TSTP Solution File: SWC395-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC395-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:02:28 EDT 2023

% Result   : Unsatisfiable 213.64s 190.73s
% Output   : CNFRefutation 214.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :  105
% Syntax   : Number of formulae    :  297 (  92 unt;  73 typ;   0 def)
%            Number of atoms       :  548 ( 158 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  627 ( 303   ~; 324   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  65   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   54 (  54 usr;   8 con; 0-2 aty)
%            Number of variables   :  154 (; 154   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > skaf48 > skaf47 > skaf46 > skaf45 > skaf43 > skaf42 > cons > app > #nlpp > tl > skaf83 > skaf82 > skaf81 > skaf80 > skaf79 > skaf78 > skaf77 > skaf76 > skaf75 > skaf74 > skaf73 > skaf72 > skaf71 > skaf70 > skaf69 > skaf68 > skaf67 > skaf66 > skaf65 > skaf64 > skaf63 > skaf62 > skaf61 > skaf60 > skaf59 > skaf58 > skaf57 > skaf56 > skaf55 > skaf54 > skaf53 > skaf52 > skaf51 > skaf50 > skaf49 > skaf44 > hd > skac3 > skac2 > sk5 > sk4 > sk3 > sk2 > sk1 > nil

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(skaf56,type,
    skaf56: $i > $i ).

tff(segmentP,type,
    segmentP: ( $i * $i ) > $o ).

tff(totalorderedP,type,
    totalorderedP: $i > $o ).

tff(equalelemsP,type,
    equalelemsP: $i > $o ).

tff(skaf74,type,
    skaf74: $i > $i ).

tff(skaf61,type,
    skaf61: $i > $i ).

tff(skaf51,type,
    skaf51: $i > $i ).

tff(skaf83,type,
    skaf83: $i > $i ).

tff(skac2,type,
    skac2: $i ).

tff(skaf63,type,
    skaf63: $i > $i ).

tff(skaf62,type,
    skaf62: $i > $i ).

tff(sk2,type,
    sk2: $i ).

tff(skaf52,type,
    skaf52: $i > $i ).

tff(skaf50,type,
    skaf50: $i > $i ).

tff(skaf42,type,
    skaf42: ( $i * $i ) > $i ).

tff(skaf44,type,
    skaf44: $i > $i ).

tff(singletonP,type,
    singletonP: $i > $o ).

tff(skaf67,type,
    skaf67: $i > $i ).

tff(skaf75,type,
    skaf75: $i > $i ).

tff(sk1,type,
    sk1: $i ).

tff(skaf58,type,
    skaf58: $i > $i ).

tff(skaf46,type,
    skaf46: ( $i * $i ) > $i ).

tff(frontsegP,type,
    frontsegP: ( $i * $i ) > $o ).

tff(skaf70,type,
    skaf70: $i > $i ).

tff(totalorderP,type,
    totalorderP: $i > $o ).

tff(ssItem,type,
    ssItem: $i > $o ).

tff(skaf82,type,
    skaf82: $i > $i ).

tff(skaf47,type,
    skaf47: ( $i * $i ) > $i ).

tff(skaf76,type,
    skaf76: $i > $i ).

tff(skac3,type,
    skac3: $i ).

tff(skaf80,type,
    skaf80: $i > $i ).

tff(skaf59,type,
    skaf59: $i > $i ).

tff(skaf53,type,
    skaf53: $i > $i ).

tff(skaf45,type,
    skaf45: ( $i * $i ) > $i ).

tff(hd,type,
    hd: $i > $i ).

tff(app,type,
    app: ( $i * $i ) > $i ).

tff(skaf72,type,
    skaf72: $i > $i ).

tff(duplicatefreeP,type,
    duplicatefreeP: $i > $o ).

tff(skaf64,type,
    skaf64: $i > $i ).

tff(sk4,type,
    sk4: $i ).

tff(gt,type,
    gt: ( $i * $i ) > $o ).

tff(skaf71,type,
    skaf71: $i > $i ).

tff(skaf78,type,
    skaf78: $i > $i ).

tff(sk5,type,
    sk5: $i ).

tff(skaf79,type,
    skaf79: $i > $i ).

tff(rearsegP,type,
    rearsegP: ( $i * $i ) > $o ).

tff(memberP,type,
    memberP: ( $i * $i ) > $o ).

tff(skaf73,type,
    skaf73: $i > $i ).

tff(ssList,type,
    ssList: $i > $o ).

tff(cons,type,
    cons: ( $i * $i ) > $i ).

tff(skaf54,type,
    skaf54: $i > $i ).

tff(skaf77,type,
    skaf77: $i > $i ).

tff(sk3,type,
    sk3: $i ).

tff(skaf66,type,
    skaf66: $i > $i ).

tff(strictorderP,type,
    strictorderP: $i > $o ).

tff(skaf81,type,
    skaf81: $i > $i ).

tff(geq,type,
    geq: ( $i * $i ) > $o ).

tff(skaf60,type,
    skaf60: $i > $i ).

tff(leq,type,
    leq: ( $i * $i ) > $o ).

tff(lt,type,
    lt: ( $i * $i ) > $o ).

tff(skaf69,type,
    skaf69: $i > $i ).

tff(tl,type,
    tl: $i > $i ).

tff(neq,type,
    neq: ( $i * $i ) > $o ).

tff(skaf43,type,
    skaf43: ( $i * $i ) > $i ).

tff(skaf48,type,
    skaf48: ( $i * $i ) > $i ).

tff(skaf65,type,
    skaf65: $i > $i ).

tff(skaf57,type,
    skaf57: $i > $i ).

tff(nil,type,
    nil: $i ).

tff(skaf49,type,
    skaf49: $i > $i ).

tff(skaf55,type,
    skaf55: $i > $i ).

tff(skaf68,type,
    skaf68: $i > $i ).

tff(strictorderedP,type,
    strictorderedP: $i > $o ).

tff(cyclefreeP,type,
    cyclefreeP: $i > $o ).

tff(f_1654,axiom,
    ~ memberP(sk2,sk5),
    file(unknown,unknown) ).

tff(f_1652,axiom,
    memberP(sk1,sk5),
    file(unknown,unknown) ).

tff(f_1649,axiom,
    sk2 = sk4,
    file(unknown,unknown) ).

tff(f_1650,axiom,
    sk1 = sk3,
    file(unknown,unknown) ).

tff(f_1658,axiom,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    file(unknown,unknown) ).

tff(f_1648,axiom,
    ssList(sk4),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ssList(nil),
    file(unknown,unknown) ).

tff(f_1647,axiom,
    ssList(sk3),
    file(unknown,unknown) ).

tff(f_334,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | ssList(app(V,U)) ),
    file(unknown,unknown) ).

tff(f_240,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | duplicatefreeP(U)
      | ssItem(V) ),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ! [U] : ssList(skaf82(U)),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [U] : ssItem(skaf83(U)),
    file(unknown,unknown) ).

tff(f_543,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( cons(skaf83(U),skaf82(U)) = U )
      | ( nil = U ) ),
    file(unknown,unknown) ).

tff(f_420,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ( tl(cons(U,V)) = V ) ),
    file(unknown,unknown) ).

tff(f_492,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( cons(hd(U),tl(U)) = U )
      | ( nil = U ) ),
    file(unknown,unknown) ).

tff(f_271,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ssList(tl(U))
      | ( nil = U ) ),
    file(unknown,unknown) ).

tff(f_456,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | neq(V,U)
      | ( V = U ) ),
    file(unknown,unknown) ).

tff(f_428,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ( hd(cons(U,V)) = U ) ),
    file(unknown,unknown) ).

tff(f_342,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    file(unknown,unknown) ).

tff(f_1693,axiom,
    ! [A,B,C,D] :
      ( ~ ssList(A)
      | ( sk3 = A )
      | ~ ssList(B)
      | ~ ssList(C)
      | ( tl(sk4) != B )
      | ( app(B,C) != A )
      | ~ ssItem(D)
      | ( cons(D,nil) != C )
      | ( hd(sk4) != D )
      | ~ neq(nil,sk4)
      | ~ neq(nil,sk4)
      | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_278,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ssItem(hd(U))
      | ( nil = U ) ),
    file(unknown,unknown) ).

tff(f_1481,axiom,
    ! [W,U,X,Y,V] :
      ( ( app(app(U,cons(V,W)),cons(V,X)) != Y )
      | ~ ssList(X)
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssItem(V)
      | ~ duplicatefreeP(Y)
      | ~ ssList(Y) ),
    file(unknown,unknown) ).

tff(f_624,axiom,
    ! [U,V] :
      ( ( cons(U,nil) != V )
      | ~ ssItem(U)
      | ~ ssList(V)
      | singletonP(V) ),
    file(unknown,unknown) ).

tff(f_474,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssItem(V)
      | neq(V,U)
      | ( V = U ) ),
    file(unknown,unknown) ).

tff(f_250,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( app(nil,U) = U ) ),
    file(unknown,unknown) ).

tff(f_1405,axiom,
    ! [U,V,W,X] :
      ( ( app(U,cons(V,W)) != X )
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssItem(V)
      | ~ ssList(X)
      | memberP(X,V) ),
    file(unknown,unknown) ).

tff(f_233,axiom,
    ! [U] :
      ( ~ memberP(nil,U)
      | ~ ssItem(U) ),
    file(unknown,unknown) ).

tff(f_464,axiom,
    ! [U] :
      ( ~ singletonP(U)
      | ~ ssList(U)
      | ( cons(skaf44(U),nil) = U ) ),
    file(unknown,unknown) ).

tff(f_1239,axiom,
    ! [U,V,W] :
      ( ~ memberP(cons(U,V),W)
      | ~ ssList(V)
      | ~ ssItem(U)
      | ~ ssItem(W)
      | memberP(V,W)
      | ( W = U ) ),
    file(unknown,unknown) ).

tff(f_1191,axiom,
    ! [U,V,W] :
      ( ~ memberP(app(U,V),W)
      | ~ ssList(V)
      | ~ ssList(U)
      | ~ ssItem(W)
      | memberP(V,W)
      | memberP(U,W) ),
    file(unknown,unknown) ).

tff(f_912,axiom,
    ! [U,V,W] :
      ( ~ memberP(U,V)
      | ~ ssList(U)
      | ~ ssItem(W)
      | ~ ssItem(V)
      | memberP(cons(W,U),V) ),
    file(unknown,unknown) ).

tff(f_898,axiom,
    ! [U,V,W] :
      ( ( U != V )
      | ~ ssList(W)
      | ~ ssItem(V)
      | ~ ssItem(U)
      | memberP(cons(V,W),U) ),
    file(unknown,unknown) ).

tff(c_388,plain,
    ~ memberP(sk2,sk5),
    inference(cnfTransformation,[status(thm)],[f_1654]) ).

tff(c_386,plain,
    memberP(sk1,sk5),
    inference(cnfTransformation,[status(thm)],[f_1652]) ).

tff(c_380,plain,
    sk4 = sk2,
    inference(cnfTransformation,[status(thm)],[f_1649]) ).

tff(c_382,plain,
    sk3 = sk1,
    inference(cnfTransformation,[status(thm)],[f_1650]) ).

tff(c_390,plain,
    ( ( sk4 != nil )
    | ( sk3 = nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1658]) ).

tff(c_393,plain,
    ( ( sk4 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).

tff(c_395,plain,
    ( ( sk2 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_393]) ).

tff(c_447,plain,
    sk2 != nil,
    inference(splitLeft,[status(thm)],[c_395]) ).

tff(c_378,plain,
    ssList(sk4),
    inference(cnfTransformation,[status(thm)],[f_1648]) ).

tff(c_397,plain,
    ssList(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).

tff(c_16,plain,
    ssList(nil),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_376,plain,
    ssList(sk3),
    inference(cnfTransformation,[status(thm)],[f_1647]) ).

tff(c_398,plain,
    ssList(sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).

tff(c_170,plain,
    ! [V_81,U_80] :
      ( ssList(app(V_81,U_80))
      | ~ ssList(V_81)
      | ~ ssList(U_80) ),
    inference(cnfTransformation,[status(thm)],[f_334]) ).

tff(c_1539,plain,
    ! [V_474,U_475] :
      ( ssList(app(V_474,U_475))
      | ~ ssList(V_474)
      | ~ ssList(U_475) ),
    inference(cnfTransformation,[status(thm)],[f_334]) ).

tff(c_144,plain,
    ! [V_67,U_66] :
      ( ssItem(V_67)
      | duplicatefreeP(U_66)
      | ~ ssList(U_66) ),
    inference(cnfTransformation,[status(thm)],[f_240]) ).

tff(c_729,plain,
    ! [U_66] :
      ( duplicatefreeP(U_66)
      | ~ ssList(U_66) ),
    inference(splitLeft,[status(thm)],[c_144]) ).

tff(c_1658,plain,
    ! [V_474,U_475] :
      ( duplicatefreeP(app(V_474,U_475))
      | ~ ssList(V_474)
      | ~ ssList(U_475) ),
    inference(resolution,[status(thm)],[c_1539,c_729]) ).

tff(c_26,plain,
    ! [U_2] : ssList(skaf82(U_2)),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_24,plain,
    ! [U_1] : ssItem(skaf83(U_1)),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_2338,plain,
    ! [U_567] :
      ( ( nil = U_567 )
      | ( cons(skaf83(U_567),skaf82(U_567)) = U_567 )
      | ~ ssList(U_567) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_192,plain,
    ! [U_93,V_94] :
      ( ( tl(cons(U_93,V_94)) = V_94 )
      | ~ ssList(V_94)
      | ~ ssItem(U_93) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_2344,plain,
    ! [U_567] :
      ( ( tl(U_567) = skaf82(U_567) )
      | ~ ssList(skaf82(U_567))
      | ~ ssItem(skaf83(U_567))
      | ( nil = U_567 )
      | ~ ssList(U_567) ),
    inference(superposition,[status(thm),theory(equality)],[c_2338,c_192]) ).

tff(c_15212,plain,
    ! [U_1336] :
      ( ( tl(U_1336) = skaf82(U_1336) )
      | ( nil = U_1336 )
      | ~ ssList(U_1336) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2344]) ).

tff(c_15317,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_397,c_15212]) ).

tff(c_15357,plain,
    tl(sk2) = skaf82(sk2),
    inference(negUnitSimplification,[status(thm)],[c_447,c_15317]) ).

tff(c_208,plain,
    ! [U_108] :
      ( ( nil = U_108 )
      | ( cons(hd(U_108),tl(U_108)) = U_108 )
      | ~ ssList(U_108) ),
    inference(cnfTransformation,[status(thm)],[f_492]) ).

tff(c_15389,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_15357,c_208]) ).

tff(c_15402,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_15389]) ).

tff(c_15403,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_447,c_15402]) ).

tff(c_154,plain,
    ! [U_72] :
      ( ( nil = U_72 )
      | ssList(tl(U_72))
      | ~ ssList(U_72) ),
    inference(cnfTransformation,[status(thm)],[f_271]) ).

tff(c_200,plain,
    ! [V_102,U_101] :
      ( ( V_102 = U_101 )
      | neq(V_102,U_101)
      | ~ ssList(V_102)
      | ~ ssList(U_101) ),
    inference(cnfTransformation,[status(thm)],[f_456]) ).

tff(c_194,plain,
    ! [U_95,V_96] :
      ( ( hd(cons(U_95,V_96)) = U_95 )
      | ~ ssList(V_96)
      | ~ ssItem(U_95) ),
    inference(cnfTransformation,[status(thm)],[f_428]) ).

tff(c_2347,plain,
    ! [U_567] :
      ( ( skaf83(U_567) = hd(U_567) )
      | ~ ssList(skaf82(U_567))
      | ~ ssItem(skaf83(U_567))
      | ( nil = U_567 )
      | ~ ssList(U_567) ),
    inference(superposition,[status(thm),theory(equality)],[c_2338,c_194]) ).

tff(c_11548,plain,
    ! [U_1145] :
      ( ( skaf83(U_1145) = hd(U_1145) )
      | ( nil = U_1145 )
      | ~ ssList(U_1145) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2347]) ).

tff(c_11647,plain,
    ( ( skaf83(sk2) = hd(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_397,c_11548]) ).

tff(c_11683,plain,
    skaf83(sk2) = hd(sk2),
    inference(negUnitSimplification,[status(thm)],[c_447,c_11647]) ).

tff(c_11699,plain,
    ssItem(hd(sk2)),
    inference(superposition,[status(thm),theory(equality)],[c_11683,c_24]) ).

tff(c_172,plain,
    ! [U_82,V_83] :
      ( ssList(cons(U_82,V_83))
      | ~ ssList(V_83)
      | ~ ssItem(U_82) ),
    inference(cnfTransformation,[status(thm)],[f_342]) ).

tff(c_218,plain,
    ! [U_117] :
      ( ( nil = U_117 )
      | ( cons(skaf83(U_117),skaf82(U_117)) = U_117 )
      | ~ ssList(U_117) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_11689,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_11683,c_218]) ).

tff(c_11703,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_11689]) ).

tff(c_11704,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_447,c_11703]) ).

tff(c_12536,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_11704,c_192]) ).

tff(c_12601,plain,
    tl(sk2) = skaf82(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_11699,c_26,c_12536]) ).

tff(c_392,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4))
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(cnfTransformation,[status(thm)],[f_1693]) ).

tff(c_394,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4))
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk1 )
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).

tff(c_396,plain,
    ( ~ neq(sk2,nil)
    | ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
    | ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_394]) ).

tff(c_10087,plain,
    ~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
    inference(splitLeft,[status(thm)],[c_396]) ).

tff(c_10224,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(resolution,[status(thm)],[c_170,c_10087]) ).

tff(c_13764,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_12601,c_10224]) ).

tff(c_13767,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_13764]) ).

tff(c_13771,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_11699,c_16,c_13767]) ).

tff(c_13772,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2))
    | ~ neq(nil,sk2)
    | ~ neq(sk2,nil)
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_396]) ).

tff(c_14094,plain,
    ~ neq(sk2,nil),
    inference(splitLeft,[status(thm)],[c_13772]) ).

tff(c_14097,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2)
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_200,c_14094]) ).

tff(c_14103,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_397,c_14097]) ).

tff(c_14105,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_14103]) ).

tff(c_14106,plain,
    ( ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_13772]) ).

tff(c_14233,plain,
    ~ ssList(tl(sk2)),
    inference(splitLeft,[status(thm)],[c_14106]) ).

tff(c_14236,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_154,c_14233]) ).

tff(c_14239,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_14236]) ).

tff(c_14241,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_14239]) ).

tff(c_14243,plain,
    ssList(tl(sk2)),
    inference(splitRight,[status(thm)],[c_14106]) ).

tff(c_156,plain,
    ! [U_73] :
      ( ( nil = U_73 )
      | ssItem(hd(U_73))
      | ~ ssList(U_73) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_14242,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2))
    | ~ neq(nil,sk2)
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_14106]) ).

tff(c_14490,plain,
    ~ neq(nil,sk2),
    inference(splitLeft,[status(thm)],[c_14242]) ).

tff(c_14493,plain,
    ( ( sk2 = nil )
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_200,c_14490]) ).

tff(c_14499,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_16,c_14493]) ).

tff(c_14501,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_14499]) ).

tff(c_14502,plain,
    ( ~ ssItem(hd(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_14242]) ).

tff(c_14524,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(splitLeft,[status(thm)],[c_14502]) ).

tff(c_14527,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_14524]) ).

tff(c_14530,plain,
    ~ ssItem(hd(sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14527]) ).

tff(c_14533,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_14530]) ).

tff(c_14536,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_14533]) ).

tff(c_14538,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_14536]) ).

tff(c_14539,plain,
    ( ~ ssItem(hd(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_14502]) ).

tff(c_14709,plain,
    ~ ssItem(hd(sk2)),
    inference(splitLeft,[status(thm)],[c_14539]) ).

tff(c_14712,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_14709]) ).

tff(c_14715,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_14712]) ).

tff(c_14717,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_14715]) ).

tff(c_14719,plain,
    ssItem(hd(sk2)),
    inference(splitRight,[status(thm)],[c_14539]) ).

tff(c_14718,plain,
    app(tl(sk2),cons(hd(sk2),nil)) = sk1,
    inference(splitRight,[status(thm)],[c_14539]) ).

tff(c_358,plain,
    ! [U_288,V_291,W_287,X_289] :
      ( ~ ssList(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
      | ~ duplicatefreeP(app(app(U_288,cons(V_291,W_287)),cons(V_291,X_289)))
      | ~ ssItem(V_291)
      | ~ ssList(U_288)
      | ~ ssList(W_287)
      | ~ ssList(X_289) ),
    inference(cnfTransformation,[status(thm)],[f_1481]) ).

tff(c_14762,plain,
    ! [X_289] :
      ( ~ ssList(app(sk1,cons(hd(sk2),X_289)))
      | ~ duplicatefreeP(app(app(tl(sk2),cons(hd(sk2),nil)),cons(hd(sk2),X_289)))
      | ~ ssItem(hd(sk2))
      | ~ ssList(tl(sk2))
      | ~ ssList(nil)
      | ~ ssList(X_289) ),
    inference(superposition,[status(thm),theory(equality)],[c_14718,c_358]) ).

tff(c_86147,plain,
    ! [X_4758] :
      ( ~ ssList(app(sk1,cons(hd(sk2),X_4758)))
      | ~ duplicatefreeP(app(sk1,cons(hd(sk2),X_4758)))
      | ~ ssList(X_4758) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_14243,c_14719,c_14718,c_14762]) ).

tff(c_86158,plain,
    ( ~ ssList(app(sk1,sk2))
    | ~ duplicatefreeP(app(sk1,cons(hd(sk2),tl(sk2))))
    | ~ ssList(tl(sk2))
    | ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_208,c_86147]) ).

tff(c_86167,plain,
    ( ~ ssList(app(sk1,sk2))
    | ~ duplicatefreeP(app(sk1,sk2))
    | ( sk2 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_26,c_15357,c_15403,c_15357,c_86158]) ).

tff(c_86168,plain,
    ( ~ ssList(app(sk1,sk2))
    | ~ duplicatefreeP(app(sk1,sk2)) ),
    inference(negUnitSimplification,[status(thm)],[c_447,c_86167]) ).

tff(c_86172,plain,
    ~ duplicatefreeP(app(sk1,sk2)),
    inference(splitLeft,[status(thm)],[c_86168]) ).

tff(c_86175,plain,
    ( ~ ssList(sk1)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_1658,c_86172]) ).

tff(c_86179,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_86175]) ).

tff(c_86180,plain,
    ~ ssList(app(sk1,sk2)),
    inference(splitRight,[status(thm)],[c_86168]) ).

tff(c_86185,plain,
    ( ~ ssList(sk1)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_170,c_86180]) ).

tff(c_86189,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_398,c_86185]) ).

tff(c_86190,plain,
    ! [V_67] : ssItem(V_67),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_86488,plain,
    ! [U_82,V_83] :
      ( ssList(cons(U_82,V_83))
      | ~ ssList(V_83) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_172]) ).

tff(c_232,plain,
    ! [U_130] :
      ( singletonP(cons(U_130,nil))
      | ~ ssList(cons(U_130,nil))
      | ~ ssItem(U_130) ),
    inference(cnfTransformation,[status(thm)],[f_624]) ).

tff(c_87430,plain,
    ! [U_4951] :
      ( singletonP(cons(U_4951,nil))
      | ~ ssList(cons(U_4951,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_232]) ).

tff(c_87437,plain,
    ! [U_82] :
      ( singletonP(cons(U_82,nil))
      | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_86488,c_87430]) ).

tff(c_87440,plain,
    ! [U_82] : singletonP(cons(U_82,nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_87437]) ).

tff(c_204,plain,
    ! [V_105,U_104] :
      ( ( V_105 = U_104 )
      | neq(V_105,U_104)
      | ~ ssItem(V_105)
      | ~ ssItem(U_104) ),
    inference(cnfTransformation,[status(thm)],[f_474]) ).

tff(c_87348,plain,
    ! [V_105,U_104] :
      ( ( V_105 = U_104 )
      | neq(V_105,U_104) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_204]) ).

tff(c_88187,plain,
    ! [U_5000] :
      ( ( nil = U_5000 )
      | ( cons(skaf83(U_5000),skaf82(U_5000)) = U_5000 )
      | ~ ssList(U_5000) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

tff(c_87293,plain,
    ! [U_95,V_96] :
      ( ( hd(cons(U_95,V_96)) = U_95 )
      | ~ ssList(V_96) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_194]) ).

tff(c_88199,plain,
    ! [U_5000] :
      ( ( skaf83(U_5000) = hd(U_5000) )
      | ~ ssList(skaf82(U_5000))
      | ( nil = U_5000 )
      | ~ ssList(U_5000) ),
    inference(superposition,[status(thm),theory(equality)],[c_88187,c_87293]) ).

tff(c_97593,plain,
    ! [U_5541] :
      ( ( skaf83(U_5541) = hd(U_5541) )
      | ( nil = U_5541 )
      | ~ ssList(U_5541) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_88199]) ).

tff(c_97692,plain,
    ( ( skaf83(sk2) = hd(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_397,c_97593]) ).

tff(c_97730,plain,
    skaf83(sk2) = hd(sk2),
    inference(negUnitSimplification,[status(thm)],[c_447,c_97692]) ).

tff(c_97734,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_97730,c_218]) ).

tff(c_97738,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_97734]) ).

tff(c_97739,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_447,c_97738]) ).

tff(c_87362,plain,
    ! [U_93,V_94] :
      ( ( tl(cons(U_93,V_94)) = V_94 )
      | ~ ssList(V_94) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_192]) ).

tff(c_97827,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ~ ssList(skaf82(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_97739,c_87362]) ).

tff(c_97893,plain,
    tl(sk2) = skaf82(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_97827]) ).

tff(c_95292,plain,
    ( ~ neq(sk2,nil)
    | ~ neq(nil,sk2)
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 )
    | ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_396]) ).

tff(c_95293,plain,
    ~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
    inference(splitLeft,[status(thm)],[c_95292]) ).

tff(c_95442,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(resolution,[status(thm)],[c_170,c_95293]) ).

tff(c_98502,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_97893,c_95442]) ).

tff(c_98505,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_86488,c_98502]) ).

tff(c_98509,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_98505]) ).

tff(c_98510,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ neq(nil,sk2)
    | ~ neq(sk2,nil)
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_95292]) ).

tff(c_98729,plain,
    ~ neq(sk2,nil),
    inference(splitLeft,[status(thm)],[c_98510]) ).

tff(c_98732,plain,
    sk2 = nil,
    inference(resolution,[status(thm)],[c_87348,c_98729]) ).

tff(c_98736,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_98732]) ).

tff(c_98737,plain,
    ( ~ neq(nil,sk2)
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_98510]) ).

tff(c_98877,plain,
    ~ ssList(tl(sk2)),
    inference(splitLeft,[status(thm)],[c_98737]) ).

tff(c_98880,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_154,c_98877]) ).

tff(c_98883,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_98880]) ).

tff(c_98885,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_98883]) ).

tff(c_98886,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ~ neq(nil,sk2)
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_98737]) ).

tff(c_99195,plain,
    ~ neq(nil,sk2),
    inference(splitLeft,[status(thm)],[c_98886]) ).

tff(c_99198,plain,
    sk2 = nil,
    inference(resolution,[status(thm)],[c_87348,c_99195]) ).

tff(c_99202,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_447,c_99198]) ).

tff(c_99203,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_98886]) ).

tff(c_99441,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(splitLeft,[status(thm)],[c_99203]) ).

tff(c_99444,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_86488,c_99441]) ).

tff(c_99448,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_99444]) ).

tff(c_99450,plain,
    ssList(cons(hd(sk2),nil)),
    inference(splitRight,[status(thm)],[c_99203]) ).

tff(c_148,plain,
    ! [U_69] :
      ( ( app(nil,U_69) = U_69 )
      | ~ ssList(U_69) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_99534,plain,
    app(nil,cons(hd(sk2),nil)) = cons(hd(sk2),nil),
    inference(resolution,[status(thm)],[c_99450,c_148]) ).

tff(c_350,plain,
    ! [U_273,V_274,W_275] :
      ( memberP(app(U_273,cons(V_274,W_275)),V_274)
      | ~ ssList(app(U_273,cons(V_274,W_275)))
      | ~ ssItem(V_274)
      | ~ ssList(U_273)
      | ~ ssList(W_275) ),
    inference(cnfTransformation,[status(thm)],[f_1405]) ).

tff(c_94757,plain,
    ! [U_273,V_274,W_275] :
      ( memberP(app(U_273,cons(V_274,W_275)),V_274)
      | ~ ssList(app(U_273,cons(V_274,W_275)))
      | ~ ssList(U_273)
      | ~ ssList(W_275) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_350]) ).

tff(c_115638,plain,
    ( memberP(cons(hd(sk2),nil),hd(sk2))
    | ~ ssList(app(nil,cons(hd(sk2),nil)))
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_99534,c_94757]) ).

tff(c_115699,plain,
    memberP(cons(hd(sk2),nil),hd(sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_99450,c_99534,c_115638]) ).

tff(c_142,plain,
    ! [U_65] :
      ( ~ ssItem(U_65)
      | ~ memberP(nil,U_65) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_86200,plain,
    ! [U_65] : ~ memberP(nil,U_65),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_142]) ).

tff(c_202,plain,
    ! [U_103] :
      ( ( cons(skaf44(U_103),nil) = U_103 )
      | ~ ssList(U_103)
      | ~ singletonP(U_103) ),
    inference(cnfTransformation,[status(thm)],[f_464]) ).

tff(c_322,plain,
    ! [W_242,U_240,V_241] :
      ( ( W_242 = U_240 )
      | memberP(V_241,W_242)
      | ~ ssItem(W_242)
      | ~ ssItem(U_240)
      | ~ ssList(V_241)
      | ~ memberP(cons(U_240,V_241),W_242) ),
    inference(cnfTransformation,[status(thm)],[f_1239]) ).

tff(c_92271,plain,
    ! [W_5232,U_5233,V_5234] :
      ( ( W_5232 = U_5233 )
      | memberP(V_5234,W_5232)
      | ~ ssList(V_5234)
      | ~ memberP(cons(U_5233,V_5234),W_5232) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_322]) ).

tff(c_92283,plain,
    ! [U_103,W_5232] :
      ( ( skaf44(U_103) = W_5232 )
      | memberP(nil,W_5232)
      | ~ ssList(nil)
      | ~ memberP(U_103,W_5232)
      | ~ ssList(U_103)
      | ~ singletonP(U_103) ),
    inference(superposition,[status(thm),theory(equality)],[c_202,c_92271]) ).

tff(c_92291,plain,
    ! [U_103,W_5232] :
      ( ( skaf44(U_103) = W_5232 )
      | memberP(nil,W_5232)
      | ~ memberP(U_103,W_5232)
      | ~ ssList(U_103)
      | ~ singletonP(U_103) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_92283]) ).

tff(c_92292,plain,
    ! [U_103,W_5232] :
      ( ( skaf44(U_103) = W_5232 )
      | ~ memberP(U_103,W_5232)
      | ~ ssList(U_103)
      | ~ singletonP(U_103) ),
    inference(negUnitSimplification,[status(thm)],[c_86200,c_92291]) ).

tff(c_115745,plain,
    ( ( skaf44(cons(hd(sk2),nil)) = hd(sk2) )
    | ~ ssList(cons(hd(sk2),nil))
    | ~ singletonP(cons(hd(sk2),nil)) ),
    inference(resolution,[status(thm)],[c_115699,c_92292]) ).

tff(c_115754,plain,
    skaf44(cons(hd(sk2),nil)) = hd(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_87440,c_99450,c_115745]) ).

tff(c_88193,plain,
    ! [U_5000] :
      ( ( tl(U_5000) = skaf82(U_5000) )
      | ~ ssList(skaf82(U_5000))
      | ( nil = U_5000 )
      | ~ ssList(U_5000) ),
    inference(superposition,[status(thm),theory(equality)],[c_88187,c_87362]) ).

tff(c_101724,plain,
    ! [U_5742] :
      ( ( tl(U_5742) = skaf82(U_5742) )
      | ( nil = U_5742 )
      | ~ ssList(U_5742) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_88193]) ).

tff(c_101829,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_397,c_101724]) ).

tff(c_101873,plain,
    tl(sk2) = skaf82(sk2),
    inference(negUnitSimplification,[status(thm)],[c_447,c_101829]) ).

tff(c_98887,plain,
    ssList(tl(sk2)),
    inference(splitRight,[status(thm)],[c_98737]) ).

tff(c_99449,plain,
    app(tl(sk2),cons(hd(sk2),nil)) = sk1,
    inference(splitRight,[status(thm)],[c_99203]) ).

tff(c_316,plain,
    ! [U_233,W_235,V_234] :
      ( memberP(U_233,W_235)
      | memberP(V_234,W_235)
      | ~ ssItem(W_235)
      | ~ ssList(U_233)
      | ~ ssList(V_234)
      | ~ memberP(app(U_233,V_234),W_235) ),
    inference(cnfTransformation,[status(thm)],[f_1191]) ).

tff(c_93224,plain,
    ! [U_233,W_235,V_234] :
      ( memberP(U_233,W_235)
      | memberP(V_234,W_235)
      | ~ ssList(U_233)
      | ~ ssList(V_234)
      | ~ memberP(app(U_233,V_234),W_235) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_316]) ).

tff(c_99733,plain,
    ! [W_235] :
      ( memberP(tl(sk2),W_235)
      | memberP(cons(hd(sk2),nil),W_235)
      | ~ ssList(tl(sk2))
      | ~ ssList(cons(hd(sk2),nil))
      | ~ memberP(sk1,W_235) ),
    inference(superposition,[status(thm),theory(equality)],[c_99449,c_93224]) ).

tff(c_99791,plain,
    ! [W_235] :
      ( memberP(tl(sk2),W_235)
      | memberP(cons(hd(sk2),nil),W_235)
      | ~ memberP(sk1,W_235) ),
    inference(demodulation,[status(thm),theory(equality)],[c_99450,c_98887,c_99733]) ).

tff(c_148650,plain,
    ! [W_8440] :
      ( memberP(skaf82(sk2),W_8440)
      | memberP(cons(hd(sk2),nil),W_8440)
      | ~ memberP(sk1,W_8440) ),
    inference(demodulation,[status(thm),theory(equality)],[c_101873,c_99791]) ).

tff(c_148657,plain,
    ! [W_8440] :
      ( ( skaf44(cons(hd(sk2),nil)) = W_8440 )
      | ~ ssList(cons(hd(sk2),nil))
      | ~ singletonP(cons(hd(sk2),nil))
      | memberP(skaf82(sk2),W_8440)
      | ~ memberP(sk1,W_8440) ),
    inference(resolution,[status(thm)],[c_148650,c_92292]) ).

tff(c_324150,plain,
    ! [W_11708] :
      ( ( hd(sk2) = W_11708 )
      | memberP(skaf82(sk2),W_11708)
      | ~ memberP(sk1,W_11708) ),
    inference(demodulation,[status(thm),theory(equality)],[c_87440,c_99450,c_115754,c_148657]) ).

tff(c_278,plain,
    ! [W_181,U_179,V_180] :
      ( memberP(cons(W_181,U_179),V_180)
      | ~ ssItem(V_180)
      | ~ ssItem(W_181)
      | ~ ssList(U_179)
      | ~ memberP(U_179,V_180) ),
    inference(cnfTransformation,[status(thm)],[f_912]) ).

tff(c_90044,plain,
    ! [W_5111,U_5112,V_5113] :
      ( memberP(cons(W_5111,U_5112),V_5113)
      | ~ ssList(U_5112)
      | ~ memberP(U_5112,V_5113) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_86190,c_278]) ).

tff(c_90047,plain,
    ! [U_117,V_5113] :
      ( memberP(U_117,V_5113)
      | ~ ssList(skaf82(U_117))
      | ~ memberP(skaf82(U_117),V_5113)
      | ( nil = U_117 )
      | ~ ssList(U_117) ),
    inference(superposition,[status(thm),theory(equality)],[c_218,c_90044]) ).

tff(c_90055,plain,
    ! [U_117,V_5113] :
      ( memberP(U_117,V_5113)
      | ~ memberP(skaf82(U_117),V_5113)
      | ( nil = U_117 )
      | ~ ssList(U_117) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_90047]) ).

tff(c_324157,plain,
    ! [W_11708] :
      ( memberP(sk2,W_11708)
      | ( sk2 = nil )
      | ~ ssList(sk2)
      | ( hd(sk2) = W_11708 )
      | ~ memberP(sk1,W_11708) ),
    inference(resolution,[status(thm)],[c_324150,c_90055]) ).

tff(c_324175,plain,
    ! [W_11708] :
      ( memberP(sk2,W_11708)
      | ( sk2 = nil )
      | ( hd(sk2) = W_11708 )
      | ~ memberP(sk1,W_11708) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_324157]) ).

tff(c_324316,plain,
    ! [W_11711] :
      ( memberP(sk2,W_11711)
      | ( hd(sk2) = W_11711 )
      | ~ memberP(sk1,W_11711) ),
    inference(negUnitSimplification,[status(thm)],[c_447,c_324175]) ).

tff(c_324329,plain,
    ( ( hd(sk2) = sk5 )
    | ~ memberP(sk1,sk5) ),
    inference(resolution,[status(thm)],[c_324316,c_388]) ).

tff(c_324342,plain,
    hd(sk2) = sk5,
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_324329]) ).

tff(c_101908,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_101873,c_208]) ).

tff(c_101918,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_101908]) ).

tff(c_101919,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_447,c_101918]) ).

tff(c_276,plain,
    ! [V_177,W_178] :
      ( memberP(cons(V_177,W_178),V_177)
      | ~ ssItem(V_177)
      | ~ ssList(W_178) ),
    inference(cnfTransformation,[status(thm)],[f_898]) ).

tff(c_87084,plain,
    ! [V_177,W_178] :
      ( memberP(cons(V_177,W_178),V_177)
      | ~ ssList(W_178) ),
    inference(demodulation,[status(thm),theory(equality)],[c_86190,c_276]) ).

tff(c_102205,plain,
    ( memberP(sk2,hd(sk2))
    | ~ ssList(skaf82(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_101919,c_87084]) ).

tff(c_102271,plain,
    memberP(sk2,hd(sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_102205]) ).

tff(c_324403,plain,
    memberP(sk2,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_324342,c_102271]) ).

tff(c_324409,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_388,c_324403]) ).

tff(c_324410,plain,
    sk1 = nil,
    inference(splitRight,[status(thm)],[c_395]) ).

tff(c_324412,plain,
    memberP(nil,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_324410,c_386]) ).

tff(c_324411,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_395]) ).

tff(c_324420,plain,
    ~ memberP(nil,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_324411,c_388]) ).

tff(c_324437,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_324412,c_324420]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC395-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 22:13:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 213.64/190.73  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 213.64/190.76  
% 213.64/190.76  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 214.04/190.81  
% 214.04/190.81  Inference rules
% 214.04/190.81  ----------------------
% 214.04/190.81  #Ref     : 44
% 214.04/190.81  #Sup     : 76533
% 214.04/190.81  #Fact    : 0
% 214.04/190.81  #Define  : 0
% 214.04/190.81  #Split   : 88
% 214.04/190.81  #Chain   : 0
% 214.04/190.81  #Close   : 0
% 214.04/190.81  
% 214.04/190.81  Ordering : KBO
% 214.04/190.81  
% 214.04/190.81  Simplification rules
% 214.04/190.81  ----------------------
% 214.04/190.81  #Subsume      : 15724
% 214.04/190.81  #Demod        : 63631
% 214.04/190.81  #Tautology    : 10488
% 214.04/190.81  #SimpNegUnit  : 6412
% 214.04/190.81  #BackRed      : 399
% 214.04/190.81  
% 214.04/190.81  #Partial instantiations: 0
% 214.04/190.81  #Strategies tried      : 1
% 214.04/190.81  
% 214.04/190.81  Timing (in seconds)
% 214.04/190.81  ----------------------
% 214.04/190.82  Preprocessing        : 0.90
% 214.04/190.82  Parsing              : 0.46
% 214.04/190.82  CNF conversion       : 0.07
% 214.04/190.82  Main loop            : 188.74
% 214.04/190.82  Inferencing          : 20.45
% 214.04/190.82  Reduction            : 83.99
% 214.04/190.82  Demodulation         : 62.92
% 214.04/190.82  BG Simplification    : 0.55
% 214.04/190.82  Subsumption          : 66.56
% 214.04/190.82  Abstraction          : 1.40
% 214.04/190.82  MUC search           : 0.00
% 214.04/190.82  Cooper               : 0.00
% 214.04/190.82  Total                : 189.73
% 214.04/190.82  Index Insertion      : 0.00
% 214.04/190.82  Index Deletion       : 0.00
% 214.04/190.82  Index Matching       : 0.00
% 214.04/190.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------