TSTP Solution File: SWC015-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWC015-1 : 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 : n019.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 11:00:45 EDT 2023
% Result : Unsatisfiable 217.63s 195.78s
% Output : CNFRefutation 217.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 112
% Syntax : Number of formulae : 604 ( 274 unt; 72 typ; 0 def)
% Number of atoms : 1111 ( 367 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1214 ( 635 ~; 579 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 53 ( 53 usr; 7 con; 0-2 aty)
% Number of variables : 207 (; 207 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > skaf48 > skaf47 > skaf46 > skaf45 > skaf43 > skaf42 > cons > app > #nlpp > tl > skaf83 > skaf82 > skaf81 > skaf80 > skaf79 > skaf78 > skaf77 > skaf76 > skaf75 > skaf74 > skaf73 > skaf72 > skaf71 > skaf70 > skaf69 > skaf68 > skaf67 > skaf66 > skaf65 > skaf64 > skaf63 > skaf62 > skaf61 > skaf60 > skaf59 > skaf58 > skaf57 > skaf56 > skaf55 > skaf54 > skaf53 > skaf52 > skaf51 > skaf50 > skaf49 > skaf44 > hd > skac3 > skac2 > sk4 > sk3 > sk2 > sk1 > nil
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(skaf56,type,
skaf56: $i > $i ).
tff(segmentP,type,
segmentP: ( $i * $i ) > $o ).
tff(totalorderedP,type,
totalorderedP: $i > $o ).
tff(equalelemsP,type,
equalelemsP: $i > $o ).
tff(skaf74,type,
skaf74: $i > $i ).
tff(skaf61,type,
skaf61: $i > $i ).
tff(skaf51,type,
skaf51: $i > $i ).
tff(skaf83,type,
skaf83: $i > $i ).
tff(skac2,type,
skac2: $i ).
tff(skaf63,type,
skaf63: $i > $i ).
tff(skaf62,type,
skaf62: $i > $i ).
tff(sk2,type,
sk2: $i ).
tff(skaf52,type,
skaf52: $i > $i ).
tff(skaf50,type,
skaf50: $i > $i ).
tff(skaf42,type,
skaf42: ( $i * $i ) > $i ).
tff(skaf44,type,
skaf44: $i > $i ).
tff(singletonP,type,
singletonP: $i > $o ).
tff(skaf67,type,
skaf67: $i > $i ).
tff(skaf75,type,
skaf75: $i > $i ).
tff(sk1,type,
sk1: $i ).
tff(skaf58,type,
skaf58: $i > $i ).
tff(skaf46,type,
skaf46: ( $i * $i ) > $i ).
tff(frontsegP,type,
frontsegP: ( $i * $i ) > $o ).
tff(skaf70,type,
skaf70: $i > $i ).
tff(totalorderP,type,
totalorderP: $i > $o ).
tff(ssItem,type,
ssItem: $i > $o ).
tff(skaf82,type,
skaf82: $i > $i ).
tff(skaf47,type,
skaf47: ( $i * $i ) > $i ).
tff(skaf76,type,
skaf76: $i > $i ).
tff(skac3,type,
skac3: $i ).
tff(skaf80,type,
skaf80: $i > $i ).
tff(skaf59,type,
skaf59: $i > $i ).
tff(skaf53,type,
skaf53: $i > $i ).
tff(skaf45,type,
skaf45: ( $i * $i ) > $i ).
tff(hd,type,
hd: $i > $i ).
tff(app,type,
app: ( $i * $i ) > $i ).
tff(skaf72,type,
skaf72: $i > $i ).
tff(duplicatefreeP,type,
duplicatefreeP: $i > $o ).
tff(skaf64,type,
skaf64: $i > $i ).
tff(sk4,type,
sk4: $i ).
tff(gt,type,
gt: ( $i * $i ) > $o ).
tff(skaf71,type,
skaf71: $i > $i ).
tff(skaf78,type,
skaf78: $i > $i ).
tff(skaf79,type,
skaf79: $i > $i ).
tff(rearsegP,type,
rearsegP: ( $i * $i ) > $o ).
tff(memberP,type,
memberP: ( $i * $i ) > $o ).
tff(skaf73,type,
skaf73: $i > $i ).
tff(ssList,type,
ssList: $i > $o ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(skaf54,type,
skaf54: $i > $i ).
tff(skaf77,type,
skaf77: $i > $i ).
tff(sk3,type,
sk3: $i ).
tff(skaf66,type,
skaf66: $i > $i ).
tff(strictorderP,type,
strictorderP: $i > $o ).
tff(skaf81,type,
skaf81: $i > $i ).
tff(geq,type,
geq: ( $i * $i ) > $o ).
tff(skaf60,type,
skaf60: $i > $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(lt,type,
lt: ( $i * $i ) > $o ).
tff(skaf69,type,
skaf69: $i > $i ).
tff(tl,type,
tl: $i > $i ).
tff(neq,type,
neq: ( $i * $i ) > $o ).
tff(skaf43,type,
skaf43: ( $i * $i ) > $i ).
tff(skaf48,type,
skaf48: ( $i * $i ) > $i ).
tff(skaf65,type,
skaf65: $i > $i ).
tff(skaf57,type,
skaf57: $i > $i ).
tff(nil,type,
nil: $i ).
tff(skaf49,type,
skaf49: $i > $i ).
tff(skaf55,type,
skaf55: $i > $i ).
tff(skaf68,type,
skaf68: $i > $i ).
tff(strictorderedP,type,
strictorderedP: $i > $o ).
tff(cyclefreeP,type,
cyclefreeP: $i > $o ).
tff(f_60,axiom,
~ singletonP(nil),
file(unknown,unknown) ).
tff(f_56,axiom,
ssList(nil),
file(unknown,unknown) ).
tff(f_250,axiom,
! [U] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file(unknown,unknown) ).
tff(f_961,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file(unknown,unknown) ).
tff(f_1650,axiom,
sk1 = sk3,
file(unknown,unknown) ).
tff(f_1647,axiom,
ssList(sk3),
file(unknown,unknown) ).
tff(f_132,axiom,
! [U] : ssItem(skaf44(U)),
file(unknown,unknown) ).
tff(f_464,axiom,
! [U] :
( ~ singletonP(U)
| ~ ssList(U)
| ( cons(skaf44(U),nil) = U ) ),
file(unknown,unknown) ).
tff(f_197,axiom,
! [U] :
( ~ ssItem(U)
| equalelemsP(cons(U,nil)) ),
file(unknown,unknown) ).
tff(f_245,axiom,
! [U] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file(unknown,unknown) ).
tff(f_975,axiom,
! [U,V,W] :
( ( app(U,V) != W )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| frontsegP(W,U) ),
file(unknown,unknown) ).
tff(f_1649,axiom,
sk2 = sk4,
file(unknown,unknown) ).
tff(f_1648,axiom,
ssList(sk4),
file(unknown,unknown) ).
tff(f_647,axiom,
! [U,V] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_456,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file(unknown,unknown) ).
tff(f_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_64,axiom,
! [U] : ssList(skaf82(U)),
file(unknown,unknown) ).
tff(f_446,axiom,
! [U,V] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file(unknown,unknown) ).
tff(f_428,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( hd(cons(U,V)) = U ) ),
file(unknown,unknown) ).
tff(f_420,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file(unknown,unknown) ).
tff(f_271,axiom,
! [U] :
( ~ ssList(U)
| ssList(tl(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_334,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file(unknown,unknown) ).
tff(f_278,axiom,
! [U] :
( ~ ssList(U)
| ssItem(hd(U))
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_492,axiom,
! [U] :
( ~ ssList(U)
| ( cons(hd(U),tl(U)) = U )
| ( nil = U ) ),
file(unknown,unknown) ).
tff(f_898,axiom,
! [U,V,W] :
( ( U != V )
| ~ ssList(W)
| ~ ssItem(V)
| ~ ssItem(U)
| memberP(cons(V,W),U) ),
file(unknown,unknown) ).
tff(f_1653,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file(unknown,unknown) ).
tff(f_1710,axiom,
! [A,B] :
( ~ ssList(A)
| ( sk4 = A )
| ~ ssList(B)
| ( tl(sk4) != B )
| ( app(sk3,B) != A )
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
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_702,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( hd(app(V,U)) = hd(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_912,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| memberP(cons(W,U),V) ),
file(unknown,unknown) ).
tff(f_342,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,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_830,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ( nil = V )
| ( tl(app(V,U)) = app(tl(V),U) ) ),
file(unknown,unknown) ).
tff(f_1079,axiom,
! [U,V,W] :
( ( app(U,V) != app(W,V) )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( U = W ) ),
file(unknown,unknown) ).
tff(f_940,axiom,
! [U,V,W] :
( ~ memberP(U,V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssItem(V)
| memberP(app(W,U),V) ),
file(unknown,unknown) ).
tff(f_1065,axiom,
! [U,V,W] :
( ( app(U,V) != app(U,W) )
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| ( V = W ) ),
file(unknown,unknown) ).
tff(f_613,axiom,
! [U,V] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file(unknown,unknown) ).
tff(f_1725,axiom,
! [A,B] :
( ~ ssItem(A)
| ~ ssList(B)
| ( cons(A,nil) != sk1 )
| ( app(cons(A,nil),B) != sk2 )
| ~ neq(sk4,nil) ),
file(unknown,unknown) ).
tff(c_22,plain,
~ singletonP(nil),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_16,plain,
ssList(nil),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_471,plain,
! [U_395] :
( ( app(nil,U_395) = U_395 )
| ~ ssList(U_395) ),
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_591,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c_16,c_471]) ).
tff(c_276334,plain,
! [U_11158,V_11159] :
( rearsegP(app(U_11158,V_11159),V_11159)
| ~ ssList(app(U_11158,V_11159))
| ~ ssList(V_11159)
| ~ ssList(U_11158) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_276474,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_276334]) ).
tff(c_276571,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_276474]) ).
tff(c_382,plain,
sk3 = sk1,
inference(cnfTransformation,[status(thm)],[f_1650]) ).
tff(c_376,plain,
ssList(sk3),
inference(cnfTransformation,[status(thm)],[f_1647]) ).
tff(c_406,plain,
ssList(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).
tff(c_94,plain,
! [U_36] : ssItem(skaf44(U_36)),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_1885,plain,
! [U_518] :
( ( cons(skaf44(U_518),nil) = U_518 )
| ~ ssList(U_518)
| ~ singletonP(U_518) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_128,plain,
! [U_58] :
( equalelemsP(cons(U_58,nil))
| ~ ssItem(U_58) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_1911,plain,
! [U_518] :
( equalelemsP(U_518)
| ~ ssItem(skaf44(U_518))
| ~ ssList(U_518)
| ~ singletonP(U_518) ),
inference(superposition,[status(thm),theory(equality)],[c_1885,c_128]) ).
tff(c_2005,plain,
! [U_528] :
( equalelemsP(U_528)
| ~ ssList(U_528)
| ~ singletonP(U_528) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_1911]) ).
tff(c_2136,plain,
( equalelemsP(sk1)
| ~ singletonP(sk1) ),
inference(resolution,[status(thm)],[c_406,c_2005]) ).
tff(c_274884,plain,
~ singletonP(sk1),
inference(splitLeft,[status(thm)],[c_2136]) ).
tff(c_608,plain,
! [U_400] :
( ( app(U_400,nil) = U_400 )
| ~ ssList(U_400) ),
inference(cnfTransformation,[status(thm)],[f_245]) ).
tff(c_727,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[c_406,c_608]) ).
tff(c_276599,plain,
! [U_11160,V_11161] :
( frontsegP(app(U_11160,V_11161),U_11160)
| ~ ssList(app(U_11160,V_11161))
| ~ ssList(U_11160)
| ~ ssList(V_11161) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_276733,plain,
( frontsegP(sk1,sk1)
| ~ ssList(app(sk1,nil))
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_276599]) ).
tff(c_276832,plain,
frontsegP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_406,c_727,c_276733]) ).
tff(c_3951,plain,
! [U_674,V_675] :
( rearsegP(app(U_674,V_675),V_675)
| ~ ssList(app(U_674,V_675))
| ~ ssList(V_675)
| ~ ssList(U_674) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_4097,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_3951]) ).
tff(c_4198,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_4097]) ).
tff(c_3664,plain,
! [U_672,V_673] :
( frontsegP(app(U_672,V_673),U_672)
| ~ ssList(app(U_672,V_673))
| ~ ssList(U_672)
| ~ ssList(V_673) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_3810,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_3664]) ).
tff(c_3911,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_3810]) ).
tff(c_380,plain,
sk4 = sk2,
inference(cnfTransformation,[status(thm)],[f_1649]) ).
tff(c_378,plain,
ssList(sk4),
inference(cnfTransformation,[status(thm)],[f_1648]) ).
tff(c_405,plain,
ssList(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).
tff(c_726,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[c_405,c_608]) ).
tff(c_2672,plain,
! [U_570,V_571] :
( ( nil = U_570 )
| ~ ssList(U_570)
| ~ ssList(V_571)
| ( app(U_570,V_571) != nil ) ),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_2769,plain,
! [V_571] :
( ( sk2 = nil )
| ~ ssList(V_571)
| ( app(sk2,V_571) != nil ) ),
inference(resolution,[status(thm)],[c_405,c_2672]) ).
tff(c_189871,plain,
! [V_7650] :
( ~ ssList(V_7650)
| ( app(sk2,V_7650) != nil ) ),
inference(splitLeft,[status(thm)],[c_2769]) ).
tff(c_189970,plain,
app(sk2,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_189871]) ).
tff(c_190004,plain,
sk2 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_726,c_189970]) ).
tff(c_200,plain,
! [V_102,U_101] :
( ( V_102 = U_101 )
| neq(V_102,U_101)
| ~ ssList(V_102)
| ~ ssList(U_101) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_24,plain,
! [U_1] : ssItem(skaf83(U_1)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
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_26,plain,
! [U_2] : ssList(skaf82(U_2)),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_1494,plain,
! [V_468,U_469] :
( ~ ssList(V_468)
| ~ ssItem(U_469)
| ( cons(U_469,V_468) != V_468 ) ),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_190041,plain,
! [U_7691,U_7692] :
( ~ ssItem(U_7691)
| ( cons(U_7691,skaf82(U_7692)) != skaf82(U_7692) ) ),
inference(resolution,[status(thm)],[c_26,c_1494]) ).
tff(c_190044,plain,
! [U_117] :
( ~ ssItem(skaf83(U_117))
| ( skaf82(U_117) != U_117 )
| ( nil = U_117 )
| ~ ssList(U_117) ),
inference(superposition,[status(thm),theory(equality)],[c_218,c_190041]) ).
tff(c_190047,plain,
! [U_7693] :
( ( skaf82(U_7693) != U_7693 )
| ( nil = U_7693 )
| ~ ssList(U_7693) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_190044]) ).
tff(c_190143,plain,
( ( skaf82(sk2) != sk2 )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_190047]) ).
tff(c_190180,plain,
skaf82(sk2) != sk2,
inference(negUnitSimplification,[status(thm)],[c_190004,c_190143]) ).
tff(c_584,plain,
! [U_2] : ( app(nil,skaf82(U_2)) = skaf82(U_2) ),
inference(resolution,[status(thm)],[c_26,c_471]) ).
tff(c_2367,plain,
! [U_543] :
( ( nil = U_543 )
| ( cons(skaf83(U_543),skaf82(U_543)) = U_543 )
| ~ ssList(U_543) ),
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_2376,plain,
! [U_543] :
( ( skaf83(U_543) = hd(U_543) )
| ~ ssList(skaf82(U_543))
| ~ ssItem(skaf83(U_543))
| ( nil = U_543 )
| ~ ssList(U_543) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_194]) ).
tff(c_190186,plain,
! [U_7697] :
( ( skaf83(U_7697) = hd(U_7697) )
| ( nil = U_7697 )
| ~ ssList(U_7697) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2376]) ).
tff(c_190282,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_190186]) ).
tff(c_190319,plain,
skaf83(sk2) = hd(sk2),
inference(negUnitSimplification,[status(thm)],[c_190004,c_190282]) ).
tff(c_190333,plain,
ssItem(hd(sk2)),
inference(superposition,[status(thm),theory(equality)],[c_190319,c_24]) ).
tff(c_190329,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_190319,c_218]) ).
tff(c_190337,plain,
( ( sk2 = nil )
| ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_190329]) ).
tff(c_190338,plain,
cons(hd(sk2),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_190004,c_190337]) ).
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_190520,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_190338,c_192]) ).
tff(c_190585,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_190333,c_26,c_190520]) ).
tff(c_154,plain,
! [U_72] :
( ( nil = U_72 )
| ssList(tl(U_72))
| ~ ssList(U_72) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
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_2157,plain,
~ singletonP(sk1),
inference(splitLeft,[status(thm)],[c_2136]) ).
tff(c_2770,plain,
! [V_571] :
( ( sk1 = nil )
| ~ ssList(V_571)
| ( app(sk1,V_571) != nil ) ),
inference(resolution,[status(thm)],[c_406,c_2672]) ).
tff(c_164380,plain,
! [V_6475] :
( ~ ssList(V_6475)
| ( app(sk1,V_6475) != nil ) ),
inference(splitLeft,[status(thm)],[c_2770]) ).
tff(c_164479,plain,
app(sk1,nil) != nil,
inference(resolution,[status(thm)],[c_16,c_164380]) ).
tff(c_164514,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_727,c_164479]) ).
tff(c_156,plain,
! [U_73] :
( ( nil = U_73 )
| ssItem(hd(U_73))
| ~ ssList(U_73) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_2373,plain,
! [U_543] :
( ( tl(U_543) = skaf82(U_543) )
| ~ ssList(skaf82(U_543))
| ~ ssItem(skaf83(U_543))
| ( nil = U_543 )
| ~ ssList(U_543) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_192]) ).
tff(c_164626,plain,
! [U_6493] :
( ( tl(U_6493) = skaf82(U_6493) )
| ( nil = U_6493 )
| ~ ssList(U_6493) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2373]) ).
tff(c_164722,plain,
( ( tl(sk1) = skaf82(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_406,c_164626]) ).
tff(c_164759,plain,
tl(sk1) = skaf82(sk1),
inference(negUnitSimplification,[status(thm)],[c_164514,c_164722]) ).
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_164792,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_164759,c_208]) ).
tff(c_164805,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_164792]) ).
tff(c_164806,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_164514,c_164805]) ).
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_165085,plain,
( memberP(sk1,hd(sk1))
| ~ ssItem(hd(sk1))
| ~ ssList(skaf82(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_164806,c_276]) ).
tff(c_165145,plain,
( memberP(sk1,hd(sk1))
| ~ ssItem(hd(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_165085]) ).
tff(c_165561,plain,
~ ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_165145]) ).
tff(c_165564,plain,
( ( sk1 = nil )
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[c_156,c_165561]) ).
tff(c_165567,plain,
sk1 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_406,c_165564]) ).
tff(c_165569,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164514,c_165567]) ).
tff(c_165571,plain,
ssItem(hd(sk1)),
inference(splitRight,[status(thm)],[c_165145]) ).
tff(c_2379,plain,
! [U_543] :
( memberP(U_543,skaf83(U_543))
| ~ ssItem(skaf83(U_543))
| ~ ssList(skaf82(U_543))
| ( nil = U_543 )
| ~ ssList(U_543) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_276]) ).
tff(c_2392,plain,
! [U_543] :
( memberP(U_543,skaf83(U_543))
| ( nil = U_543 )
| ~ ssList(U_543) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_2379]) ).
tff(c_590,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[c_406,c_471]) ).
tff(c_3813,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_3664]) ).
tff(c_3913,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_590,c_3813]) ).
tff(c_384,plain,
neq(sk2,nil),
inference(cnfTransformation,[status(thm)],[f_1653]) ).
tff(c_392,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ( app(sk3,tl(sk4)) = sk4 )
| ~ ssList(app(sk3,tl(sk4))) ),
inference(cnfTransformation,[status(thm)],[f_1710]) ).
tff(c_398,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssList(tl(sk4))
| ( app(sk1,tl(sk4)) = sk4 )
| ~ ssList(app(sk1,tl(sk4))) ),
inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_392]) ).
tff(c_400,plain,
( ~ neq(sk2,nil)
| ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 )
| ~ ssList(app(sk1,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_398]) ).
tff(c_404,plain,
( ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 )
| ~ ssList(app(sk1,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_400]) ).
tff(c_7825,plain,
~ ssList(app(sk1,tl(sk2))),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_7828,plain,
( ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_7825]) ).
tff(c_7831,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_7828]) ).
tff(c_7834,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_7831]) ).
tff(c_7837,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_7834]) ).
tff(c_4094,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_726,c_3951]) ).
tff(c_4196,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_726,c_4094]) ).
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_4209,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_4196,c_256]) ).
tff(c_4212,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_4209]) ).
tff(c_6754,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_4212]) ).
tff(c_7840,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_7837,c_6754]) ).
tff(c_7893,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_7840]) ).
tff(c_7894,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_8224,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_7894]) ).
tff(c_8227,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_8224]) ).
tff(c_8233,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_8227]) ).
tff(c_8238,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8233,c_6754]) ).
tff(c_8291,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_8238]) ).
tff(c_8292,plain,
( ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_7894]) ).
tff(c_8343,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_8292]) ).
tff(c_8346,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_8343]) ).
tff(c_8349,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_8346]) ).
tff(c_8354,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_8349,c_6754]) ).
tff(c_8407,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_8354]) ).
tff(c_8409,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_8292]) ).
tff(c_8408,plain,
app(sk1,tl(sk2)) = sk2,
inference(splitRight,[status(thm)],[c_8292]) ).
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_8571,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_8408,c_246]) ).
tff(c_8596,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8409,c_406,c_8571]) ).
tff(c_9202,plain,
sk1 = nil,
inference(splitLeft,[status(thm)],[c_8596]) ).
tff(c_4091,plain,
( rearsegP(sk1,nil)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_3951]) ).
tff(c_4194,plain,
rearsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_727,c_4091]) ).
tff(c_4204,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_4194,c_256]) ).
tff(c_4207,plain,
( ( sk1 = nil )
| ~ rearsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_4204]) ).
tff(c_6755,plain,
~ rearsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_4207]) ).
tff(c_9248,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_9202,c_6755]) ).
tff(c_9301,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_9248]) ).
tff(c_9302,plain,
hd(sk2) = hd(sk1),
inference(splitRight,[status(thm)],[c_8596]) ).
tff(c_9322,plain,
( ( sk2 = nil )
| ssItem(hd(sk1))
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_9302,c_156]) ).
tff(c_9336,plain,
( ( sk2 = nil )
| ssItem(hd(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_9322]) ).
tff(c_9380,plain,
ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_9336]) ).
tff(c_11227,plain,
! [U_1016] :
( ( skaf83(U_1016) = hd(U_1016) )
| ( nil = U_1016 )
| ~ ssList(U_1016) ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2376]) ).
tff(c_11323,plain,
( ( skaf83(sk2) = hd(sk2) )
| ( sk2 = nil ) ),
inference(resolution,[status(thm)],[c_405,c_11227]) ).
tff(c_11362,plain,
( ( skaf83(sk2) = hd(sk1) )
| ( sk2 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9302,c_11323]) ).
tff(c_11391,plain,
sk2 = nil,
inference(splitLeft,[status(thm)],[c_11362]) ).
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_8568,plain,
( frontsegP(sk2,sk1)
| ~ ssList(app(sk1,tl(sk2)))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_8408,c_288]) ).
tff(c_8594,plain,
frontsegP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_8409,c_406,c_405,c_8408,c_8568]) ).
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_8603,plain,
( ( sk2 = sk1 )
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk2) ),
inference(resolution,[status(thm)],[c_8594,c_258]) ).
tff(c_8609,plain,
( ( sk2 = sk1 )
| ~ frontsegP(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_405,c_8603]) ).
tff(c_8620,plain,
~ frontsegP(sk1,sk2),
inference(splitLeft,[status(thm)],[c_8609]) ).
tff(c_11404,plain,
~ frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_11391,c_8620]) ).
tff(c_11464,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3913,c_11404]) ).
tff(c_11466,plain,
sk2 != nil,
inference(splitRight,[status(thm)],[c_11362]) ).
tff(c_11465,plain,
skaf83(sk2) = hd(sk1),
inference(splitRight,[status(thm)],[c_11362]) ).
tff(c_11477,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_11465,c_218]) ).
tff(c_11487,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),skaf82(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_11477]) ).
tff(c_11488,plain,
cons(hd(sk1),skaf82(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_11466,c_11487]) ).
tff(c_11748,plain,
( ( tl(sk2) = skaf82(sk2) )
| ~ ssList(skaf82(sk2))
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_11488,c_192]) ).
tff(c_11811,plain,
tl(sk2) = skaf82(sk2),
inference(demodulation,[status(thm),theory(equality)],[c_9380,c_26,c_11748]) ).
tff(c_11829,plain,
app(sk1,skaf82(sk2)) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_11811,c_8408]) ).
tff(c_9303,plain,
sk1 != nil,
inference(splitRight,[status(thm)],[c_8596]) ).
tff(c_11326,plain,
( ( skaf83(sk1) = hd(sk1) )
| ( sk1 = nil ) ),
inference(resolution,[status(thm)],[c_406,c_11227]) ).
tff(c_11365,plain,
skaf83(sk1) = hd(sk1),
inference(negUnitSimplification,[status(thm)],[c_9303,c_11326]) ).
tff(c_11377,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_11365,c_218]) ).
tff(c_11387,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),skaf82(sk1)) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_11377]) ).
tff(c_11388,plain,
cons(hd(sk1),skaf82(sk1)) = sk1,
inference(negUnitSimplification,[status(thm)],[c_9303,c_11387]) ).
tff(c_278,plain,
! [W_181,U_179,V_180] :
( memberP(cons(W_181,U_179),V_180)
| ~ ssItem(V_180)
| ~ ssItem(W_181)
| ~ ssList(U_179)
| ~ memberP(U_179,V_180) ),
inference(cnfTransformation,[status(thm)],[f_912]) ).
tff(c_11560,plain,
! [V_180] :
( memberP(sk1,V_180)
| ~ ssItem(V_180)
| ~ ssItem(hd(sk1))
| ~ ssList(skaf82(sk1))
| ~ memberP(skaf82(sk1),V_180) ),
inference(superposition,[status(thm),theory(equality)],[c_11388,c_278]) ).
tff(c_40960,plain,
! [V_2489] :
( memberP(sk1,V_2489)
| ~ ssItem(V_2489)
| ~ memberP(skaf82(sk1),V_2489) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_9380,c_11560]) ).
tff(c_40976,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ~ ssItem(skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1)) ),
inference(resolution,[status(thm)],[c_2392,c_40960]) ).
tff(c_40986,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_40976]) ).
tff(c_41088,plain,
skaf82(sk1) = nil,
inference(splitLeft,[status(thm)],[c_40986]) ).
tff(c_41093,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_41088,c_11388]) ).
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_2868,plain,
! [U_580] :
( singletonP(cons(U_580,nil))
| ~ ssList(cons(U_580,nil))
| ~ ssItem(U_580) ),
inference(cnfTransformation,[status(thm)],[f_624]) ).
tff(c_2875,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssList(nil)
| ~ ssItem(U_82) ),
inference(resolution,[status(thm)],[c_172,c_2868]) ).
tff(c_2880,plain,
! [U_82] :
( singletonP(cons(U_82,nil))
| ~ ssItem(U_82) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2875]) ).
tff(c_41648,plain,
( singletonP(sk1)
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_41093,c_2880]) ).
tff(c_41755,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_9380,c_41648]) ).
tff(c_41757,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2157,c_41755]) ).
tff(c_41759,plain,
skaf82(sk1) != nil,
inference(splitRight,[status(thm)],[c_40986]) ).
tff(c_4981,plain,
! [V_709,U_710] :
( ( app(tl(V_709),U_710) = tl(app(V_709,U_710)) )
| ( nil = V_709 )
| ~ ssList(V_709)
| ~ ssList(U_710) ),
inference(cnfTransformation,[status(thm)],[f_830]) ).
tff(c_136493,plain,
! [U_6048,V_6049,U_6050] :
( ( tl(app(cons(U_6048,V_6049),U_6050)) = app(V_6049,U_6050) )
| ( cons(U_6048,V_6049) = nil )
| ~ ssList(cons(U_6048,V_6049))
| ~ ssList(U_6050)
| ~ ssList(V_6049)
| ~ ssItem(U_6048) ),
inference(superposition,[status(thm),theory(equality)],[c_192,c_4981]) ).
tff(c_136707,plain,
! [U_6050] :
( ( app(skaf82(sk1),U_6050) = tl(app(sk1,U_6050)) )
| ( cons(hd(sk1),skaf82(sk1)) = nil )
| ~ ssList(cons(hd(sk1),skaf82(sk1)))
| ~ ssList(U_6050)
| ~ ssList(skaf82(sk1))
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_11388,c_136493]) ).
tff(c_136784,plain,
! [U_6050] :
( ( app(skaf82(sk1),U_6050) = tl(app(sk1,U_6050)) )
| ( sk1 = nil )
| ~ ssList(U_6050) ),
inference(demodulation,[status(thm),theory(equality)],[c_9380,c_26,c_406,c_11388,c_11388,c_136707]) ).
tff(c_156808,plain,
! [U_6273] :
( ( app(skaf82(sk1),U_6273) = tl(app(sk1,U_6273)) )
| ~ ssList(U_6273) ),
inference(negUnitSimplification,[status(thm)],[c_9303,c_136784]) ).
tff(c_4270,plain,
! [W_681,U_682,V_683] :
( ( W_681 = U_682 )
| ~ ssList(W_681)
| ~ ssList(V_683)
| ~ ssList(U_682)
| ( app(W_681,V_683) != app(U_682,V_683) ) ),
inference(cnfTransformation,[status(thm)],[f_1079]) ).
tff(c_27127,plain,
! [U_1862,V_1863] :
( ( nil = U_1862 )
| ~ ssList(V_1863)
| ~ ssList(U_1862)
| ( app(nil,V_1863) != app(U_1862,V_1863) ) ),
inference(resolution,[status(thm)],[c_16,c_4270]) ).
tff(c_27179,plain,
! [U_1862,U_2] :
( ( nil = U_1862 )
| ~ ssList(U_1862)
| ( app(nil,skaf82(U_2)) != app(U_1862,skaf82(U_2)) ) ),
inference(resolution,[status(thm)],[c_26,c_27127]) ).
tff(c_27242,plain,
! [U_1862,U_2] :
( ( nil = U_1862 )
| ~ ssList(U_1862)
| ( app(U_1862,skaf82(U_2)) != skaf82(U_2) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_584,c_27179]) ).
tff(c_157214,plain,
! [U_2] :
( ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1))
| ( tl(app(sk1,skaf82(U_2))) != skaf82(U_2) )
| ~ ssList(skaf82(U_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_156808,c_27242]) ).
tff(c_157810,plain,
! [U_2] :
( ( skaf82(sk1) = nil )
| ( tl(app(sk1,skaf82(U_2))) != skaf82(U_2) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_26,c_157214]) ).
tff(c_161591,plain,
! [U_6297] : ( tl(app(sk1,skaf82(U_6297))) != skaf82(U_6297) ),
inference(negUnitSimplification,[status(thm)],[c_41759,c_157810]) ).
tff(c_161594,plain,
tl(sk2) != skaf82(sk2),
inference(superposition,[status(thm),theory(equality)],[c_11829,c_161591]) ).
tff(c_161597,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11811,c_161594]) ).
tff(c_161598,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_9336]) ).
tff(c_161607,plain,
~ frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_161598,c_8620]) ).
tff(c_161667,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3913,c_161607]) ).
tff(c_161668,plain,
sk2 = sk1,
inference(splitRight,[status(thm)],[c_8609]) ).
tff(c_282,plain,
! [W_187,U_185,V_186] :
( memberP(app(W_187,U_185),V_186)
| ~ ssItem(V_186)
| ~ ssList(W_187)
| ~ ssList(U_185)
| ~ memberP(U_185,V_186) ),
inference(cnfTransformation,[status(thm)],[f_940]) ).
tff(c_8556,plain,
! [V_186] :
( memberP(sk2,V_186)
| ~ ssItem(V_186)
| ~ ssList(sk1)
| ~ ssList(tl(sk2))
| ~ memberP(tl(sk2),V_186) ),
inference(superposition,[status(thm),theory(equality)],[c_8408,c_282]) ).
tff(c_8586,plain,
! [V_186] :
( memberP(sk2,V_186)
| ~ ssItem(V_186)
| ~ memberP(tl(sk2),V_186) ),
inference(demodulation,[status(thm),theory(equality)],[c_8409,c_406,c_8556]) ).
tff(c_167534,plain,
! [V_6779] :
( memberP(sk1,V_6779)
| ~ ssItem(V_6779)
| ~ memberP(skaf82(sk1),V_6779) ),
inference(demodulation,[status(thm),theory(equality)],[c_164759,c_161668,c_161668,c_8586]) ).
tff(c_167538,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ~ ssItem(skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil )
| ~ ssList(skaf82(sk1)) ),
inference(resolution,[status(thm)],[c_2392,c_167534]) ).
tff(c_167545,plain,
( memberP(sk1,skaf83(skaf82(sk1)))
| ( skaf82(sk1) = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_167538]) ).
tff(c_167549,plain,
skaf82(sk1) = nil,
inference(splitLeft,[status(thm)],[c_167545]) ).
tff(c_167553,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_167549,c_164806]) ).
tff(c_167772,plain,
( singletonP(sk1)
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_167553,c_2880]) ).
tff(c_167863,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_165571,c_167772]) ).
tff(c_167865,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2157,c_167863]) ).
tff(c_167867,plain,
skaf82(sk1) != nil,
inference(splitRight,[status(thm)],[c_167545]) ).
tff(c_161967,plain,
app(sk1,tl(sk1)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_161668,c_161668,c_8408]) ).
tff(c_164771,plain,
app(sk1,skaf82(sk1)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_164759,c_161967]) ).
tff(c_5094,plain,
! [W_721,V_722,U_723] :
( ( W_721 = V_722 )
| ~ ssList(W_721)
| ~ ssList(U_723)
| ~ ssList(V_722)
| ( app(U_723,W_721) != app(U_723,V_722) ) ),
inference(cnfTransformation,[status(thm)],[f_1065]) ).
tff(c_185530,plain,
! [V_7423,U_7424] :
( ( nil = V_7423 )
| ~ ssList(U_7424)
| ~ ssList(V_7423)
| ( app(U_7424,nil) != app(U_7424,V_7423) ) ),
inference(resolution,[status(thm)],[c_16,c_5094]) ).
tff(c_185592,plain,
! [V_7423] :
( ( nil = V_7423 )
| ~ ssList(V_7423)
| ( app(sk1,nil) != app(sk1,V_7423) ) ),
inference(resolution,[status(thm)],[c_406,c_185530]) ).
tff(c_185656,plain,
! [V_7425] :
( ( nil = V_7425 )
| ~ ssList(V_7425)
| ( app(sk1,V_7425) != sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_727,c_185592]) ).
tff(c_185795,plain,
! [U_7432] :
( ( skaf82(U_7432) = nil )
| ( app(sk1,skaf82(U_7432)) != sk1 ) ),
inference(resolution,[status(thm)],[c_26,c_185656]) ).
tff(c_185798,plain,
skaf82(sk1) = nil,
inference(superposition,[status(thm),theory(equality)],[c_164771,c_185795]) ).
tff(c_185802,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_167867,c_185798]) ).
tff(c_185803,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_2770]) ).
tff(c_185821,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_185803,c_6755]) ).
tff(c_185872,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_185821]) ).
tff(c_185873,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_4207]) ).
tff(c_3942,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_3913,c_258]) ).
tff(c_3945,plain,
( ( sk1 = nil )
| ~ frontsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_3942]) ).
tff(c_6731,plain,
~ frontsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_3945]) ).
tff(c_185924,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_185873,c_6731]) ).
tff(c_185975,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3911,c_185924]) ).
tff(c_185976,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_4212]) ).
tff(c_589,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[c_405,c_471]) ).
tff(c_3816,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_589,c_3664]) ).
tff(c_3915,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_589,c_3816]) ).
tff(c_3947,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_3915,c_258]) ).
tff(c_3950,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_3947]) ).
tff(c_6753,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_3950]) ).
tff(c_185978,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_185976,c_6753]) ).
tff(c_186030,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3911,c_185978]) ).
tff(c_186031,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_3950]) ).
tff(c_186079,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_186031,c_384]) ).
tff(c_230,plain,
! [V_129] :
( ~ ssList(V_129)
| ~ neq(V_129,V_129) ),
inference(cnfTransformation,[status(thm)],[f_613]) ).
tff(c_186149,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_186079,c_230]) ).
tff(c_186156,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_186149]) ).
tff(c_186157,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_3945]) ).
tff(c_186502,plain,
( ~ neq(nil,sk2)
| ~ ssList(tl(sk2))
| ( app(nil,tl(sk2)) = sk2 )
| ~ ssList(app(nil,tl(sk2))) ),
inference(demodulation,[status(thm),theory(equality)],[c_186157,c_186157,c_404]) ).
tff(c_186503,plain,
~ ssList(app(nil,tl(sk2))),
inference(splitLeft,[status(thm)],[c_186502]) ).
tff(c_186506,plain,
( ~ ssList(nil)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_186503]) ).
tff(c_186509,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_186506]) ).
tff(c_186512,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_186509]) ).
tff(c_186515,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_186512]) ).
tff(c_186297,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_3950]) ).
tff(c_186518,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_186515,c_186297]) ).
tff(c_186570,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3911,c_186518]) ).
tff(c_186571,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(nil,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_186502]) ).
tff(c_265112,plain,
( ~ neq(nil,sk2)
| ( skaf82(sk2) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_584,c_190585,c_26,c_190585,c_186571]) ).
tff(c_265113,plain,
~ neq(nil,sk2),
inference(negUnitSimplification,[status(thm)],[c_190180,c_265112]) ).
tff(c_265116,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_265113]) ).
tff(c_265122,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_265116]) ).
tff(c_265124,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_190004,c_265122]) ).
tff(c_265125,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_2769]) ).
tff(c_265128,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_265125,c_186297]) ).
tff(c_265180,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3911,c_265128]) ).
tff(c_265181,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_3950]) ).
tff(c_186245,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_4212]) ).
tff(c_265183,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_265181,c_186245]) ).
tff(c_265234,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4198,c_265183]) ).
tff(c_265235,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_4212]) ).
tff(c_265282,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_265235,c_384]) ).
tff(c_265353,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_265282,c_230]) ).
tff(c_265360,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_265353]) ).
tff(c_265362,plain,
singletonP(sk1),
inference(splitRight,[status(thm)],[c_2136]) ).
tff(c_267155,plain,
! [U_10755,V_10756] :
( frontsegP(app(U_10755,V_10756),U_10755)
| ~ ssList(app(U_10755,V_10756))
| ~ ssList(U_10755)
| ~ ssList(V_10756) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_267304,plain,
( frontsegP(sk1,nil)
| ~ ssList(app(nil,sk1))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_590,c_267155]) ).
tff(c_267404,plain,
frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_590,c_267304]) ).
tff(c_266868,plain,
! [U_10753,V_10754] :
( rearsegP(app(U_10753,V_10754),V_10754)
| ~ ssList(app(U_10753,V_10754))
| ~ ssList(V_10754)
| ~ ssList(U_10753) ),
inference(cnfTransformation,[status(thm)],[f_961]) ).
tff(c_267014,plain,
( rearsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_266868]) ).
tff(c_267115,plain,
rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_267014]) ).
tff(c_267301,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_267155]) ).
tff(c_267402,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_267301]) ).
tff(c_269750,plain,
~ ssList(app(sk1,tl(sk2))),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_269753,plain,
( ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_269750]) ).
tff(c_269756,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_269753]) ).
tff(c_269759,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_269756]) ).
tff(c_269762,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_269759]) ).
tff(c_269811,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_269762,c_384]) ).
tff(c_270103,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_269811,c_230]) ).
tff(c_270110,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_270103]) ).
tff(c_270111,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_270167,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_270111]) ).
tff(c_270170,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_270167]) ).
tff(c_270176,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_270170]) ).
tff(c_270178,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_270176,c_270167]) ).
tff(c_270227,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_270176,c_384]) ).
tff(c_270355,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_270178,c_270227]) ).
tff(c_270356,plain,
( ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_270111]) ).
tff(c_270382,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_270356]) ).
tff(c_270385,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_270382]) ).
tff(c_270388,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_270385]) ).
tff(c_270357,plain,
neq(nil,sk2),
inference(splitRight,[status(thm)],[c_270111]) ).
tff(c_270390,plain,
neq(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_270388,c_270357]) ).
tff(c_270752,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[c_270390,c_230]) ).
tff(c_270759,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_16,c_270752]) ).
tff(c_270760,plain,
app(sk1,tl(sk2)) = sk2,
inference(splitRight,[status(thm)],[c_270356]) ).
tff(c_270761,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_270356]) ).
tff(c_270829,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_270760,c_246]) ).
tff(c_270848,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_270761,c_406,c_270829]) ).
tff(c_271626,plain,
sk1 = nil,
inference(splitLeft,[status(thm)],[c_270848]) ).
tff(c_267008,plain,
( rearsegP(sk1,nil)
| ~ ssList(app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_266868]) ).
tff(c_267111,plain,
rearsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_16,c_406,c_727,c_267008]) ).
tff(c_267121,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_267111,c_256]) ).
tff(c_267124,plain,
( ( sk1 = nil )
| ~ rearsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_267121]) ).
tff(c_271224,plain,
~ rearsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_267124]) ).
tff(c_271627,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_271626,c_271224]) ).
tff(c_271684,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_267115,c_271627]) ).
tff(c_271685,plain,
hd(sk2) = hd(sk1),
inference(splitRight,[status(thm)],[c_270848]) ).
tff(c_271702,plain,
( ( sk2 = nil )
| ssItem(hd(sk1))
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_271685,c_156]) ).
tff(c_271714,plain,
( ( sk2 = nil )
| ssItem(hd(sk1)) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_271702]) ).
tff(c_271742,plain,
ssItem(hd(sk1)),
inference(splitLeft,[status(thm)],[c_271714]) ).
tff(c_271686,plain,
sk1 != nil,
inference(splitRight,[status(thm)],[c_270848]) ).
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_2140,plain,
! [U_529,V_530] :
( ( tl(cons(U_529,V_530)) = V_530 )
| ~ ssList(V_530)
| ~ ssItem(U_529) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_2152,plain,
! [U_103] :
( ( tl(U_103) = nil )
| ~ ssList(nil)
| ~ ssItem(skaf44(U_103))
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_2140]) ).
tff(c_273618,plain,
! [U_11016] :
( ( tl(U_11016) = nil )
| ~ ssList(U_11016)
| ~ singletonP(U_11016) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_2152]) ).
tff(c_273717,plain,
( ( tl(sk1) = nil )
| ~ singletonP(sk1) ),
inference(resolution,[status(thm)],[c_406,c_273618]) ).
tff(c_273755,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_265362,c_273717]) ).
tff(c_273828,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),nil) = sk1 )
| ~ ssList(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_273755,c_208]) ).
tff(c_273838,plain,
( ( sk1 = nil )
| ( cons(hd(sk1),nil) = sk1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_273828]) ).
tff(c_273839,plain,
cons(hd(sk1),nil) = sk1,
inference(negUnitSimplification,[status(thm)],[c_271686,c_273838]) ).
tff(c_394,plain,
! [A_333,B_334] :
( ~ neq(sk4,nil)
| ( app(cons(A_333,nil),B_334) != sk2 )
| ( cons(A_333,nil) != sk1 )
| ~ ssList(B_334)
| ~ ssItem(A_333) ),
inference(cnfTransformation,[status(thm)],[f_1725]) ).
tff(c_399,plain,
! [A_333,B_334] :
( ~ neq(sk2,nil)
| ( app(cons(A_333,nil),B_334) != sk2 )
| ( cons(A_333,nil) != sk1 )
| ~ ssList(B_334)
| ~ ssItem(A_333) ),
inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).
tff(c_402,plain,
! [A_333,B_334] :
( ( app(cons(A_333,nil),B_334) != sk2 )
| ( cons(A_333,nil) != sk1 )
| ~ ssList(B_334)
| ~ ssItem(A_333) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_273872,plain,
! [B_334] :
( ( app(sk1,B_334) != sk2 )
| ( cons(hd(sk1),nil) != sk1 )
| ~ ssList(B_334)
| ~ ssItem(hd(sk1)) ),
inference(superposition,[status(thm),theory(equality)],[c_273839,c_402]) ).
tff(c_274322,plain,
! [B_11021] :
( ( app(sk1,B_11021) != sk2 )
| ~ ssList(B_11021) ),
inference(demodulation,[status(thm),theory(equality)],[c_271742,c_273839,c_273872]) ).
tff(c_274325,plain,
app(sk1,tl(sk2)) != sk2,
inference(resolution,[status(thm)],[c_270761,c_274322]) ).
tff(c_274428,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_270760,c_274325]) ).
tff(c_274429,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_271714]) ).
tff(c_267307,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_589,c_267155]) ).
tff(c_267406,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_589,c_267307]) ).
tff(c_267538,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_267406,c_258]) ).
tff(c_267541,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_267538]) ).
tff(c_271222,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_267541]) ).
tff(c_274461,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_274429,c_271222]) ).
tff(c_274521,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_267402,c_274461]) ).
tff(c_274522,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_267124]) ).
tff(c_267533,plain,
( ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(nil,sk1) ),
inference(resolution,[status(thm)],[c_267404,c_258]) ).
tff(c_267536,plain,
( ( sk1 = nil )
| ~ frontsegP(nil,sk1) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_267533]) ).
tff(c_271223,plain,
~ frontsegP(nil,sk1),
inference(splitLeft,[status(thm)],[c_267536]) ).
tff(c_274524,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_274522,c_271223]) ).
tff(c_274580,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_267402,c_274524]) ).
tff(c_274581,plain,
sk1 = nil,
inference(splitRight,[status(thm)],[c_267536]) ).
tff(c_274610,plain,
singletonP(nil),
inference(demodulation,[status(thm),theory(equality)],[c_274581,c_265362]) ).
tff(c_274643,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_274610]) ).
tff(c_274644,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_267541]) ).
tff(c_267011,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_726,c_266868]) ).
tff(c_267113,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_726,c_267011]) ).
tff(c_267126,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_267113,c_256]) ).
tff(c_267129,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_267126]) ).
tff(c_271118,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_267129]) ).
tff(c_274679,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_274644,c_271118]) ).
tff(c_274738,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_267115,c_274679]) ).
tff(c_274739,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_267129]) ).
tff(c_270823,plain,
( frontsegP(sk2,sk1)
| ~ ssList(app(sk1,tl(sk2)))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_270760,c_288]) ).
tff(c_270844,plain,
frontsegP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_270761,c_406,c_405,c_270760,c_270823]) ).
tff(c_270855,plain,
( ( sk2 = sk1 )
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk2) ),
inference(resolution,[status(thm)],[c_270844,c_258]) ).
tff(c_270861,plain,
( ( sk2 = sk1 )
| ~ frontsegP(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_405,c_270855]) ).
tff(c_270933,plain,
~ frontsegP(sk1,sk2),
inference(splitLeft,[status(thm)],[c_270861]) ).
tff(c_274741,plain,
~ frontsegP(sk1,nil),
inference(demodulation,[status(thm),theory(equality)],[c_274739,c_270933]) ).
tff(c_274799,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_267404,c_274741]) ).
tff(c_274800,plain,
sk2 = sk1,
inference(splitRight,[status(thm)],[c_270861]) ).
tff(c_2135,plain,
( equalelemsP(sk2)
| ~ singletonP(sk2) ),
inference(resolution,[status(thm)],[c_405,c_2005]) ).
tff(c_2139,plain,
~ singletonP(sk2),
inference(splitLeft,[status(thm)],[c_2135]) ).
tff(c_274849,plain,
~ singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_274800,c_2139]) ).
tff(c_274864,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_265362,c_274849]) ).
tff(c_274866,plain,
singletonP(sk2),
inference(splitRight,[status(thm)],[c_2135]) ).
tff(c_274867,plain,
! [U_11028,V_11029] :
( ( tl(cons(U_11028,V_11029)) = V_11029 )
| ~ ssList(V_11029)
| ~ ssItem(U_11028) ),
inference(cnfTransformation,[status(thm)],[f_420]) ).
tff(c_274879,plain,
! [U_103] :
( ( tl(U_103) = nil )
| ~ ssList(nil)
| ~ ssItem(skaf44(U_103))
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_274867]) ).
tff(c_282827,plain,
! [U_11419] :
( ( tl(U_11419) = nil )
| ~ ssList(U_11419)
| ~ singletonP(U_11419) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_274879]) ).
tff(c_282923,plain,
( ( tl(sk2) = nil )
| ~ singletonP(sk2) ),
inference(resolution,[status(thm)],[c_405,c_282827]) ).
tff(c_282963,plain,
tl(sk2) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_274866,c_282923]) ).
tff(c_276739,plain,
( frontsegP(nil,nil)
| ~ ssList(app(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_591,c_276599]) ).
tff(c_276836,plain,
frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_276739]) ).
tff(c_280139,plain,
~ ssList(app(sk1,tl(sk2))),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_280142,plain,
( ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_280139]) ).
tff(c_280145,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_280142]) ).
tff(c_280148,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_280145]) ).
tff(c_280151,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_280148]) ).
tff(c_276745,plain,
( frontsegP(sk2,nil)
| ~ ssList(app(nil,sk2))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_589,c_276599]) ).
tff(c_276840,plain,
frontsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_589,c_276745]) ).
tff(c_276925,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_276840,c_258]) ).
tff(c_276928,plain,
( ( sk2 = nil )
| ~ frontsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_276925]) ).
tff(c_279695,plain,
~ frontsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_276928]) ).
tff(c_280154,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_280151,c_279695]) ).
tff(c_280209,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276836,c_280154]) ).
tff(c_280210,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_280319,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_280210]) ).
tff(c_280322,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_280319]) ).
tff(c_280328,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_280322]) ).
tff(c_280333,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_280328,c_279695]) ).
tff(c_280388,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276836,c_280333]) ).
tff(c_280389,plain,
( ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_280210]) ).
tff(c_280417,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_280389]) ).
tff(c_280420,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_280417]) ).
tff(c_280423,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_280420]) ).
tff(c_280428,plain,
~ frontsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_280423,c_279695]) ).
tff(c_280483,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276836,c_280428]) ).
tff(c_280484,plain,
app(sk1,tl(sk2)) = sk2,
inference(splitRight,[status(thm)],[c_280389]) ).
tff(c_282974,plain,
app(sk1,nil) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_282963,c_280484]) ).
tff(c_282984,plain,
sk2 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_727,c_282974]) ).
tff(c_280485,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_280389]) ).
tff(c_280662,plain,
( frontsegP(sk2,sk1)
| ~ ssList(app(sk1,tl(sk2)))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_280484,c_288]) ).
tff(c_280687,plain,
frontsegP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_280485,c_406,c_405,c_280484,c_280662]) ).
tff(c_280698,plain,
( ( sk2 = sk1 )
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk2) ),
inference(resolution,[status(thm)],[c_280687,c_258]) ).
tff(c_280704,plain,
( ( sk2 = sk1 )
| ~ frontsegP(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_405,c_280698]) ).
tff(c_280715,plain,
~ frontsegP(sk1,sk2),
inference(splitLeft,[status(thm)],[c_280704]) ).
tff(c_283014,plain,
~ frontsegP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_282984,c_280715]) ).
tff(c_283072,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276832,c_283014]) ).
tff(c_283073,plain,
sk2 = sk1,
inference(splitRight,[status(thm)],[c_280704]) ).
tff(c_283125,plain,
singletonP(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_283073,c_274866]) ).
tff(c_283140,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_274884,c_283125]) ).
tff(c_283141,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_276928]) ).
tff(c_276471,plain,
( rearsegP(sk2,nil)
| ~ ssList(app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_726,c_276334]) ).
tff(c_276569,plain,
rearsegP(sk2,nil),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_726,c_276471]) ).
tff(c_276582,plain,
( ( sk2 = nil )
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(nil,sk2) ),
inference(resolution,[status(thm)],[c_276569,c_256]) ).
tff(c_276585,plain,
( ( sk2 = nil )
| ~ rearsegP(nil,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_276582]) ).
tff(c_279655,plain,
~ rearsegP(nil,sk2),
inference(splitLeft,[status(thm)],[c_276585]) ).
tff(c_283143,plain,
~ rearsegP(nil,nil),
inference(demodulation,[status(thm),theory(equality)],[c_283141,c_279655]) ).
tff(c_283197,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_276571,c_283143]) ).
tff(c_283198,plain,
sk2 = nil,
inference(splitRight,[status(thm)],[c_276585]) ).
tff(c_283242,plain,
singletonP(nil),
inference(demodulation,[status(thm),theory(equality)],[c_283198,c_274866]) ).
tff(c_283257,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22,c_283242]) ).
tff(c_283259,plain,
singletonP(sk1),
inference(splitRight,[status(thm)],[c_2136]) ).
tff(c_293796,plain,
! [U_11930] :
( ( tl(U_11930) = nil )
| ~ ssList(U_11930)
| ~ singletonP(U_11930) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_274879]) ).
tff(c_293892,plain,
( ( tl(sk1) = nil )
| ~ singletonP(sk1) ),
inference(resolution,[status(thm)],[c_406,c_293796]) ).
tff(c_293929,plain,
tl(sk1) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_283259,c_293892]) ).
tff(c_284764,plain,
! [U_11555,V_11556] :
( frontsegP(app(U_11555,V_11556),U_11555)
| ~ ssList(app(U_11555,V_11556))
| ~ ssList(U_11555)
| ~ ssList(V_11556) ),
inference(cnfTransformation,[status(thm)],[f_975]) ).
tff(c_284904,plain,
( frontsegP(sk1,sk1)
| ~ ssList(app(sk1,nil))
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_284764]) ).
tff(c_285007,plain,
frontsegP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_406,c_727,c_284904]) ).
tff(c_291458,plain,
! [U_11855] :
( ( tl(U_11855) = nil )
| ~ ssList(U_11855)
| ~ singletonP(U_11855) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_274879]) ).
tff(c_291554,plain,
( ( tl(sk2) = nil )
| ~ singletonP(sk2) ),
inference(resolution,[status(thm)],[c_405,c_291458]) ).
tff(c_291594,plain,
tl(sk2) = nil,
inference(demodulation,[status(thm),theory(equality)],[c_274866,c_291554]) ).
tff(c_1663,plain,
! [U_476] :
( ~ ssItem(U_476)
| ( cons(U_476,nil) != nil ) ),
inference(resolution,[status(thm)],[c_16,c_1494]) ).
tff(c_1731,plain,
! [U_36] : ( cons(skaf44(U_36),nil) != nil ),
inference(resolution,[status(thm)],[c_94,c_1663]) ).
tff(c_289000,plain,
! [U_11746] :
( ( nil != U_11746 )
| ~ ssList(U_11746)
| ~ singletonP(U_11746) ),
inference(superposition,[status(thm),theory(equality)],[c_1885,c_1731]) ).
tff(c_289093,plain,
( ( sk2 != nil )
| ~ singletonP(sk2) ),
inference(resolution,[status(thm)],[c_405,c_289000]) ).
tff(c_289132,plain,
sk2 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_274866,c_289093]) ).
tff(c_289137,plain,
~ ssList(app(sk1,tl(sk2))),
inference(splitLeft,[status(thm)],[c_404]) ).
tff(c_289140,plain,
( ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(resolution,[status(thm)],[c_170,c_289137]) ).
tff(c_289143,plain,
~ ssList(tl(sk2)),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_289140]) ).
tff(c_289221,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_289143]) ).
tff(c_289224,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_289221]) ).
tff(c_289226,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_289132,c_289224]) ).
tff(c_289227,plain,
( ~ ssList(tl(sk2))
| ~ neq(nil,sk2)
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_404]) ).
tff(c_289281,plain,
~ neq(nil,sk2),
inference(splitLeft,[status(thm)],[c_289227]) ).
tff(c_289284,plain,
( ( sk2 = nil )
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_200,c_289281]) ).
tff(c_289290,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_289284]) ).
tff(c_289292,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_289132,c_289290]) ).
tff(c_289293,plain,
( ~ ssList(tl(sk2))
| ( app(sk1,tl(sk2)) = sk2 ) ),
inference(splitRight,[status(thm)],[c_289227]) ).
tff(c_289345,plain,
~ ssList(tl(sk2)),
inference(splitLeft,[status(thm)],[c_289293]) ).
tff(c_289348,plain,
( ( sk2 = nil )
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[c_154,c_289345]) ).
tff(c_289351,plain,
sk2 = nil,
inference(demodulation,[status(thm),theory(equality)],[c_405,c_289348]) ).
tff(c_289353,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_289132,c_289351]) ).
tff(c_289354,plain,
app(sk1,tl(sk2)) = sk2,
inference(splitRight,[status(thm)],[c_289293]) ).
tff(c_291609,plain,
app(sk1,nil) = sk2,
inference(demodulation,[status(thm),theory(equality)],[c_291594,c_289354]) ).
tff(c_291619,plain,
sk2 = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_727,c_291609]) ).
tff(c_289355,plain,
ssList(tl(sk2)),
inference(splitRight,[status(thm)],[c_289293]) ).
tff(c_289514,plain,
( frontsegP(sk2,sk1)
| ~ ssList(app(sk1,tl(sk2)))
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_289354,c_288]) ).
tff(c_289540,plain,
frontsegP(sk2,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_289355,c_406,c_405,c_289354,c_289514]) ).
tff(c_289550,plain,
( ( sk2 = sk1 )
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk2) ),
inference(resolution,[status(thm)],[c_289540,c_258]) ).
tff(c_289556,plain,
( ( sk2 = sk1 )
| ~ frontsegP(sk1,sk2) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_405,c_289550]) ).
tff(c_289691,plain,
~ frontsegP(sk1,sk2),
inference(splitLeft,[status(thm)],[c_289556]) ).
tff(c_291648,plain,
~ frontsegP(sk1,sk1),
inference(demodulation,[status(thm),theory(equality)],[c_291619,c_289691]) ).
tff(c_291708,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_285007,c_291648]) ).
tff(c_291709,plain,
sk2 = sk1,
inference(splitRight,[status(thm)],[c_289556]) ).
tff(c_289096,plain,
( ( sk1 != nil )
| ~ singletonP(sk1) ),
inference(resolution,[status(thm)],[c_406,c_289000]) ).
tff(c_289135,plain,
sk1 != nil,
inference(demodulation,[status(thm),theory(equality)],[c_283259,c_289096]) ).
tff(c_289517,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil )
| ~ ssList(sk1)
| ~ ssList(tl(sk2)) ),
inference(superposition,[status(thm),theory(equality)],[c_289354,c_246]) ).
tff(c_289542,plain,
( ( hd(sk2) = hd(sk1) )
| ( sk1 = nil ) ),
inference(demodulation,[status(thm),theory(equality)],[c_289355,c_406,c_289517]) ).
tff(c_289543,plain,
hd(sk2) = hd(sk1),
inference(negUnitSimplification,[status(thm)],[c_289135,c_289542]) ).
tff(c_289582,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),tl(sk2)) = sk2 )
| ~ ssList(sk2) ),
inference(superposition,[status(thm),theory(equality)],[c_289543,c_208]) ).
tff(c_289601,plain,
( ( sk2 = nil )
| ( cons(hd(sk1),tl(sk2)) = sk2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_405,c_289582]) ).
tff(c_289602,plain,
cons(hd(sk1),tl(sk2)) = sk2,
inference(negUnitSimplification,[status(thm)],[c_289132,c_289601]) ).
tff(c_292725,plain,
cons(hd(sk1),tl(sk1)) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_291709,c_291709,c_289602]) ).
tff(c_293931,plain,
cons(hd(sk1),nil) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_293929,c_292725]) ).
tff(c_1988,plain,
! [U_526,V_527] :
( ( hd(cons(U_526,V_527)) = U_526 )
| ~ ssList(V_527)
| ~ ssItem(U_526) ),
inference(cnfTransformation,[status(thm)],[f_428]) ).
tff(c_2000,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_1988]) ).
tff(c_295579,plain,
! [U_12136] :
( ( skaf44(U_12136) = hd(U_12136) )
| ~ ssList(U_12136)
| ~ singletonP(U_12136) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_16,c_2000]) ).
tff(c_295672,plain,
( ( skaf44(sk1) = hd(sk1) )
| ~ singletonP(sk1) ),
inference(resolution,[status(thm)],[c_406,c_295579]) ).
tff(c_295708,plain,
skaf44(sk1) = hd(sk1),
inference(demodulation,[status(thm),theory(equality)],[c_283259,c_295672]) ).
tff(c_286907,plain,
! [A_11632,B_11633] :
( ( app(cons(A_11632,nil),B_11633) != sk2 )
| ( cons(A_11632,nil) != sk1 )
| ~ ssList(B_11633)
| ~ ssItem(A_11632) ),
inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).
tff(c_286917,plain,
! [U_103,B_11633] :
( ( app(U_103,B_11633) != sk2 )
| ( cons(skaf44(U_103),nil) != sk1 )
| ~ ssList(B_11633)
| ~ ssItem(skaf44(U_103))
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(superposition,[status(thm),theory(equality)],[c_202,c_286907]) ).
tff(c_286921,plain,
! [U_103,B_11633] :
( ( app(U_103,B_11633) != sk2 )
| ( cons(skaf44(U_103),nil) != sk1 )
| ~ ssList(B_11633)
| ~ ssList(U_103)
| ~ singletonP(U_103) ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_286917]) ).
tff(c_340193,plain,
! [U_14088,B_14089] :
( ( app(U_14088,B_14089) != sk1 )
| ( cons(skaf44(U_14088),nil) != sk1 )
| ~ ssList(B_14089)
| ~ ssList(U_14088)
| ~ singletonP(U_14088) ),
inference(demodulation,[status(thm),theory(equality)],[c_291709,c_286921]) ).
tff(c_340359,plain,
( ( cons(skaf44(sk1),nil) != sk1 )
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ singletonP(sk1) ),
inference(superposition,[status(thm),theory(equality)],[c_727,c_340193]) ).
tff(c_340515,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_283259,c_406,c_16,c_293931,c_295708,c_340359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC015-1 : 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 : n019.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 21:38:31 EDT 2023
% 0.12/0.35 % CPUTime :
% 217.63/195.78 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 217.98/195.83
% 217.98/195.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 217.98/195.91
% 217.98/195.91 Inference rules
% 217.98/195.91 ----------------------
% 217.98/195.91 #Ref : 58
% 217.98/195.91 #Sup : 80929
% 217.98/195.91 #Fact : 0
% 217.98/195.91 #Define : 0
% 217.98/195.91 #Split : 84
% 217.98/195.91 #Chain : 0
% 217.98/195.91 #Close : 0
% 217.98/195.91
% 217.98/195.91 Ordering : KBO
% 217.98/195.91
% 217.98/195.91 Simplification rules
% 217.98/195.91 ----------------------
% 217.98/195.91 #Subsume : 19189
% 217.98/195.91 #Demod : 74686
% 217.98/195.91 #Tautology : 14195
% 217.98/195.91 #SimpNegUnit : 1111
% 217.98/195.91 #BackRed : 2314
% 217.98/195.91
% 217.98/195.91 #Partial instantiations: 0
% 217.98/195.91 #Strategies tried : 1
% 217.98/195.91
% 217.98/195.91 Timing (in seconds)
% 217.98/195.91 ----------------------
% 217.98/195.91 Preprocessing : 0.88
% 217.98/195.91 Parsing : 0.44
% 217.98/195.91 CNF conversion : 0.07
% 217.98/195.91 Main loop : 193.88
% 217.98/195.91 Inferencing : 25.38
% 217.98/195.91 Reduction : 91.84
% 217.98/195.91 Demodulation : 67.75
% 217.98/195.91 BG Simplification : 0.56
% 217.98/195.91 Subsumption : 62.76
% 217.98/195.91 Abstraction : 1.38
% 217.98/195.91 MUC search : 0.00
% 217.98/195.91 Cooper : 0.00
% 217.98/195.91 Total : 194.90
% 217.98/195.91 Index Insertion : 0.00
% 217.98/195.91 Index Deletion : 0.00
% 217.98/195.91 Index Matching : 0.00
% 217.98/195.91 BG Taut test : 0.00
%------------------------------------------------------------------------------