hd(sk6),nil) = sk6,
inference(negUnitSimplification,[status(thm)],[c_88119,c_88309]) ).
tff(c_120454,plain,
cons(sk5,nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_120398,c_88310]) ).
tff(c_120459,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_118655,c_120454]) ).
tff(c_93858,plain,
cons(sk8,sk6) = app(sk1,sk6),
inference(resolution,[status(thm)],[c_386,c_93718]) ).
tff(c_118998,plain,
cons(sk5,sk6) = app(sk1,sk6),
inference(demodulation,[status(thm),theory(equality)],[c_118906,c_93858]) ).
tff(c_121425,plain,
cons(sk5,sk1) = app(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_120459,c_120459,c_118998]) ).
tff(c_83930,plain,
! [X_3179,U_3180,V_3181] :
( frontsegP(cons(X_3179,U_3180),cons(X_3179,V_3181))
| ~ ssItem(X_3179)
| ~ ssList(U_3180)
| ~ ssList(V_3181)
| ~ frontsegP(U_3180,V_3181) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_83958,plain,
! [U_3180] :
( frontsegP(cons(sk8,U_3180),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_3180)
| ~ ssList(nil)
| ~ frontsegP(U_3180,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_952,c_83930]) ).
tff(c_83972,plain,
! [U_3180] :
( frontsegP(cons(sk8,U_3180),sk1)
| ~ ssList(U_3180)
| ~ frontsegP(U_3180,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_83958]) ).
tff(c_120114,plain,
! [U_3180] :
( frontsegP(cons(sk5,U_3180),sk1)
| ~ ssList(U_3180)
| ~ frontsegP(U_3180,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_118906,c_83972]) ).
tff(c_121457,plain,
( frontsegP(app(sk1,sk1),sk1)
| ~ ssList(sk1)
| ~ frontsegP(sk1,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_121425,c_120114]) ).
tff(c_121560,plain,
frontsegP(app(sk1,sk1),sk1),
inference(demodulation,[status(thm),theory(equality)],[c_81272,c_421,c_121457]) ).
tff(c_121693,plain,
( ( app(sk1,sk1) = sk1 )
| ~ ssList(app(sk1,sk1))
| ~ ssList(sk1)
| ~ frontsegP(sk1,app(sk1,sk1)) ),
inference(resolution,[status(thm)],[c_121560,c_258]) ).
tff(c_121702,plain,
( ( app(sk1,sk1) = sk1 )
| ~ frontsegP(sk1,app(sk1,sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_95079,c_121693]) ).
tff(c_121703,plain,
~ frontsegP(sk1,app(sk1,sk1)),
inference(negUnitSimplification,[status(thm)],[c_94929,c_121702]) ).
tff(c_120532,plain,
app(app(sk1,sk1),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_120459,c_118703]) ).
tff(c_124359,plain,
( frontsegP(sk1,app(sk1,sk1))
| ~ ssList(app(app(sk1,sk1),sk7))
| ~ ssList(app(sk1,sk1))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_120532,c_288]) ).
tff(c_124405,plain,
frontsegP(sk1,app(sk1,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_95079,c_421,c_120532,c_124359]) ).
tff(c_124407,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_121703,c_124405]) ).
tff(c_124408,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_415]) ).
tff(c_400,plain,
( ( sk4 = nil )
| memberP(sk4,sk8) ),
inference(cnfTransformation,[status(thm)],[f_1669]) ).
tff(c_414,plain,
( ( sk2 = nil )
| memberP(sk2,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_400]) ).
tff(c_487,plain,
memberP(sk2,sk8),
inference(splitLeft,[status(thm)],[c_414]) ).
tff(c_124413,plain,
memberP(nil,sk8),
inference(demodulation,[status(thm),theory(equality)],[c_124408,c_487]) ).
tff(c_124430,plain,
~ ssItem(sk8),
inference(resolution,[status(thm)],[c_124413,c_142]) ).
tff(c_124434,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_124430]) ).
tff(c_124436,plain,
~ memberP(sk6,sk5),
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_170677,plain,
( ~ ssItem(sk5)
| ~ memberP(sk1,sk5) ),
inference(resolution,[status(thm)],[c_170674,c_124436]) ).
tff(c_170680,plain,
~ memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_170677]) ).
tff(c_131067,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_131027,c_390]) ).
tff(c_131235,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_131067]) ).
tff(c_174316,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_140781,c_131235]) ).
tff(c_174366,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_174316]) ).
tff(c_174400,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_174366]) ).
tff(c_174470,plain,
( memberP(sk1,sk5)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_174400,c_350]) ).
tff(c_174526,plain,
memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_384,c_421,c_174400,c_174470]) ).
tff(c_174528,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_170680,c_174526]) ).
tff(c_174529,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_135491]) ).
tff(c_128050,plain,
( frontsegP(sk6,nil)
| ~ ssList(app(nil,sk6))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_886,c_127925]) ).
tff(c_128152,plain,
frontsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_886,c_128050]) ).
tff(c_128180,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_128152,c_258]) ).
tff(c_128183,plain,
( ( sk6 = nil )
| ~ frontsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_128180]) ).
tff(c_131337,plain,
~ frontsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_128183]) ).
tff(c_174555,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_174529,c_131337]) ).
tff(c_174595,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_128166,c_174555]) ).
tff(c_174596,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_128183]) ).
tff(c_127730,plain,
( rearsegP(sk6,nil)
| ~ ssList(app(sk6,nil))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_749,c_127599]) ).
tff(c_127827,plain,
rearsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_749,c_127730]) ).
tff(c_127860,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ rearsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_127827,c_256]) ).
tff(c_127863,plain,
( ( sk6 = nil )
| ~ rearsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_127860]) ).
tff(c_130745,plain,
~ rearsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_127863]) ).
tff(c_174598,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_174596,c_130745]) ).
tff(c_174633,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_127835,c_174598]) ).
tff(c_174634,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_127863]) ).
tff(c_174944,plain,
~ memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_174634,c_124436]) ).
tff(c_180033,plain,
! [U_6868] :
( ( tl(U_6868) = skaf82(U_6868) )
| ( nil = U_6868 )
| ~ ssList(U_6868) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_126344]) ).
tff(c_180174,plain,
( ( tl(sk7) = skaf82(sk7) )
| ( sk7 = nil ) ),
inference(resolution,[status(thm)],[c_388,c_180033]) ).
tff(c_180475,plain,
sk7 = nil,
inference(splitLeft,[status(thm)],[c_180174]) ).
tff(c_750,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_622]) ).
tff(c_127718,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_750,c_127599]) ).
tff(c_127819,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_750,c_127718]) ).
tff(c_127837,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_127819,c_256]) ).
tff(c_127840,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_127837]) ).
tff(c_175247,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_127840]) ).
tff(c_180478,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_180475,c_175247]) ).
tff(c_180535,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_127835,c_180478]) ).
tff(c_180537,plain,
sk7 != nil,
inference(splitRight,[status(thm)],[c_180174]) ).
tff(c_125010,plain,
! [V_4654,U_4655] :
( ~ ssList(V_4654)
| ~ ssItem(U_4655)
| ( cons(U_4655,V_4654) != V_4654 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_126033,plain,
! [U_4711] :
( ~ ssItem(U_4711)
| ( cons(U_4711,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_125010]) ).
tff(c_126039,plain,
cons(sk8,nil) != nil,
inference(resolution,[status(thm)],[c_469,c_126033]) ).
tff(c_126096,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_124452,c_126039]) ).
tff(c_126148,plain,
! [U_4715,V_4716] :
( ( tl(cons(U_4715,V_4716)) = V_4716 )
| ~ ssList(V_4716)
| ~ ssItem(U_4715) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_126163,plain,
( ( tl(sk1) = nil )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_126148]) ).
tff(c_126169,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_16,c_126163]) ).
tff(c_180132,plain,
( ( tl(sk1) = skaf82(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_421,c_180033]) ).
tff(c_180172,plain,
( ( skaf82(sk1) = nil )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_126169,c_180132]) ).
tff(c_180173,plain,
skaf82(sk1) = nil,
inference(negUnitSimplification,[status(thm)],[c_126096,c_180172]) ).
tff(c_124435,plain,
memberP(sk7,sk5),
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_127649,plain,
( rearsegP(sk1,sk7)
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_390,c_127599]) ).
tff(c_127773,plain,
( rearsegP(sk1,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_421,c_390,c_127649]) ).
tff(c_192471,plain,
( rearsegP(sk1,sk7)
| ~ ssList(app(nil,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_174634,c_127773]) ).
tff(c_192472,plain,
~ ssList(app(nil,cons(sk5,nil))),
inference(splitLeft,[status(thm)],[c_192471]) ).
tff(c_192475,plain,
( ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_192472]) ).
tff(c_192478,plain,
~ ssList(cons(sk5,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_192475]) ).
tff(c_192481,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_192478]) ).
tff(c_192485,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_192481]) ).
tff(c_192487,plain,
ssList(app(nil,cons(sk5,nil))),
inference(splitRight,[status(thm)],[c_192471]) ).
tff(c_174941,plain,
app(app(nil,cons(sk5,nil)),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_174634,c_390]) ).
tff(c_282,plain,
! [W_187,U_185,V_186] :
( memberP(app(W_187,U_185),V_186)
| ~ ssItem(V_186)
| ~ ssList(W_187)
| ~ ssList(U_185)
| ~ memberP(U_185,V_186) ),
inference(cnfTransformation,[status(thm)],[f_940]) ).
tff(c_192805,plain,
! [V_186] :
( memberP(sk1,V_186)
| ~ ssItem(V_186)
| ~ ssList(app(nil,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(sk7,V_186) ),
inference(superposition,[status(thm),theory(equality)],[c_174941,c_282]) ).
tff(c_194233,plain,
! [V_7404] :
( memberP(sk1,V_7404)
| ~ ssItem(V_7404)
| ~ memberP(sk7,V_7404) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_192487,c_192805]) ).
tff(c_194247,plain,
( memberP(sk1,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_124435,c_194233]) ).
tff(c_194260,plain,
memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_194247]) ).
tff(c_130452,plain,
! [W_4967,U_4968,V_4969] :
( ( W_4967 = U_4968 )
| memberP(V_4969,W_4967)
| ~ ssItem(W_4967)
| ~ ssItem(U_4968)
| ~ ssList(V_4969)
| ~ memberP(cons(U_4968,V_4969),W_4967) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_130470,plain,
! [W_4967] :
( ( sk8 = W_4967 )
| memberP(nil,W_4967)
| ~ ssItem(W_4967)
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ memberP(sk1,W_4967) ),
inference(superposition,[status(thm),theory(equality)],[c_124452,c_130452]) ).
tff(c_207999,plain,
! [W_7768] :
( ( sk8 = W_7768 )
| memberP(nil,W_7768)
| ~ ssItem(W_7768)
| ~ memberP(sk1,W_7768) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_469,c_130470]) ).
tff(c_208005,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_194260,c_207999]) ).
tff(c_208022,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_208005]) ).
tff(c_208023,plain,
sk8 = sk5,
inference(negUnitSimplification,[status(thm)],[c_174944,c_208022]) ).
tff(c_208127,plain,
cons(sk5,nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_208023,c_124452]) ).
tff(c_208362,plain,
app(app(nil,sk1),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_208127,c_174941]) ).
tff(c_208370,plain,
app(sk1,sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_885,c_208362]) ).
tff(c_183070,plain,
! [V_7032] :
( ( cons(sk8,V_7032) = app(sk1,V_7032) )
| ~ ssList(V_7032) ),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_126805]) ).
tff(c_183207,plain,
cons(sk8,sk7) = app(sk1,sk7),
inference(resolution,[status(thm)],[c_388,c_183070]) ).
tff(c_183441,plain,
( ( tl(app(sk1,sk7)) = sk7 )
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_183207,c_192]) ).
tff(c_183506,plain,
tl(app(sk1,sk7)) = sk7,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_388,c_183441]) ).
tff(c_126595,plain,
! [U_4763,V_4764] :
( ( nil = U_4763 )
| ~ ssList(U_4763)
| ~ ssList(V_4764)
| ( app(U_4763,V_4764) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_126661,plain,
! [V_4764] :
( ( sk1 = nil )
| ~ ssList(V_4764)
| ( app(sk1,V_4764) != nil ) ),
inference(resolution,[status(thm)],[c_421,c_126595]) ).
tff(c_177016,plain,
! [V_6566] :
( ~ ssList(V_6566)
| ( app(sk1,V_6566) != nil ) ),
inference(negUnitSimplification,[status(thm)],[c_126096,c_126661]) ).
tff(c_177153,plain,
app(sk1,sk7) != nil,
inference(resolution,[status(thm)],[c_388,c_177016]) ).
tff(c_183450,plain,
( ssList(app(sk1,sk7))
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_183207,c_172]) ).
tff(c_183512,plain,
ssList(app(sk1,sk7)),
inference(demodulation,[status(thm),theory(equality)],[c_469,c_388,c_183450]) ).
tff(c_126359,plain,
! [U_4736] :
( ( tl(U_4736) = skaf82(U_4736) )
| ( nil = U_4736 )
| ~ ssList(U_4736) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_126344]) ).
tff(c_183641,plain,
( ( tl(app(sk1,sk7)) = skaf82(app(sk1,sk7)) )
| ( app(sk1,sk7) = nil ) ),
inference(resolution,[status(thm)],[c_183512,c_126359]) ).
tff(c_183702,plain,
tl(app(sk1,sk7)) = skaf82(app(sk1,sk7)),
inference(negUnitSimplification,[status(thm)],[c_177153,c_183641]) ).
tff(c_193286,plain,
skaf82(app(sk1,sk7)) = sk7,
inference(demodulation,[status(thm),theory(equality)],[c_183506,c_183702]) ).
tff(c_208587,plain,
skaf82(sk1) = sk7,
inference(demodulation,[status(thm),theory(equality)],[c_208370,c_193286]) ).
tff(c_208608,plain,
sk7 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_180173,c_208587]) ).
tff(c_208610,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180537,c_208608]) ).
tff(c_208611,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_127840]) ).
tff(c_887,plain,
app(nil,sk7) = sk7,
inference(resolution,[status(thm)],[c_388,c_759]) ).
tff(c_128065,plain,
( frontsegP(sk7,nil)
| ~ ssList(app(nil,sk7))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_887,c_127925]) ).
tff(c_128162,plain,
frontsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_887,c_128065]) ).
tff(c_128495,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_128162,c_258]) ).
tff(c_128498,plain,
( ( sk7 = nil )
| ~ frontsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_128495]) ).
tff(c_174961,plain,
~ frontsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_128498]) ).
tff(c_208640,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_208611,c_174961]) ).
tff(c_208694,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_128166,c_208640]) ).
tff(c_208695,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_128498]) ).
tff(c_208745,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_208695,c_124435]) ).
tff(c_208757,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_174944,c_208745]) ).
tff(c_208758,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_208759,plain,
cons(sk8,nil) != sk1,
inference(splitRight,[status(thm)],[c_410]) ).
tff(c_208773,plain,
cons(sk8,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_208758,c_208759]) ).
tff(c_208799,plain,
( ( sk2 = nil )
| ( cons(sk8,nil) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_208758,c_415]) ).
tff(c_208800,plain,
sk2 = nil,
inference(negUnitSimplification,[status(thm)],[c_208773,c_208799]) ).
tff(c_208804,plain,
memberP(nil,sk8),
inference(demodulation,[status(thm),theory(equality)],[c_208800,c_487]) ).
tff(c_208821,plain,
~ ssItem(sk8),
inference(resolution,[status(thm)],[c_208804,c_142]) ).
tff(c_208825,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_469,c_208821]) ).
tff(c_208826,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_414]) ).
tff(c_208827,plain,
~ memberP(sk2,sk8),
inference(splitRight,[status(thm)],[c_414]) ).
tff(c_208840,plain,
~ memberP(nil,sk8),
inference(demodulation,[status(thm),theory(equality)],[c_208826,c_208827]) ).
tff(c_406,plain,
( ( sk3 = nil )
| memberP(sk4,sk8) ),
inference(cnfTransformation,[status(thm)],[f_1688]) ).
tff(c_413,plain,
( ( sk1 = nil )
| memberP(sk4,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_406]) ).
tff(c_416,plain,
( ( sk1 = nil )
| memberP(sk2,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_413]) ).
tff(c_208841,plain,
( ( sk1 = nil )
| memberP(nil,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_208826,c_416]) ).
tff(c_208842,plain,
sk1 = nil,
inference(negUnitSimplification,[status(thm)],[c_208840,c_208841]) ).
tff(c_209612,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_208842,c_390]) ).
tff(c_212172,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_209612,c_212083]) ).
tff(c_212292,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_209612,c_212172]) ).
tff(c_222901,plain,
~ ssList(app(sk6,cons(sk5,nil))),
inference(negUnitSimplification,[status(thm)],[c_215285,c_212292]) ).
tff(c_222904,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_222901]) ).
tff(c_222907,plain,
~ ssList(cons(sk5,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_222904]) ).
tff(c_222910,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_222907]) ).
tff(c_222914,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_222910]) ).
tff(c_222915,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_212344]) ).
tff(c_222996,plain,
app(app(sk6,cons(sk5,nil)),nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_222915,c_209612]) ).
tff(c_346,plain,
! [U_265,V_266,W_267] :
( segmentP(app(app(U_265,V_266),W_267),V_266)
| ~ ssList(app(app(U_265,V_266),W_267))
| ~ ssList(V_266)
| ~ ssList(U_265)
| ~ ssList(W_267) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_229314,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_222996,c_346]) ).
tff(c_229367,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_16,c_222996,c_229314]) ).
tff(c_243355,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_229367]) ).
tff(c_243358,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_243355]) ).
tff(c_243362,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_243358]) ).
tff(c_243364,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_229367]) ).
tff(c_243363,plain,
segmentP(nil,cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_229367]) ).
tff(c_160,plain,
! [U_75] :
( ( nil = U_75 )
| ~ ssList(U_75)
| ~ segmentP(nil,U_75) ),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_243640,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_243363,c_160]) ).
tff(c_243650,plain,
cons(sk5,nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_243364,c_243640]) ).
tff(c_243652,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_210635,c_243650]) ).
tff(c_243654,plain,
~ ssItem(sk8),
inference(splitRight,[status(thm)],[c_417]) ).
tff(c_396,plain,
( ( sk3 = nil )
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1663]) ).
tff(c_409,plain,
( ( sk1 = nil )
| ssItem(sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_396]) ).
tff(c_243671,plain,
sk1 = nil,
inference(negUnitSimplification,[status(thm)],[c_243654,c_409]) ).
tff(c_244365,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_243671,c_390]) ).
tff(c_247440,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(superposition,[status(thm),theory(equality)],[c_244365,c_247360]) ).
tff(c_247566,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_244365,c_247440]) ).
tff(c_257232,plain,
~ ssList(app(sk6,cons(sk5,nil))),
inference(negUnitSimplification,[status(thm)],[c_250869,c_247566]) ).
tff(c_257235,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_257232]) ).
tff(c_257238,plain,
~ ssList(cons(sk5,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_257235]) ).
tff(c_257247,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_257238]) ).
tff(c_257251,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_257247]) ).
tff(c_257252,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_247911]) ).
tff(c_243988,plain,
! [U_9937] :
( ( app(nil,U_9937) = U_9937 )
| ~ ssList(U_9937) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_244109,plain,
app(nil,sk7) = sk7,
inference(resolution,[status(thm)],[c_388,c_243988]) ).
tff(c_247230,plain,
( frontsegP(sk7,nil)
| ~ ssList(app(nil,sk7))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_244109,c_247087]) ).
tff(c_247335,plain,
frontsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_244109,c_247230]) ).
tff(c_247345,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_247335,c_258]) ).
tff(c_247348,plain,
( ( sk7 = nil )
| ~ frontsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_247345]) ).
tff(c_250824,plain,
~ frontsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_247348]) ).
tff(c_257254,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_257252,c_250824]) ).
tff(c_257306,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_247343,c_257254]) ).
tff(c_257307,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_247348]) ).
tff(c_257374,plain,
app(app(sk6,cons(sk5,nil)),nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_257307,c_244365]) ).
tff(c_262931,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_257374,c_346]) ).
tff(c_262984,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_16,c_257374,c_262931]) ).
tff(c_276163,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_262984]) ).
tff(c_276166,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_276163]) ).
tff(c_276170,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_276166]) ).
tff(c_276172,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_262984]) ).
tff(c_276171,plain,
segmentP(nil,cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_262984]) ).
tff(c_276422,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_276171,c_160]) ).
tff(c_276432,plain,
cons(sk5,nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_276172,c_276422]) ).
tff(c_276434,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_245348,c_276432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC184-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 21:28:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 146.83/126.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 147.09/127.02
% 147.09/127.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 147.09/127.10
% 147.09/127.10 Inference rules
% 147.09/127.10 ----------------------
% 147.09/127.10 #Ref : 0
% 147.09/127.10 #Sup : 61030
% 147.09/127.10 #Fact : 0
% 147.09/127.10 #Define : 0
% 147.09/127.10 #Split : 193
% 147.09/127.10 #Chain : 0
% 147.09/127.10 #Close : 0
% 147.09/127.10
% 147.09/127.10 Ordering : KBO
% 147.09/127.10
% 147.09/127.10 Simplification rules
% 147.09/127.10 ----------------------
% 147.09/127.10 #Subsume : 13006
% 147.09/127.10 #Demod : 75936
% 147.09/127.10 #Tautology : 19117
% 147.09/127.10 #SimpNegUnit : 4671
% 147.09/127.10 #BackRed : 2276
% 147.09/127.10
% 147.09/127.10 #Partial instantiations: 0
% 147.09/127.10 #Strategies tried : 1
% 147.09/127.10
% 147.09/127.10 Timing (in seconds)
% 147.09/127.10 ----------------------
% 147.09/127.11 Preprocessing : 0.89
% 147.09/127.11 Parsing : 0.46
% 147.09/127.11 CNF conversion : 0.07
% 147.09/127.11 Main loop : 124.97
% 147.09/127.11 Inferencing : 20.80
% 147.09/127.11 Reduction : 68.38
% 147.09/127.11 Demodulation : 51.22
% 147.09/127.11 BG Simplification : 0.36
% 147.09/127.11 Subsumption : 28.22
% 147.09/127.11 Abstraction : 0.91
% 147.09/127.11 MUC search : 0.00
% 147.09/127.11 Cooper : 0.00
% 147.09/127.11 Total : 126.03
% 147.09/127.11 Index Insertion : 0.00
% 147.09/127.11 Index Deletion : 0.00
% 147.09/127.11 Index Matching : 0.00
% 147.09/127.11 BG Taut test : 0.00
%------------------------------------------------------------------------------