TSTP Solution File: SWC187-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC187-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 11:01:32 EDT 2023
% Result : Unsatisfiable 166.63s 145.43s
% Output : CNFRefutation 166.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 125
% Syntax : Number of formulae : 729 ( 301 unt; 76 typ; 0 def)
% Number of atoms : 1432 ( 395 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1594 ( 815 ~; 779 |; 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 : 283 (; 283 !; 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_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_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_961,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file(unknown,unknown) ).
tff(f_770,axiom,
! [U,V] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_975,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1660,axiom,
( ssItem(sk8)
| ( nil = sk4 ) ),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_1666,axiom,
( ( cons(sk8,nil) = sk3 )
| ( nil = sk4 ) ),
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_446,axiom,
! [U,V] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
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_784,axiom,
! [U,V] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = 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_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_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [U] : ssItem(skaf83(U)),
file(unknown,unknown) ).
tff(f_543,axiom,
! [U] :
( ~ ssList(U)
| ( cons(skaf83(U),skaf82(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_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_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_227,axiom,
! [U] :
( ~ ssItem(U)
| cyclefreeP(cons(U,nil)) ),
file(unknown,unknown) ).
tff(f_212,axiom,
! [U] :
( ~ ssItem(U)
| totalorderedP(cons(U,nil)) ),
file(unknown,unknown) ).
tff(f_728,axiom,
! [U,V] :
( ~ totalorderedP(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U)
| totalorderedP(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_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
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_658,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file(unknown,unknown) ).
tff(f_898,axiom,
! [U,V,W] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file(unknown,unknown) ).
tff(f_1675,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_287400,plain,
! [V_11696,U_11697] :
( ~ ssList(V_11696)
| ~ ssItem(U_11697)
| ( cons(U_11697,V_11696) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_288328,plain,
! [U_11806] :
( ~ ssItem(U_11806)
| ( cons(U_11806,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_287400]) ).
tff(c_288402,plain,
cons(sk5,nil) != nil,
inference(resolution,[status(thm)],[c_384,c_288328]) ).
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_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_286771,plain,
! [U_11646] :
( ( app(U_11646,nil) = U_11646 )
| ~ ssList(U_11646) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_286892,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_286771]) ).
tff(c_290059,plain,
! [U_11907,V_11908] :
( rearsegP(app(U_11907,V_11908),V_11908)
| ~ ssList(app(U_11907,V_11908))
| ~ ssList(V_11908)
| ~ ssList(U_11907) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_290202,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_286892,c_290059]) ).
tff(c_290307,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_286892,c_290202]) ).
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_290317,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_290307,c_256]) ).
tff(c_290320,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_290317]) ).
tff(c_292845,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_290320]) ).
tff(c_252564,plain,
! [V_9565,U_9566] :
( ~ ssList(V_9565)
| ~ ssItem(U_9566)
| ( cons(U_9566,V_9565) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_253879,plain,
! [U_9692] :
( ~ ssItem(U_9692)
| ( cons(U_9692,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_252564]) ).
tff(c_253957,plain,
cons(sk5,nil) != nil,
inference(resolution,[status(thm)],[c_384,c_253879]) ).
tff(c_251680,plain,
! [U_9502] :
( ( app(nil,U_9502) = U_9502 )
| ~ ssList(U_9502) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_251798,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_251680]) ).
tff(c_255143,plain,
! [U_9759,V_9760] :
( frontsegP(app(U_9759,V_9760),U_9759)
| ~ ssList(app(U_9759,V_9760))
| ~ ssList(U_9759)
| ~ ssList(V_9760) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_255292,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_251798,c_255143]) ).
tff(c_255389,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_251798,c_255292]) ).
tff(c_251948,plain,
! [U_9515] :
( ( app(U_9515,nil) = U_9515 )
| ~ ssList(U_9515) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_252069,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_251948]) ).
tff(c_254861,plain,
! [U_9757,V_9758] :
( rearsegP(app(U_9757,V_9758),V_9758)
| ~ ssList(app(U_9757,V_9758))
| ~ ssList(V_9758)
| ~ ssList(U_9757) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_255001,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_252069,c_254861]) ).
tff(c_255101,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_252069,c_255001]) ).
tff(c_255114,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_255101,c_256]) ).
tff(c_255117,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_255114]) ).
tff(c_258278,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_255117]) ).
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_409,plain,
( ( sk2 = nil )
| ssItem(sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).
tff(c_463,plain,
ssItem(sk8),
inference(splitLeft,[status(thm)],[c_409]) ).
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_414,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_398,plain,
( ( sk4 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnfTransformation,[status(thm)],[f_1666]) ).
tff(c_406,plain,
( ( sk4 = nil )
| ( cons(sk8,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_398]) ).
tff(c_412,plain,
( ( sk2 = nil )
| ( cons(sk8,nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_406]) ).
tff(c_485,plain,
cons(sk8,nil) = sk1,
inference(splitLeft,[status(thm)],[c_412]) ).
tff(c_61248,plain,
! [U_2446,V_2447] :
( ( app(cons(U_2446,nil),V_2447) = cons(U_2446,V_2447) )
| ~ ssList(V_2447)
| ~ ssItem(U_2446) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_61266,plain,
! [V_2447] :
( ( cons(sk8,V_2447) = app(sk1,V_2447) )
| ~ ssList(V_2447)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_61248]) ).
tff(c_74576,plain,
! [V_3209] :
( ( cons(sk8,V_3209) = app(sk1,V_3209) )
| ~ ssList(V_3209) ),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_61266]) ).
tff(c_74714,plain,
cons(sk8,sk1) = app(sk1,sk1),
inference(resolution,[status(thm)],[c_414,c_74576]) ).
tff(c_1594,plain,
! [V_452,U_453] :
( ~ ssList(V_452)
| ~ ssItem(U_453)
| ( cons(U_453,V_452) != V_452 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_61081,plain,
! [U_2431] :
( ~ ssItem(U_2431)
| ( cons(U_2431,sk1) != sk1 ) ),
inference(resolution,[status(thm)],[c_414,c_1594]) ).
tff(c_61143,plain,
cons(sk8,sk1) != sk1,
inference(resolution,[status(thm)],[c_463,c_61081]) ).
tff(c_74718,plain,
app(sk1,sk1) != sk1,
inference(demodulation,[status(thm),theory(equality)],[c_74714,c_61143]) ).
tff(c_74807,plain,
( ssList(app(sk1,sk1))
| ~ ssList(sk1)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_74714,c_172]) ).
tff(c_74869,plain,
ssList(app(sk1,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_414,c_74807]) ).
tff(c_512,plain,
! [U_391] :
( ( app(nil,U_391) = U_391 )
| ~ ssList(U_391) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_637,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_414,c_512]) ).
tff(c_61569,plain,
! [U_2460,V_2461] :
( frontsegP(app(U_2460,V_2461),U_2460)
| ~ ssList(app(U_2460,V_2461))
| ~ ssList(U_2460)
| ~ ssList(V_2461) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_61697,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_637,c_61569]) ).
tff(c_61783,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_16,c_414,c_637,c_61697]) ).
tff(c_64432,plain,
! [X_2587,U_2588,V_2589] :
( frontsegP(cons(X_2587,U_2588),cons(X_2587,V_2589))
| ~ ssItem(X_2587)
| ~ ssList(U_2588)
| ~ ssList(V_2589)
| ~ frontsegP(U_2588,V_2589) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_64460,plain,
! [U_2588] :
( frontsegP(cons(sk8,U_2588),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_2588)
| ~ ssList(nil)
| ~ frontsegP(U_2588,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_64432]) ).
tff(c_95638,plain,
! [U_3879] :
( frontsegP(cons(sk8,U_3879),sk1)
| ~ ssList(U_3879)
| ~ frontsegP(U_3879,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_64460]) ).
tff(c_95720,plain,
( frontsegP(app(sk1,sk1),sk1)
| ~ ssList(sk1)
| ~ frontsegP(sk1,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_74714,c_95638]) ).
tff(c_95784,plain,
frontsegP(app(sk1,sk1),sk1),
inference(demodulation,[status(thm),theory(equality)],[c_61783,c_414,c_95720]) ).
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_95898,plain,
( ( app(sk1,sk1) = sk1 )
| ~ ssList(app(sk1,sk1))
| ~ ssList(sk1)
| ~ frontsegP(sk1,app(sk1,sk1)) ),
inference(resolution,[status(thm)],[c_95784,c_258]) ).
tff(c_95907,plain,
( ( app(sk1,sk1) = sk1 )
| ~ frontsegP(sk1,app(sk1,sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_74869,c_95898]) ).
tff(c_95908,plain,
~ frontsegP(sk1,app(sk1,sk1)),
inference(negUnitSimplification,[status(thm)],[c_74718,c_95907]) ).
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_66500,plain,
! [U_2674,V_2675,W_2676] :
( segmentP(app(app(U_2674,V_2675),W_2676),V_2675)
| ~ ssList(app(app(U_2674,V_2675),W_2676))
| ~ ssList(V_2675)
| ~ ssList(U_2674)
| ~ ssList(W_2676) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_66658,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_66500]) ).
tff(c_66777,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_414,c_390,c_66658]) ).
tff(c_76204,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_66777]) ).
tff(c_76207,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_76204]) ).
tff(c_76211,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_76207]) ).
tff(c_76213,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_66777]) ).
tff(c_64040,plain,
! [W_2580,V_2581,U_2582] :
( ( app(app(W_2580,V_2581),U_2582) = app(W_2580,app(V_2581,U_2582)) )
| ~ ssList(W_2580)
| ~ ssList(V_2581)
| ~ ssList(U_2582) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_64077,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_64040,c_390]) ).
tff(c_64230,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_64077]) ).
tff(c_98868,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_76213,c_64230]) ).
tff(c_98918,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_98868]) ).
tff(c_98951,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_98918]) ).
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_98979,plain,
( memberP(sk1,sk5)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_98951,c_350]) ).
tff(c_99036,plain,
memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_384,c_414,c_98951,c_98979]) ).
tff(c_64011,plain,
! [W_2577,U_2578,V_2579] :
( ( W_2577 = U_2578 )
| memberP(V_2579,W_2577)
| ~ ssItem(W_2577)
| ~ ssItem(U_2578)
| ~ ssList(V_2579)
| ~ memberP(cons(U_2578,V_2579),W_2577) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_64029,plain,
! [W_2577] :
( ( sk8 = W_2577 )
| memberP(nil,W_2577)
| ~ ssItem(W_2577)
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ memberP(sk1,W_2577) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_64011]) ).
tff(c_64038,plain,
! [W_2577] :
( ( sk8 = W_2577 )
| memberP(nil,W_2577)
| ~ ssItem(W_2577)
| ~ memberP(sk1,W_2577) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_64029]) ).
tff(c_99067,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_99036,c_64038]) ).
tff(c_99070,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_99067]) ).
tff(c_99071,plain,
memberP(nil,sk5),
inference(splitLeft,[status(thm)],[c_99070]) ).
tff(c_142,plain,
! [U_65] :
( ~ ssItem(U_65)
| ~ memberP(nil,U_65) ),
inference(cnfTransformation,[status(thm)],[f_233]) ).
tff(c_99075,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_99071,c_142]) ).
tff(c_99079,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_99075]) ).
tff(c_99080,plain,
sk8 = sk5,
inference(splitRight,[status(thm)],[c_99070]) ).
tff(c_99172,plain,
cons(sk5,nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_99080,c_485]) ).
tff(c_636,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_512]) ).
tff(c_3877,plain,
! [U_640,V_641] :
( frontsegP(app(U_640,V_641),U_640)
| ~ ssList(app(U_640,V_641))
| ~ ssList(U_640)
| ~ ssList(V_641) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_4005,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_3877]) ).
tff(c_4088,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_636,c_4005]) ).
tff(c_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_1740,plain,
! [U_467,V_468] :
( ( tl(cons(U_467,V_468)) = V_468 )
| ~ ssList(V_468)
| ~ ssItem(U_467) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_1752,plain,
( ( tl(sk1) = nil )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_1740]) ).
tff(c_1756,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_16,c_1752]) ).
tff(c_1252,plain,
! [V_443,U_444] :
( ~ ssList(V_443)
| ~ ssItem(U_444)
| ( cons(U_444,V_443) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_8343,plain,
! [U_828] :
( ~ ssItem(U_828)
| ( cons(U_828,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1252]) ).
tff(c_8349,plain,
cons(sk8,nil) != nil,
inference(resolution,[status(thm)],[c_463,c_8343]) ).
tff(c_8406,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_485,c_8349]) ).
tff(c_2071,plain,
! [U_521,V_522] :
( ( hd(cons(U_521,V_522)) = U_521 )
| ~ ssList(V_522)
| ~ ssItem(U_521) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_2086,plain,
( ( hd(sk1) = sk8 )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_2071]) ).
tff(c_2092,plain,
hd(sk1) = sk8,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_16,c_2086]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2406,plain,
! [U_551] :
( ( nil = U_551 )
| ( cons(skaf83(U_551),skaf82(U_551)) = U_551 )
| ~ ssList(U_551) ),
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_2412,plain,
! [U_551] :
( ( skaf83(U_551) = hd(U_551) )
| ~ ssList(skaf82(U_551))
| ~ ssItem(skaf83(U_551))
| ( nil = U_551 )
| ~ ssList(U_551) ),
inference(superposition,[status(thm),theory(equality)],[c_2406,c_194]) ).
tff(c_12882,plain,
! [U_1185] :
( ( skaf83(U_1185) = hd(U_1185) )
| ( nil = U_1185 )
| ~ ssList(U_1185) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2412]) ).
tff(c_12978,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_414,c_12882]) ).
tff(c_13021,plain,
( ( skaf83(sk1) = sk8 )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2092,c_12978]) ).
tff(c_13022,plain,
skaf83(sk1) = sk8,
inference(negUnitSimplification,[status(thm)],[c_8406,c_13021]) ).
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_13044,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_13022,c_218]) ).
tff(c_13062,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_13044]) ).
tff(c_13063,plain,
cons(sk8,skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_8406,c_13062]) ).
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_13701,plain,
( ( tl(sk1) = skaf82(sk1) )
| ~ ssList(skaf82(sk1))
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_13063,c_192]) ).
tff(c_13765,plain,
skaf82(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_26,c_1756,c_13701]) ).
tff(c_3632,plain,
! [U_638,V_639] :
( rearsegP(app(U_638,V_639),V_639)
| ~ ssList(app(U_638,V_639))
| ~ ssList(V_639)
| ~ ssList(U_638) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_3760,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_3632]) ).
tff(c_3843,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_636,c_3760]) ).
tff(c_13026,plain,
( ( skaf83(sk6) = hd(sk6) )
| ( sk6 = nil ) ),
inference(resolution,[status(thm)],[c_386,c_12882]) ).
tff(c_13156,plain,
sk6 = nil,
inference(splitLeft,[status(thm)],[c_13026]) ).
tff(c_818,plain,
! [U_402] :
( ( app(U_402,nil) = U_402 )
| ~ ssList(U_402) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_946,plain,
app(sk6,nil) = sk6,
inference(resolution,[status(thm)],[c_386,c_818]) ).
tff(c_3736,plain,
( rearsegP(sk6,nil)
| ~ ssList(app(sk6,nil))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_946,c_3632]) ).
tff(c_3827,plain,
rearsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_946,c_3736]) ).
tff(c_3845,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ rearsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_3827,c_256]) ).
tff(c_3848,plain,
( ( sk6 = nil )
| ~ rearsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_3845]) ).
tff(c_6405,plain,
~ rearsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_3848]) ).
tff(c_13182,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_13156,c_6405]) ).
tff(c_13222,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3843,c_13182]) ).
tff(c_13223,plain,
skaf83(sk6) = hd(sk6),
inference(splitRight,[status(thm)],[c_13026]) ).
tff(c_13251,plain,
ssItem(hd(sk6)),
inference(superposition,[status(thm),theory(equality)],[c_13223,c_24]) ).
tff(c_13224,plain,
sk6 != nil,
inference(splitRight,[status(thm)],[c_13026]) ).
tff(c_13241,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13223,c_218]) ).
tff(c_13258,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_13241]) ).
tff(c_13259,plain,
cons(hd(sk6),skaf82(sk6)) = sk6,
inference(negUnitSimplification,[status(thm)],[c_13224,c_13258]) ).
tff(c_8266,plain,
! [W_822,U_823,V_824,X_825] :
( ( W_822 = U_823 )
| ~ ssItem(U_823)
| ~ ssItem(W_822)
| ~ ssList(V_824)
| ~ ssList(X_825)
| ~ frontsegP(cons(U_823,V_824),cons(W_822,X_825)) ),
inference(cnfTransformation,[status(thm)],[f_1422]) ).
tff(c_8299,plain,
! [U_823,V_824] :
( ( sk8 = U_823 )
| ~ ssItem(U_823)
| ~ ssItem(sk8)
| ~ ssList(V_824)
| ~ ssList(nil)
| ~ frontsegP(cons(U_823,V_824),sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_8266]) ).
tff(c_56233,plain,
! [U_2375,V_2376] :
( ( sk8 = U_2375 )
| ~ ssItem(U_2375)
| ~ ssList(V_2376)
| ~ frontsegP(cons(U_2375,V_2376),sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_8299]) ).
tff(c_56314,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk6,sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_13259,c_56233]) ).
tff(c_56416,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk6,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13251,c_56314]) ).
tff(c_56428,plain,
~ frontsegP(sk6,sk1),
inference(splitLeft,[status(thm)],[c_56416]) ).
tff(c_628,plain,
! [U_2] : ( app(nil,skaf82(U_2)) = skaf82(U_2) ),
inference(resolution,[status(thm)],[c_26,c_512]) ).
tff(c_3888,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_628,c_3877]) ).
tff(c_4010,plain,
! [U_2] : frontsegP(skaf82(U_2),nil),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_16,c_26,c_628,c_3888]) ).
tff(c_8296,plain,
! [W_822,X_825] :
( ( sk8 = W_822 )
| ~ ssItem(sk8)
| ~ ssItem(W_822)
| ~ ssList(nil)
| ~ ssList(X_825)
| ~ frontsegP(sk1,cons(W_822,X_825)) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_8266]) ).
tff(c_56542,plain,
! [W_2377,X_2378] :
( ( sk8 = W_2377 )
| ~ ssItem(W_2377)
| ~ ssList(X_2378)
| ~ frontsegP(sk1,cons(W_2377,X_2378)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_8296]) ).
tff(c_56626,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13259,c_56542]) ).
tff(c_56728,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13251,c_56626]) ).
tff(c_56740,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_56728]) ).
tff(c_9039,plain,
! [U_857,V_858,W_859] :
( segmentP(app(app(U_857,V_858),W_859),V_858)
| ~ ssList(app(app(U_857,V_858),W_859))
| ~ ssList(V_858)
| ~ ssList(U_857)
| ~ ssList(W_859) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_9203,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_9039]) ).
tff(c_9328,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_414,c_390,c_9203]) ).
tff(c_17154,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_9328]) ).
tff(c_17157,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_17154]) ).
tff(c_17161,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_17157]) ).
tff(c_17163,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_9328]) ).
tff(c_6595,plain,
! [W_766,V_767,U_768] :
( ( app(app(W_766,V_767),U_768) = app(W_766,app(V_767,U_768)) )
| ~ ssList(W_766)
| ~ ssList(V_767)
| ~ ssList(U_768) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_6750,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_6595]) ).
tff(c_6853,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_6750]) ).
tff(c_58878,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_17163,c_6853]) ).
tff(c_58928,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_58878]) ).
tff(c_58962,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_58928]) ).
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_59020,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_58962,c_288]) ).
tff(c_59067,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_414,c_58962,c_59020]) ).
tff(c_59068,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_56740,c_59067]) ).
tff(c_59085,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_59068]) ).
tff(c_59089,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_59085]) ).
tff(c_59090,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_56728]) ).
tff(c_59271,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_59090,c_13259]) ).
tff(c_6874,plain,
! [X_771,U_772,V_773] :
( frontsegP(cons(X_771,U_772),cons(X_771,V_773))
| ~ ssItem(X_771)
| ~ ssList(U_772)
| ~ ssList(V_773)
| ~ frontsegP(U_772,V_773) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_6902,plain,
! [U_772] :
( frontsegP(cons(sk8,U_772),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_772)
| ~ ssList(nil)
| ~ frontsegP(U_772,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_6874]) ).
tff(c_6916,plain,
! [U_772] :
( frontsegP(cons(sk8,U_772),sk1)
| ~ ssList(U_772)
| ~ frontsegP(U_772,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_6902]) ).
tff(c_59398,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_59271,c_6916]) ).
tff(c_59508,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_4010,c_26,c_59398]) ).
tff(c_59510,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_56428,c_59508]) ).
tff(c_59512,plain,
frontsegP(sk6,sk1),
inference(splitRight,[status(thm)],[c_56416]) ).
tff(c_59780,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_59512,c_258]) ).
tff(c_59789,plain,
( ( sk6 = sk1 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_386,c_59780]) ).
tff(c_60026,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_59789]) ).
tff(c_6632,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_6595,c_390]) ).
tff(c_6782,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_6632]) ).
tff(c_60151,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_17163,c_6782]) ).
tff(c_60201,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_60151]) ).
tff(c_60235,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_60201]) ).
tff(c_60308,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_60235,c_288]) ).
tff(c_60355,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_414,c_60235,c_60308]) ).
tff(c_60356,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_60026,c_60355]) ).
tff(c_60373,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_60356]) ).
tff(c_60377,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_60373]) ).
tff(c_60378,plain,
sk6 = sk1,
inference(splitRight,[status(thm)],[c_59789]) ).
tff(c_94,plain,
! [U_36] : ssItem(skaf44(U_36)),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_1967,plain,
! [U_499] :
( ( cons(skaf44(U_499),nil) = U_499 )
| ~ ssList(U_499)
| ~ singletonP(U_499) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_140,plain,
! [U_64] :
( cyclefreeP(cons(U_64,nil))
| ~ ssItem(U_64) ),
inference(cnfTransformation,[status(thm)],[f_227]) ).
tff(c_1994,plain,
! [U_499] :
( cyclefreeP(U_499)
| ~ ssItem(skaf44(U_499))
| ~ ssList(U_499)
| ~ singletonP(U_499) ),
inference(superposition,[status(thm),theory(equality)],[c_1967,c_140]) ).
tff(c_3143,plain,
! [U_601] :
( cyclefreeP(U_601)
| ~ ssList(U_601)
| ~ singletonP(U_601) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_1994]) ).
tff(c_3285,plain,
( cyclefreeP(sk6)
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_3143]) ).
tff(c_3294,plain,
~ singletonP(sk6),
inference(splitLeft,[status(thm)],[c_3285]) ).
tff(c_661,plain,
! [U_392] :
( totalorderedP(cons(U_392,nil))
| ~ ssItem(U_392) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_664,plain,
( totalorderedP(sk1)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_661]) ).
tff(c_666,plain,
totalorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_664]) ).
tff(c_39416,plain,
! [W_2074,X_2075] :
( ( sk8 = W_2074 )
| ~ ssItem(W_2074)
| ~ ssList(X_2075)
| ~ frontsegP(sk1,cons(W_2074,X_2075)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_8296]) ).
tff(c_39500,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13259,c_39416]) ).
tff(c_39602,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13251,c_39500]) ).
tff(c_39648,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_39602]) ).
tff(c_43767,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_17163,c_6782]) ).
tff(c_43820,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_43767]) ).
tff(c_43856,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_43820]) ).
tff(c_43917,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_43856,c_288]) ).
tff(c_43966,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_414,c_43856,c_43917]) ).
tff(c_43967,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_39648,c_43966]) ).
tff(c_43984,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_43967]) ).
tff(c_43988,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_43984]) ).
tff(c_43990,plain,
frontsegP(sk1,sk6),
inference(splitRight,[status(thm)],[c_39602]) ).
tff(c_43989,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_39602]) ).
tff(c_44008,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_43989,c_13259]) ).
tff(c_44123,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_44008,c_6916]) ).
tff(c_44232,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_4010,c_26,c_44123]) ).
tff(c_44500,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_44232,c_258]) ).
tff(c_44509,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_43990,c_414,c_386,c_44500]) ).
tff(c_250,plain,
! [V_149,U_148] :
( ( nil = V_149 )
| totalorderedP(V_149)
| ~ ssItem(U_148)
| ~ ssList(V_149)
| ~ totalorderedP(cons(U_148,V_149)) ),
inference(cnfTransformation,[status(thm)],[f_728]) ).
tff(c_14487,plain,
( ( skaf82(sk6) = nil )
| totalorderedP(skaf82(sk6))
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ totalorderedP(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_13259,c_250]) ).
tff(c_14554,plain,
( ( skaf82(sk6) = nil )
| totalorderedP(skaf82(sk6))
| ~ totalorderedP(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_13251,c_14487]) ).
tff(c_28613,plain,
~ totalorderedP(sk6),
inference(splitLeft,[status(thm)],[c_14554]) ).
tff(c_44538,plain,
~ totalorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_44509,c_28613]) ).
tff(c_44709,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_666,c_44538]) ).
tff(c_44710,plain,
( totalorderedP(skaf82(sk6))
| ( skaf82(sk6) = nil ) ),
inference(splitRight,[status(thm)],[c_14554]) ).
tff(c_44799,plain,
skaf82(sk6) = nil,
inference(splitLeft,[status(thm)],[c_44710]) ).
tff(c_44801,plain,
cons(hd(sk6),nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_44799,c_13259]) ).
tff(c_2526,plain,
! [U_562] :
( singletonP(cons(U_562,nil))
| ~ ssList(cons(U_562,nil))
| ~ ssItem(U_562) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_2533,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_2526]) ).
tff(c_2541,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2533]) ).
tff(c_45088,plain,
( singletonP(sk6)
| ~ ssItem(hd(sk6)) ),
inference(superposition,[status(thm),theory(equality)],[c_44801,c_2541]) ).
tff(c_45178,plain,
singletonP(sk6),
inference(demodulation,[status(thm),theory(equality)],[c_13251,c_45088]) ).
tff(c_45180,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3294,c_45178]) ).
tff(c_45182,plain,
skaf82(sk6) != nil,
inference(splitRight,[status(thm)],[c_44710]) ).
tff(c_60494,plain,
skaf82(sk1) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_60378,c_45182]) ).
tff(c_60666,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13765,c_60494]) ).
tff(c_60667,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_3848]) ).
tff(c_639,plain,
app(nil,sk6) = sk6,
inference(resolution,[status(thm)],[c_386,c_512]) ).
tff(c_3996,plain,
( frontsegP(sk6,nil)
| ~ ssList(app(nil,sk6))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_639,c_3877]) ).
tff(c_4082,plain,
frontsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_639,c_3996]) ).
tff(c_4172,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_4082,c_258]) ).
tff(c_4175,plain,
( ( sk6 = nil )
| ~ frontsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_4172]) ).
tff(c_6058,plain,
~ frontsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_4175]) ).
tff(c_60669,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_60667,c_6058]) ).
tff(c_60704,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4088,c_60669]) ).
tff(c_60705,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_4175]) ).
tff(c_392,plain,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnfTransformation,[status(thm)],[f_1657]) ).
tff(c_669,plain,
memberP(sk6,sk5),
inference(splitLeft,[status(thm)],[c_392]) ).
tff(c_60736,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_60705,c_669]) ).
tff(c_60955,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_60736,c_142]) ).
tff(c_60959,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_60955]) ).
tff(c_60961,plain,
singletonP(sk6),
inference(splitRight,[status(thm)],[c_3285]) ).
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_64657,plain,
! [U_2598] :
( ~ ssItem(U_2598)
| ( cons(U_2598,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1594]) ).
tff(c_64766,plain,
! [U_2601] : ( cons(skaf44(U_2601),nil) != nil ),
inference(resolution,[status(thm)],[c_94,c_64657]) ).
tff(c_68863,plain,
! [U_2798] :
( ( nil != U_2798 )
| ~ ssList(U_2798)
| ~ singletonP(U_2798) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_64766]) ).
tff(c_68965,plain,
( ( sk6 != nil )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_68863]) ).
tff(c_69006,plain,
sk6 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_60961,c_68965]) ).
tff(c_74717,plain,
cons(sk8,sk7) = app(sk1,sk7),
inference(resolution,[status(thm)],[c_388,c_74576]) ).
tff(c_75338,plain,
( ssList(app(sk1,sk7))
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_74717,c_172]) ).
tff(c_75400,plain,
ssList(app(sk1,sk7)),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_388,c_75338]) ).
tff(c_99170,plain,
hd(sk1) = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_99080,c_2092]) ).
tff(c_99445,plain,
app(sk6,app(sk1,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_99172,c_98868]) ).
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_101640,plain,
( ( hd(sk6) = hd(sk1) )
| ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(app(sk1,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_99445,c_246]) ).
tff(c_101675,plain,
( ( hd(sk6) = sk5 )
| ( sk6 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_75400,c_386,c_99170,c_101640]) ).
tff(c_101676,plain,
hd(sk6) = sk5,
inference(negUnitSimplification,[status(thm)],[c_69006,c_101675]) ).
tff(c_1973,plain,
! [U_499] :
( ( tl(U_499) = nil )
| ~ ssList(nil)
| ~ ssItem(skaf44(U_499))
| ~ ssList(U_499)
| ~ singletonP(U_499) ),
inference(superposition,[status(thm),theory(equality)],[c_1967,c_192]) ).
tff(c_69037,plain,
! [U_2836] :
( ( tl(U_2836) = nil )
| ~ ssList(U_2836)
| ~ singletonP(U_2836) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_1973]) ).
tff(c_69139,plain,
( ( tl(sk6) = nil )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_69037]) ).
tff(c_69180,plain,
tl(sk6) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_60961,c_69139]) ).
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_69188,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),nil) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_69180,c_208]) ).
tff(c_69198,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),nil) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_69188]) ).
tff(c_69199,plain,
cons(hd(sk6),nil) = sk6,
inference(negUnitSimplification,[status(thm)],[c_69006,c_69198]) ).
tff(c_101808,plain,
cons(sk5,nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_101676,c_69199]) ).
tff(c_101813,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_99172,c_101808]) ).
tff(c_61319,plain,
! [U_2458,V_2459] :
( rearsegP(app(U_2458,V_2459),V_2459)
| ~ ssList(app(U_2458,V_2459))
| ~ ssList(V_2459)
| ~ ssList(U_2458) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_61423,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_61319]) ).
tff(c_61517,plain,
( rearsegP(sk1,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_414,c_390,c_61423]) ).
tff(c_76703,plain,
~ ssList(app(sk6,cons(sk5,nil))),
inference(splitLeft,[status(thm)],[c_61517]) ).
tff(c_76706,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_76703]) ).
tff(c_76710,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_76213,c_386,c_76706]) ).
tff(c_76712,plain,
ssList(app(sk6,cons(sk5,nil))),
inference(splitRight,[status(thm)],[c_61517]) ).
tff(c_99473,plain,
ssList(app(sk6,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_99172,c_76712]) ).
tff(c_99493,plain,
app(app(sk6,sk1),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_99172,c_390]) ).
tff(c_101725,plain,
( frontsegP(sk1,app(sk6,sk1))
| ~ ssList(app(app(sk6,sk1),sk7))
| ~ ssList(app(sk6,sk1))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_99493,c_288]) ).
tff(c_101769,plain,
frontsegP(sk1,app(sk6,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_99473,c_414,c_99493,c_101725]) ).
tff(c_102752,plain,
frontsegP(sk1,app(sk1,sk1)),
inference(demodulation,[status(thm),theory(equality)],[c_101813,c_101769]) ).
tff(c_102753,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_95908,c_102752]) ).
tff(c_102755,plain,
~ memberP(sk6,sk5),
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_105941,plain,
! [U_4191,V_4192] :
( rearsegP(app(U_4191,V_4192),V_4192)
| ~ ssList(app(U_4191,V_4192))
| ~ ssList(V_4192)
| ~ ssList(U_4191) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_106060,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_105941]) ).
tff(c_106137,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_636,c_106060]) ).
tff(c_103790,plain,
! [U_4013,V_4014] :
( ( tl(cons(U_4013,V_4014)) = V_4014 )
| ~ ssList(V_4014)
| ~ ssItem(U_4013) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_103802,plain,
( ( tl(sk1) = nil )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_103790]) ).
tff(c_103806,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_16,c_103802]) ).
tff(c_103320,plain,
! [V_3993,U_3994] :
( ~ ssList(V_3993)
| ~ ssItem(U_3994)
| ( cons(U_3994,V_3993) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_437]) ).
tff(c_103882,plain,
! [U_4028] :
( ~ ssItem(U_4028)
| ( cons(U_4028,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_103320]) ).
tff(c_103888,plain,
cons(sk8,nil) != nil,
inference(resolution,[status(thm)],[c_463,c_103882]) ).
tff(c_103945,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_485,c_103888]) ).
tff(c_103964,plain,
! [U_4029,V_4030] :
( ( hd(cons(U_4029,V_4030)) = U_4029 )
| ~ ssList(V_4030)
| ~ ssItem(U_4029) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_103979,plain,
( ( hd(sk1) = sk8 )
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_103964]) ).
tff(c_103985,plain,
hd(sk1) = sk8,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_16,c_103979]) ).
tff(c_104324,plain,
! [U_4077] :
( ( nil = U_4077 )
| ( cons(skaf83(U_4077),skaf82(U_4077)) = U_4077 )
| ~ ssList(U_4077) ),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_104333,plain,
! [U_4077] :
( ( skaf83(U_4077) = hd(U_4077) )
| ~ ssList(skaf82(U_4077))
| ~ ssItem(skaf83(U_4077))
| ( nil = U_4077 )
| ~ ssList(U_4077) ),
inference(superposition,[status(thm),theory(equality)],[c_104324,c_194]) ).
tff(c_114184,plain,
! [U_4671] :
( ( skaf83(U_4671) = hd(U_4671) )
| ( nil = U_4671 )
| ~ ssList(U_4671) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_104333]) ).
tff(c_114280,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_414,c_114184]) ).
tff(c_114323,plain,
( ( skaf83(sk1) = sk8 )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_103985,c_114280]) ).
tff(c_114324,plain,
skaf83(sk1) = sk8,
inference(negUnitSimplification,[status(thm)],[c_103945,c_114323]) ).
tff(c_114348,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_114324,c_218]) ).
tff(c_114363,plain,
( ( sk1 = nil )
| ( cons(sk8,skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_114348]) ).
tff(c_114364,plain,
cons(sk8,skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_103945,c_114363]) ).
tff(c_114842,plain,
( ( tl(sk1) = skaf82(sk1) )
| ~ ssList(skaf82(sk1))
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_114364,c_192]) ).
tff(c_114903,plain,
skaf82(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_26,c_103806,c_114842]) ).
tff(c_105630,plain,
! [U_4184,V_4185] :
( frontsegP(app(U_4184,V_4185),U_4184)
| ~ ssList(app(U_4184,V_4185))
| ~ ssList(U_4184)
| ~ ssList(V_4185) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_105743,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_636,c_105630]) ).
tff(c_105816,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_636,c_105743]) ).
tff(c_114326,plain,
( ( skaf83(sk6) = hd(sk6) )
| ( sk6 = nil ) ),
inference(resolution,[status(thm)],[c_386,c_114184]) ).
tff(c_114531,plain,
sk6 = nil,
inference(splitLeft,[status(thm)],[c_114326]) ).
tff(c_105734,plain,
( frontsegP(sk6,nil)
| ~ ssList(app(nil,sk6))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_639,c_105630]) ).
tff(c_105810,plain,
frontsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_639,c_105734]) ).
tff(c_105890,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_105810,c_258]) ).
tff(c_105893,plain,
( ( sk6 = nil )
| ~ frontsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_105890]) ).
tff(c_108078,plain,
~ frontsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_105893]) ).
tff(c_114555,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_114531,c_108078]) ).
tff(c_114593,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_105816,c_114555]) ).
tff(c_114594,plain,
skaf83(sk6) = hd(sk6),
inference(splitRight,[status(thm)],[c_114326]) ).
tff(c_114622,plain,
ssItem(hd(sk6)),
inference(superposition,[status(thm),theory(equality)],[c_114594,c_24]) ).
tff(c_114595,plain,
sk6 != nil,
inference(splitRight,[status(thm)],[c_114326]) ).
tff(c_114614,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 )
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_114594,c_218]) ).
tff(c_114629,plain,
( ( sk6 = nil )
| ( cons(hd(sk6),skaf82(sk6)) = sk6 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_114614]) ).
tff(c_114630,plain,
cons(hd(sk6),skaf82(sk6)) = sk6,
inference(negUnitSimplification,[status(thm)],[c_114595,c_114629]) ).
tff(c_110361,plain,
! [W_4371,U_4372,V_4373,X_4374] :
( ( W_4371 = U_4372 )
| ~ ssItem(U_4372)
| ~ ssItem(W_4371)
| ~ ssList(V_4373)
| ~ ssList(X_4374)
| ~ frontsegP(cons(U_4372,V_4373),cons(W_4371,X_4374)) ),
inference(cnfTransformation,[status(thm)],[f_1422]) ).
tff(c_110391,plain,
! [W_4371,X_4374] :
( ( sk8 = W_4371 )
| ~ ssItem(sk8)
| ~ ssItem(W_4371)
| ~ ssList(nil)
| ~ ssList(X_4374)
| ~ frontsegP(sk1,cons(W_4371,X_4374)) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_110361]) ).
tff(c_158235,plain,
! [W_6036,X_6037] :
( ( sk8 = W_6036 )
| ~ ssItem(W_6036)
| ~ ssList(X_6037)
| ~ frontsegP(sk1,cons(W_6036,X_6037)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_110391]) ).
tff(c_158322,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_114630,c_158235]) ).
tff(c_158423,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_114622,c_158322]) ).
tff(c_158440,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_158423]) ).
tff(c_111350,plain,
! [U_4409,V_4410,W_4411] :
( segmentP(app(app(U_4409,V_4410),W_4411),V_4410)
| ~ ssList(app(app(U_4409,V_4410),W_4411))
| ~ ssList(V_4410)
| ~ ssList(U_4409)
| ~ ssList(W_4411) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_111514,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_111350]) ).
tff(c_111639,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_414,c_390,c_111514]) ).
tff(c_126609,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_111639]) ).
tff(c_126612,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_126609]) ).
tff(c_126616,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_126612]) ).
tff(c_126618,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_111639]) ).
tff(c_108409,plain,
! [W_4310,V_4311,U_4312] :
( ( app(app(W_4310,V_4311),U_4312) = app(W_4310,app(V_4311,U_4312)) )
| ~ ssList(W_4310)
| ~ ssList(V_4311)
| ~ ssList(U_4312) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_108446,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_108409,c_390]) ).
tff(c_108596,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_108446]) ).
tff(c_161347,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_126618,c_108596]) ).
tff(c_161397,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_161347]) ).
tff(c_161431,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_161397]) ).
tff(c_161776,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_161431,c_288]) ).
tff(c_161822,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_414,c_161431,c_161776]) ).
tff(c_161823,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_158440,c_161822]) ).
tff(c_161926,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_161823]) ).
tff(c_161930,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_161926]) ).
tff(c_161932,plain,
frontsegP(sk1,sk6),
inference(splitRight,[status(thm)],[c_158423]) ).
tff(c_105686,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_628,c_105630]) ).
tff(c_105778,plain,
! [U_2] : frontsegP(skaf82(U_2),nil),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_16,c_26,c_628,c_105686]) ).
tff(c_161931,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_158423]) ).
tff(c_161949,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_161931,c_114630]) ).
tff(c_109341,plain,
! [X_4334,U_4335,V_4336] :
( frontsegP(cons(X_4334,U_4335),cons(X_4334,V_4336))
| ~ ssItem(X_4334)
| ~ ssList(U_4335)
| ~ ssList(V_4336)
| ~ frontsegP(U_4335,V_4336) ),
inference(cnfTransformation,[status(thm)],[f_1460]) ).
tff(c_109369,plain,
! [U_4335] :
( frontsegP(cons(sk8,U_4335),sk1)
| ~ ssItem(sk8)
| ~ ssList(U_4335)
| ~ ssList(nil)
| ~ frontsegP(U_4335,nil) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_109341]) ).
tff(c_109383,plain,
! [U_4335] :
( frontsegP(cons(sk8,U_4335),sk1)
| ~ ssList(U_4335)
| ~ frontsegP(U_4335,nil) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_109369]) ).
tff(c_162133,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_161949,c_109383]) ).
tff(c_162241,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_105778,c_26,c_162133]) ).
tff(c_162313,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_162241,c_258]) ).
tff(c_162322,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_161932,c_414,c_386,c_162313]) ).
tff(c_103818,plain,
! [U_4017] :
( ( cons(skaf44(U_4017),nil) = U_4017 )
| ~ ssList(U_4017)
| ~ singletonP(U_4017) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_103842,plain,
! [U_4017] :
( cyclefreeP(U_4017)
| ~ ssItem(skaf44(U_4017))
| ~ ssList(U_4017)
| ~ singletonP(U_4017) ),
inference(superposition,[status(thm),theory(equality)],[c_103818,c_140]) ).
tff(c_104180,plain,
! [U_4076] :
( cyclefreeP(U_4076)
| ~ ssList(U_4076)
| ~ singletonP(U_4076) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_103842]) ).
tff(c_104321,plain,
( cyclefreeP(sk6)
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_104180]) ).
tff(c_104372,plain,
~ singletonP(sk6),
inference(splitLeft,[status(thm)],[c_104321]) ).
tff(c_506,plain,
! [U_390] :
( strictorderedP(cons(U_390,nil))
| ~ ssItem(U_390) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_509,plain,
( strictorderedP(sk1)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_506]) ).
tff(c_511,plain,
strictorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_509]) ).
tff(c_140899,plain,
! [W_5678,X_5679] :
( ( sk8 = W_5678 )
| ~ ssItem(W_5678)
| ~ ssList(X_5679)
| ~ frontsegP(sk1,cons(W_5678,X_5679)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_110391]) ).
tff(c_140986,plain,
( ( hd(sk6) = sk8 )
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ frontsegP(sk1,sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_114630,c_140899]) ).
tff(c_141087,plain,
( ( hd(sk6) = sk8 )
| ~ frontsegP(sk1,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_114622,c_140986]) ).
tff(c_141104,plain,
~ frontsegP(sk1,sk6),
inference(splitLeft,[status(thm)],[c_141087]) ).
tff(c_108564,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_108409]) ).
tff(c_108667,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_108564]) ).
tff(c_146173,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_126618,c_108667]) ).
tff(c_146223,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_146173]) ).
tff(c_146257,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_146223]) ).
tff(c_146318,plain,
( frontsegP(sk1,sk6)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_146257,c_288]) ).
tff(c_146364,plain,
( frontsegP(sk1,sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_414,c_146257,c_146318]) ).
tff(c_146365,plain,
~ ssList(cons(sk5,sk7)),
inference(negUnitSimplification,[status(thm)],[c_141104,c_146364]) ).
tff(c_146380,plain,
( ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_146365]) ).
tff(c_146384,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_146380]) ).
tff(c_146386,plain,
frontsegP(sk1,sk6),
inference(splitRight,[status(thm)],[c_141087]) ).
tff(c_146385,plain,
hd(sk6) = sk8,
inference(splitRight,[status(thm)],[c_141087]) ).
tff(c_146558,plain,
cons(sk8,skaf82(sk6)) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_146385,c_114630]) ).
tff(c_146718,plain,
( frontsegP(sk6,sk1)
| ~ ssList(skaf82(sk6))
| ~ frontsegP(skaf82(sk6),nil) ),
inference(superposition,[status(thm),theory(equality)],[c_146558,c_109383]) ).
tff(c_146826,plain,
frontsegP(sk6,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_105778,c_26,c_146718]) ).
tff(c_147092,plain,
( ( sk6 = sk1 )
| ~ ssList(sk6)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk6) ),
inference(resolution,[status(thm)],[c_146826,c_258]) ).
tff(c_147101,plain,
sk6 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_146386,c_414,c_386,c_147092]) ).
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_116162,plain,
( ( skaf82(sk6) = nil )
| strictorderedP(skaf82(sk6))
| ~ ssItem(hd(sk6))
| ~ ssList(skaf82(sk6))
| ~ strictorderedP(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_114630,c_248]) ).
tff(c_116227,plain,
( ( skaf82(sk6) = nil )
| strictorderedP(skaf82(sk6))
| ~ strictorderedP(sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_114622,c_116162]) ).
tff(c_130399,plain,
~ strictorderedP(sk6),
inference(splitLeft,[status(thm)],[c_116227]) ).
tff(c_147130,plain,
~ strictorderedP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_147101,c_130399]) ).
tff(c_147300,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_511,c_147130]) ).
tff(c_147301,plain,
( strictorderedP(skaf82(sk6))
| ( skaf82(sk6) = nil ) ),
inference(splitRight,[status(thm)],[c_116227]) ).
tff(c_147390,plain,
skaf82(sk6) = nil,
inference(splitLeft,[status(thm)],[c_147301]) ).
tff(c_147393,plain,
cons(hd(sk6),nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_147390,c_114630]) ).
tff(c_104784,plain,
! [U_4113] :
( singletonP(cons(U_4113,nil))
| ~ ssList(cons(U_4113,nil))
| ~ ssItem(U_4113) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_104791,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_104784]) ).
tff(c_104799,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_104791]) ).
tff(c_147673,plain,
( singletonP(sk6)
| ~ ssItem(hd(sk6)) ),
inference(superposition,[status(thm),theory(equality)],[c_147393,c_104799]) ).
tff(c_147763,plain,
singletonP(sk6),
inference(demodulation,[status(thm),theory(equality)],[c_114622,c_147673]) ).
tff(c_147765,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_104372,c_147763]) ).
tff(c_147767,plain,
skaf82(sk6) != nil,
inference(splitRight,[status(thm)],[c_147301]) ).
tff(c_162349,plain,
skaf82(sk1) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_162322,c_147767]) ).
tff(c_162522,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_114903,c_162349]) ).
tff(c_162523,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_105893]) ).
tff(c_102902,plain,
! [U_3952] :
( ( app(U_3952,nil) = U_3952 )
| ~ ssList(U_3952) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_103030,plain,
app(sk6,nil) = sk6,
inference(resolution,[status(thm)],[c_386,c_102902]) ).
tff(c_106036,plain,
( rearsegP(sk6,nil)
| ~ ssList(app(sk6,nil))
| ~ ssList(nil)
| ~ ssList(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_103030,c_105941]) ).
tff(c_106121,plain,
rearsegP(sk6,nil),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_103030,c_106036]) ).
tff(c_106139,plain,
( ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ rearsegP(nil,sk6) ),
inference(resolution,[status(thm)],[c_106121,c_256]) ).
tff(c_106142,plain,
( ( sk6 = nil )
| ~ rearsegP(nil,sk6) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_106139]) ).
tff(c_108055,plain,
~ rearsegP(nil,sk6),
inference(splitLeft,[status(thm)],[c_106142]) ).
tff(c_162529,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_162523,c_108055]) ).
tff(c_162563,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_106137,c_162529]) ).
tff(c_162564,plain,
sk6 = nil,
inference(splitRight,[status(thm)],[c_106142]) ).
tff(c_162594,plain,
~ memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_162564,c_102755]) ).
tff(c_104336,plain,
! [U_4077] :
( ( tl(U_4077) = skaf82(U_4077) )
| ~ ssList(skaf82(U_4077))
| ~ ssItem(skaf83(U_4077))
| ( nil = U_4077 )
| ~ ssList(U_4077) ),
inference(superposition,[status(thm),theory(equality)],[c_104324,c_192]) ).
tff(c_168737,plain,
! [U_6507] :
( ( tl(U_6507) = skaf82(U_6507) )
| ( nil = U_6507 )
| ~ ssList(U_6507) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_104336]) ).
tff(c_168876,plain,
( ( tl(sk7) = skaf82(sk7) )
| ( sk7 = nil ) ),
inference(resolution,[status(thm)],[c_388,c_168737]) ).
tff(c_169178,plain,
sk7 = nil,
inference(splitLeft,[status(thm)],[c_168876]) ).
tff(c_104572,plain,
! [V_4094,U_4095] :
( ( nil = V_4094 )
| ~ ssList(U_4095)
| ~ ssList(V_4094)
| ( app(U_4095,V_4094) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_658]) ).
tff(c_168475,plain,
! [V_6475] :
( ( nil = V_6475 )
| ~ ssList(V_6475)
| ( app(sk7,V_6475) != nil ) ),
inference(resolution,[status(thm)],[c_388,c_104572]) ).
tff(c_168615,plain,
( ( sk7 = nil )
| ( app(sk7,sk7) != nil ) ),
inference(resolution,[status(thm)],[c_388,c_168475]) ).
tff(c_168617,plain,
app(sk7,sk7) != nil,
inference(splitLeft,[status(thm)],[c_168615]) ).
tff(c_169179,plain,
app(nil,nil) != nil,
inference(demodulation,[status(thm),theory(equality)],[c_169178,c_169178,c_168617]) ).
tff(c_169239,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_636,c_169179]) ).
tff(c_169241,plain,
sk7 != nil,
inference(splitRight,[status(thm)],[c_168876]) ).
tff(c_103757,plain,
! [U_4006,V_4007] :
( ssList(cons(U_4006,V_4007))
| ~ ssList(V_4007)
| ~ ssItem(U_4006) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_148,plain,
! [U_69] :
( ( app(nil,U_69) = U_69 )
| ~ ssList(U_69) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_207506,plain,
! [U_7835,V_7836] :
( ( app(nil,cons(U_7835,V_7836)) = cons(U_7835,V_7836) )
| ~ ssList(V_7836)
| ~ ssItem(U_7835) ),
inference(resolution,[status(thm)],[c_103757,c_148]) ).
tff(c_162591,plain,
app(app(nil,cons(sk5,nil)),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_162564,c_390]) ).
tff(c_207536,plain,
( ( app(cons(sk5,nil),sk7) = sk1 )
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_207506,c_162591]) ).
tff(c_207719,plain,
app(cons(sk5,nil),sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_207536]) ).
tff(c_208239,plain,
( ( cons(sk5,sk7) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_207719,c_240]) ).
tff(c_208282,plain,
cons(sk5,sk7) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_208239]) ).
tff(c_208389,plain,
( ( tl(sk1) = sk7 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_208282,c_192]) ).
tff(c_208462,plain,
sk7 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_103806,c_208389]) ).
tff(c_208464,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_169241,c_208462]) ).
tff(c_208465,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_168615]) ).
tff(c_103031,plain,
app(sk7,nil) = sk7,
inference(resolution,[status(thm)],[c_388,c_102902]) ).
tff(c_106039,plain,
( rearsegP(sk7,nil)
| ~ ssList(app(sk7,nil))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_103031,c_105941]) ).
tff(c_106123,plain,
rearsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_103031,c_106039]) ).
tff(c_106144,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ rearsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_106123,c_256]) ).
tff(c_106147,plain,
( ( sk7 = nil )
| ~ rearsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_106144]) ).
tff(c_162627,plain,
~ rearsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_106147]) ).
tff(c_208493,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_208465,c_162627]) ).
tff(c_208531,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_106137,c_208493]) ).
tff(c_208532,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_106147]) ).
tff(c_640,plain,
app(nil,sk7) = sk7,
inference(resolution,[status(thm)],[c_388,c_512]) ).
tff(c_105731,plain,
( frontsegP(sk7,nil)
| ~ ssList(app(nil,sk7))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_640,c_105630]) ).
tff(c_105808,plain,
frontsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_640,c_105731]) ).
tff(c_105931,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_105808,c_258]) ).
tff(c_105934,plain,
( ( sk7 = nil )
| ~ frontsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_105931]) ).
tff(c_162626,plain,
~ frontsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_105934]) ).
tff(c_208534,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_208532,c_162626]) ).
tff(c_208567,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_105816,c_208534]) ).
tff(c_208568,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_105934]) ).
tff(c_102754,plain,
memberP(sk7,sk5),
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_208597,plain,
memberP(nil,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_208568,c_102754]) ).
tff(c_208608,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_162594,c_208597]) ).
tff(c_208610,plain,
singletonP(sk6),
inference(splitRight,[status(thm)],[c_104321]) ).
tff(c_104015,plain,
! [U_4039] : ( cons(skaf44(U_4039),nil) != nil ),
inference(resolution,[status(thm)],[c_94,c_103882]) ).
tff(c_217871,plain,
! [U_8334] :
( ( nil != U_8334 )
| ~ ssList(U_8334)
| ~ singletonP(U_8334) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_104015]) ).
tff(c_217973,plain,
( ( sk6 != nil )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_217871]) ).
tff(c_218014,plain,
sk6 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_208610,c_217973]) ).
tff(c_209711,plain,
! [U_7915,V_7916] :
( ( app(cons(U_7915,nil),V_7916) = cons(U_7915,V_7916) )
| ~ ssList(V_7916)
| ~ ssItem(U_7915) ),
inference(cnfTransformation,[status(thm)],[f_666]) ).
tff(c_209729,plain,
! [V_7916] :
( ( cons(sk8,V_7916) = app(sk1,V_7916) )
| ~ ssList(V_7916)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_209711]) ).
tff(c_222900,plain,
! [V_8699] :
( ( cons(sk8,V_8699) = app(sk1,V_8699) )
| ~ ssList(V_8699) ),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_209729]) ).
tff(c_223041,plain,
cons(sk8,sk7) = app(sk1,sk7),
inference(resolution,[status(thm)],[c_388,c_222900]) ).
tff(c_223425,plain,
( ssList(app(sk1,sk7))
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm),theory(equality)],[c_223041,c_172]) ).
tff(c_223487,plain,
ssList(app(sk1,sk7)),
inference(demodulation,[status(thm),theory(equality)],[c_463,c_388,c_223425]) ).
tff(c_215767,plain,
! [U_8167,V_8168,W_8169] :
( segmentP(app(app(U_8167,V_8168),W_8169),V_8168)
| ~ ssList(app(app(U_8167,V_8168),W_8169))
| ~ ssList(V_8168)
| ~ ssList(U_8167)
| ~ ssList(W_8169) ),
inference(cnfTransformation,[status(thm)],[f_1371]) ).
tff(c_215937,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_215767]) ).
tff(c_216066,plain,
( segmentP(sk1,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_414,c_390,c_215937]) ).
tff(c_233084,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_216066]) ).
tff(c_233087,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_233084]) ).
tff(c_233091,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_233087]) ).
tff(c_233093,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_216066]) ).
tff(c_213085,plain,
! [W_8079,V_8080,U_8081] :
( ( app(app(W_8079,V_8080),U_8081) = app(W_8079,app(V_8080,U_8081)) )
| ~ ssList(W_8079)
| ~ ssList(V_8080)
| ~ ssList(U_8081) ),
inference(cnfTransformation,[status(thm)],[f_1051]) ).
tff(c_213122,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_213085,c_390]) ).
tff(c_213284,plain,
( ( app(sk6,app(cons(sk5,nil),sk7)) = sk1 )
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_213122]) ).
tff(c_248502,plain,
app(sk6,app(cons(sk5,nil),sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_233093,c_213284]) ).
tff(c_248552,plain,
( ( app(sk6,cons(sk5,sk7)) = sk1 )
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_248502]) ).
tff(c_248585,plain,
app(sk6,cons(sk5,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_388,c_248552]) ).
tff(c_248616,plain,
( memberP(sk1,sk5)
| ~ ssList(app(sk6,cons(sk5,sk7)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_248585,c_350]) ).
tff(c_248672,plain,
memberP(sk1,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_386,c_384,c_414,c_248585,c_248616]) ).
tff(c_214137,plain,
! [W_8107,U_8108,V_8109] :
( ( W_8107 = U_8108 )
| memberP(V_8109,W_8107)
| ~ ssItem(W_8107)
| ~ ssItem(U_8108)
| ~ ssList(V_8109)
| ~ memberP(cons(U_8108,V_8109),W_8107) ),
inference(cnfTransformation,[status(thm)],[f_1239]) ).
tff(c_214158,plain,
! [W_8107] :
( ( sk8 = W_8107 )
| memberP(nil,W_8107)
| ~ ssItem(W_8107)
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ memberP(sk1,W_8107) ),
inference(superposition,[status(thm),theory(equality)],[c_485,c_214137]) ).
tff(c_214167,plain,
! [W_8107] :
( ( sk8 = W_8107 )
| memberP(nil,W_8107)
| ~ ssItem(W_8107)
| ~ memberP(sk1,W_8107) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_463,c_214158]) ).
tff(c_248701,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_248672,c_214167]) ).
tff(c_248704,plain,
( ( sk8 = sk5 )
| memberP(nil,sk5) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_248701]) ).
tff(c_248705,plain,
memberP(nil,sk5),
inference(splitLeft,[status(thm)],[c_248704]) ).
tff(c_248709,plain,
~ ssItem(sk5),
inference(resolution,[status(thm)],[c_248705,c_142]) ).
tff(c_248713,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_248709]) ).
tff(c_248714,plain,
sk8 = sk5,
inference(splitRight,[status(thm)],[c_248704]) ).
tff(c_248805,plain,
hd(sk1) = sk5,
inference(demodulation,[status(thm),theory(equality)],[c_248714,c_103985]) ).
tff(c_248806,plain,
cons(sk5,nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_248714,c_485]) ).
tff(c_249156,plain,
app(sk6,app(sk1,sk7)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_248806,c_248502]) ).
tff(c_251548,plain,
( ( hd(sk6) = hd(sk1) )
| ( sk6 = nil )
| ~ ssList(sk6)
| ~ ssList(app(sk1,sk7)) ),
inference(superposition,[status(thm),theory(equality)],[c_249156,c_246]) ).
tff(c_251583,plain,
( ( hd(sk6) = sk5 )
| ( sk6 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_223487,c_386,c_248805,c_251548]) ).
tff(c_251584,plain,
hd(sk6) = sk5,
inference(negUnitSimplification,[status(thm)],[c_218014,c_251583]) ).
tff(c_103976,plain,
! [U_103] :
( ( skaf44(U_103) = hd(U_103) )
| ~ ssList(nil)
| ~ ssItem(skaf44(U_103))
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_103964]) ).
tff(c_218418,plain,
! [U_8446] :
( ( skaf44(U_8446) = hd(U_8446) )
| ~ ssList(U_8446)
| ~ singletonP(U_8446) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_103976]) ).
tff(c_218520,plain,
( ( skaf44(sk6) = hd(sk6) )
| ~ singletonP(sk6) ),
inference(resolution,[status(thm)],[c_386,c_218418]) ).
tff(c_218561,plain,
skaf44(sk6) = hd(sk6),
inference(demodulation,[status(thm),theory(equality)],[c_208610,c_218520]) ).
tff(c_218617,plain,
ssItem(hd(sk6)),
inference(superposition,[status(thm),theory(equality)],[c_218561,c_94]) ).
tff(c_218613,plain,
( ( cons(hd(sk6),nil) = sk6 )
| ~ ssList(sk6)
| ~ singletonP(sk6) ),
inference(superposition,[status(thm),theory(equality)],[c_218561,c_202]) ).
tff(c_218621,plain,
cons(hd(sk6),nil) = sk6,
inference(demodulation,[status(thm),theory(equality)],[c_208610,c_386,c_218613]) ).
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_218741,plain,
( memberP(sk6,hd(sk6))
| ~ ssItem(hd(sk6))
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_218621,c_276]) ).
tff(c_218829,plain,
memberP(sk6,hd(sk6)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_218617,c_218741]) ).
tff(c_251611,plain,
memberP(sk6,sk5),
inference(demodulation,[status(thm),theory(equality)],[c_251584,c_218829]) ).
tff(c_251618,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102755,c_251611]) ).
tff(c_251619,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_412]) ).
tff(c_404,plain,
( ( sk3 = nil )
| memberP(sk4,sk8) ),
inference(cnfTransformation,[status(thm)],[f_1675]) ).
tff(c_405,plain,
( ( sk1 = nil )
| memberP(sk4,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_404]) ).
tff(c_411,plain,
( ( sk1 = nil )
| memberP(sk2,sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_405]) ).
tff(c_473,plain,
memberP(sk2,sk8),
inference(splitLeft,[status(thm)],[c_411]) ).
tff(c_251621,plain,
memberP(nil,sk8),
inference(demodulation,[status(thm),theory(equality)],[c_251619,c_473]) ).
tff(c_251635,plain,
~ ssItem(sk8),
inference(resolution,[status(thm)],[c_251621,c_142]) ).
tff(c_251639,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_463,c_251635]) ).
tff(c_251640,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_411]) ).
tff(c_252360,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_251640,c_390]) ).
tff(c_254971,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_252360,c_254861]) ).
tff(c_255081,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_252360,c_254971]) ).
tff(c_265583,plain,
~ ssList(app(sk6,cons(sk5,nil))),
inference(negUnitSimplification,[status(thm)],[c_258278,c_255081]) ).
tff(c_265586,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_265583]) ).
tff(c_265589,plain,
~ ssList(cons(sk5,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_265586]) ).
tff(c_265592,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_265589]) ).
tff(c_265596,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_265592]) ).
tff(c_265597,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_255117]) ).
tff(c_251800,plain,
app(nil,sk7) = sk7,
inference(resolution,[status(thm)],[c_388,c_251680]) ).
tff(c_255289,plain,
( frontsegP(sk7,nil)
| ~ ssList(app(nil,sk7))
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(superposition,[status(thm),theory(equality)],[c_251800,c_255143]) ).
tff(c_255387,plain,
frontsegP(sk7,nil),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_388,c_251800,c_255289]) ).
tff(c_255437,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(nil,sk7) ),
inference(resolution,[status(thm)],[c_255387,c_258]) ).
tff(c_255440,plain,
( ( sk7 = nil )
| ~ frontsegP(nil,sk7) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_388,c_255437]) ).
tff(c_257960,plain,
~ frontsegP(nil,sk7),
inference(splitLeft,[status(thm)],[c_255440]) ).
tff(c_265599,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_265597,c_257960]) ).
tff(c_265653,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_255389,c_265599]) ).
tff(c_265654,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_255440]) ).
tff(c_266019,plain,
app(app(sk6,cons(sk5,nil)),nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_265654,c_252360]) ).
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_272321,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_266019,c_346]) ).
tff(c_272374,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_16,c_266019,c_272321]) ).
tff(c_286169,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_272374]) ).
tff(c_286172,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_286169]) ).
tff(c_286176,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_286172]) ).
tff(c_286178,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_272374]) ).
tff(c_286177,plain,
segmentP(nil,cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_272374]) ).
tff(c_160,plain,
! [U_75] :
( ( nil = U_75 )
| ~ ssList(U_75)
| ~ segmentP(nil,U_75) ),
inference(cnfTransformation,[status(thm)],[f_294]) ).
tff(c_286440,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_286177,c_160]) ).
tff(c_286450,plain,
cons(sk5,nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_286178,c_286440]) ).
tff(c_286452,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_253957,c_286450]) ).
tff(c_286454,plain,
~ ssItem(sk8),
inference(splitRight,[status(thm)],[c_409]) ).
tff(c_396,plain,
( ( sk3 = nil )
| ssItem(sk8) ),
inference(cnfTransformation,[status(thm)],[f_1663]) ).
tff(c_408,plain,
( ( sk1 = nil )
| ssItem(sk8) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_396]) ).
tff(c_286470,plain,
sk1 = nil,
inference(negUnitSimplification,[status(thm)],[c_286454,c_408]) ).
tff(c_287191,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_286470,c_390]) ).
tff(c_290172,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_287191,c_290059]) ).
tff(c_290287,plain,
( rearsegP(nil,sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(demodulation,[status(thm),theory(equality)],[c_388,c_16,c_287191,c_290172]) ).
tff(c_299746,plain,
~ ssList(app(sk6,cons(sk5,nil))),
inference(negUnitSimplification,[status(thm)],[c_292845,c_290287]) ).
tff(c_299749,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_170,c_299746]) ).
tff(c_299752,plain,
~ ssList(cons(sk5,nil)),
inference(demodulation,[status(thm),theory(equality)],[c_386,c_299749]) ).
tff(c_299755,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_299752]) ).
tff(c_299759,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_299755]) ).
tff(c_299760,plain,
sk7 = nil,
inference(splitRight,[status(thm)],[c_290320]) ).
tff(c_299806,plain,
app(app(sk6,cons(sk5,nil)),nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_299760,c_287191]) ).
tff(c_306444,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_299806,c_346]) ).
tff(c_306497,plain,
( segmentP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_16,c_299806,c_306444]) ).
tff(c_319398,plain,
~ ssList(cons(sk5,nil)),
inference(splitLeft,[status(thm)],[c_306497]) ).
tff(c_319401,plain,
( ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[c_172,c_319398]) ).
tff(c_319405,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_384,c_16,c_319401]) ).
tff(c_319407,plain,
ssList(cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_306497]) ).
tff(c_319406,plain,
segmentP(nil,cons(sk5,nil)),
inference(splitRight,[status(thm)],[c_306497]) ).
tff(c_319552,plain,
( ( cons(sk5,nil) = nil )
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[c_319406,c_160]) ).
tff(c_319562,plain,
cons(sk5,nil) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_319407,c_319552]) ).
tff(c_319564,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_288402,c_319562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC187-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 21:40:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 166.63/145.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 166.70/145.50
% 166.70/145.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 166.95/145.58
% 166.95/145.58 Inference rules
% 166.95/145.58 ----------------------
% 166.95/145.58 #Ref : 0
% 166.95/145.58 #Sup : 70700
% 166.95/145.58 #Fact : 0
% 166.95/145.58 #Define : 0
% 166.95/145.58 #Split : 237
% 166.95/145.58 #Chain : 0
% 166.95/145.58 #Close : 0
% 166.95/145.58
% 166.95/145.58 Ordering : KBO
% 166.95/145.58
% 166.95/145.58 Simplification rules
% 166.95/145.58 ----------------------
% 166.95/145.58 #Subsume : 15321
% 166.95/145.58 #Demod : 89012
% 166.95/145.58 #Tautology : 22717
% 166.95/145.58 #SimpNegUnit : 5385
% 166.95/145.58 #BackRed : 2579
% 166.95/145.58
% 166.95/145.58 #Partial instantiations: 0
% 166.95/145.58 #Strategies tried : 1
% 166.95/145.58
% 166.95/145.58 Timing (in seconds)
% 166.95/145.58 ----------------------
% 167.20/145.59 Preprocessing : 0.88
% 167.20/145.59 Parsing : 0.45
% 167.20/145.59 CNF conversion : 0.07
% 167.20/145.59 Main loop : 143.55
% 167.20/145.59 Inferencing : 22.96
% 167.20/145.59 Reduction : 79.63
% 167.20/145.59 Demodulation : 60.36
% 167.20/145.59 BG Simplification : 0.38
% 167.20/145.59 Subsumption : 32.56
% 167.20/145.59 Abstraction : 1.02
% 167.20/145.59 MUC search : 0.00
% 167.20/145.59 Cooper : 0.00
% 167.20/145.59 Total : 144.60
% 167.20/145.59 Index Insertion : 0.00
% 167.20/145.59 Index Deletion : 0.00
% 167.20/145.59 Index Matching : 0.00
% 167.20/145.59 BG Taut test : 0.00
%------------------------------------------------------------------------------