TSTP Solution File: SWC377-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC377-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n010.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 11:02:22 EDT 2023

% Result   : Unsatisfiable 171.72s 151.39s
% Output   : CNFRefutation 172.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :  106
% Syntax   : Number of formulae    :  276 (  72 unt;  75 typ;   0 def)
%            Number of atoms       :  490 (  81 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  583 ( 294   ~; 289   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 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    :   56 (  56 usr;  10 con; 0-2 aty)
%            Number of variables   :  181 (; 181   !;   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 > sk7 > sk6 > sk5 > sk4 > sk3 > sk2 > sk1 > nil

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(sk6,type,
    sk6: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(sk7,type,
    sk7: $i ).

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

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

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

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

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

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

tff(f_1659,axiom,
    ( ~ memberP(sk2,sk5)
    | ~ memberP(sk1,sk5) ),
    file(unknown,unknown) ).

tff(f_1654,axiom,
    ( memberP(sk2,sk5)
    | 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_1663,axiom,
    ( ( nil = sk3 )
    | ( nil != sk4 ) ),
    file(unknown,unknown) ).

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

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

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

tff(f_1671,axiom,
    ( ssList(sk7)
    | ~ neq(sk4,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_1667,axiom,
    ( ssItem(sk6)
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_666,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ( app(cons(U,nil),V) = cons(U,V) ) ),
    file(unknown,unknown) ).

tff(f_1675,axiom,
    ( ( app(cons(sk6,nil),sk7) = sk3 )
    | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_1679,axiom,
    ( ( app(sk7,cons(sk6,nil)) = sk4 )
    | ~ neq(sk4,nil) ),
    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_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_342,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    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_926,axiom,
    ! [U,V,W] :
      ( ~ memberP(U,V)
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(app(U,W),V) ),
    file(unknown,unknown) ).

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

tff(f_245,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    file(unknown,unknown) ).

tff(f_140,axiom,
    ! [U,V] : ssList(skaf45(U,V)),
    file(unknown,unknown) ).

tff(f_820,axiom,
    ! [U,V] :
      ( ~ frontsegP(U,V)
      | ~ ssList(V)
      | ~ ssList(U)
      | ( app(V,skaf45(U,V)) = U ) ),
    file(unknown,unknown) ).

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

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

tff(f_1175,axiom,
    ! [U,V,W] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ~ ssList(W)
      | ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
    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(sk1,sk5)
    | ~ memberP(sk2,sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1659]) ).

tff(c_1747,plain,
    ~ memberP(sk2,sk5),
    inference(splitLeft,[status(thm)],[c_388]) ).

tff(c_386,plain,
    ( memberP(sk1,sk5)
    | memberP(sk2,sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1654]) ).

tff(c_58973,plain,
    memberP(sk1,sk5),
    inference(negUnitSimplification,[status(thm)],[c_1747,c_386]) ).

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_1663]) ).

tff(c_399,plain,
    ( ( sk4 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).

tff(c_401,plain,
    ( ( sk2 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_399]) ).

tff(c_457,plain,
    sk2 != nil,
    inference(splitLeft,[status(thm)],[c_401]) ).

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

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

tff(c_406,plain,
    ssList(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).

tff(c_1566,plain,
    ! [V_471,U_472] :
      ( ( V_471 = U_472 )
      | neq(V_471,U_472)
      | ~ ssList(V_471)
      | ~ ssList(U_472) ),
    inference(cnfTransformation,[status(thm)],[f_456]) ).

tff(c_394,plain,
    ( ~ neq(sk4,nil)
    | ssList(sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1671]) ).

tff(c_404,plain,
    ( ~ neq(sk2,nil)
    | ssList(sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).

tff(c_461,plain,
    ~ neq(sk2,nil),
    inference(splitLeft,[status(thm)],[c_404]) ).

tff(c_1577,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2)
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_1566,c_461]) ).

tff(c_1584,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_1577]) ).

tff(c_1586,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_457,c_1584]) ).

tff(c_1587,plain,
    ssList(sk7),
    inference(splitRight,[status(thm)],[c_404]) ).

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

tff(c_407,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_2270,plain,
    ! [V_542,U_543] :
      ( ssList(app(V_542,U_543))
      | ~ ssList(V_542)
      | ~ ssList(U_543) ),
    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_1880,plain,
    ! [U_66] :
      ( duplicatefreeP(U_66)
      | ~ ssList(U_66) ),
    inference(splitLeft,[status(thm)],[c_144]) ).

tff(c_2325,plain,
    ! [V_542,U_543] :
      ( duplicatefreeP(app(V_542,U_543))
      | ~ ssList(V_542)
      | ~ ssList(U_543) ),
    inference(resolution,[status(thm)],[c_2270,c_1880]) ).

tff(c_1588,plain,
    neq(sk2,nil),
    inference(splitRight,[status(thm)],[c_404]) ).

tff(c_392,plain,
    ( ~ neq(sk4,nil)
    | ssItem(sk6) ),
    inference(cnfTransformation,[status(thm)],[f_1667]) ).

tff(c_402,plain,
    ( ~ neq(sk2,nil)
    | ssItem(sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_392]) ).

tff(c_1596,plain,
    ssItem(sk6),
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_402]) ).

tff(c_4959,plain,
    ! [U_731,V_732] :
      ( ( app(cons(U_731,nil),V_732) = cons(U_731,V_732) )
      | ~ ssList(V_732)
      | ~ ssItem(U_731) ),
    inference(cnfTransformation,[status(thm)],[f_666]) ).

tff(c_396,plain,
    ( ~ neq(sk4,nil)
    | ( app(cons(sk6,nil),sk7) = sk3 ) ),
    inference(cnfTransformation,[status(thm)],[f_1675]) ).

tff(c_400,plain,
    ( ~ neq(sk4,nil)
    | ( app(cons(sk6,nil),sk7) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_396]) ).

tff(c_405,plain,
    ( ~ neq(sk2,nil)
    | ( app(cons(sk6,nil),sk7) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_400]) ).

tff(c_3288,plain,
    app(cons(sk6,nil),sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_405]) ).

tff(c_4968,plain,
    ( ( cons(sk6,sk7) = sk1 )
    | ~ ssList(sk7)
    | ~ ssItem(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_4959,c_3288]) ).

tff(c_4983,plain,
    cons(sk6,sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1596,c_1587,c_4968]) ).

tff(c_398,plain,
    ( ~ neq(sk4,nil)
    | ( app(sk7,cons(sk6,nil)) = sk4 ) ),
    inference(cnfTransformation,[status(thm)],[f_1679]) ).

tff(c_403,plain,
    ( ~ neq(sk2,nil)
    | ( app(sk7,cons(sk6,nil)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_398]) ).

tff(c_3194,plain,
    app(sk7,cons(sk6,nil)) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_403]) ).

tff(c_11289,plain,
    ! [U_1010,V_1011,W_1012,X_1013] :
      ( ~ ssList(app(app(U_1010,cons(V_1011,W_1012)),cons(V_1011,X_1013)))
      | ~ duplicatefreeP(app(app(U_1010,cons(V_1011,W_1012)),cons(V_1011,X_1013)))
      | ~ ssItem(V_1011)
      | ~ ssList(U_1010)
      | ~ ssList(W_1012)
      | ~ ssList(X_1013) ),
    inference(cnfTransformation,[status(thm)],[f_1481]) ).

tff(c_11357,plain,
    ! [X_1013] :
      ( ~ ssList(app(sk2,cons(sk6,X_1013)))
      | ~ duplicatefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,X_1013)))
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ~ ssList(nil)
      | ~ ssList(X_1013) ),
    inference(superposition,[status(thm),theory(equality)],[c_3194,c_11289]) ).

tff(c_58889,plain,
    ! [X_3136] :
      ( ~ ssList(app(sk2,cons(sk6,X_3136)))
      | ~ duplicatefreeP(app(sk2,cons(sk6,X_3136)))
      | ~ ssList(X_3136) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_1587,c_1596,c_3194,c_11357]) ).

tff(c_58896,plain,
    ( ~ ssList(app(sk2,sk1))
    | ~ duplicatefreeP(app(sk2,cons(sk6,sk7)))
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_4983,c_58889]) ).

tff(c_58903,plain,
    ( ~ ssList(app(sk2,sk1))
    | ~ duplicatefreeP(app(sk2,sk1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_4983,c_58896]) ).

tff(c_58907,plain,
    ~ duplicatefreeP(app(sk2,sk1)),
    inference(splitLeft,[status(thm)],[c_58903]) ).

tff(c_58910,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk1) ),
    inference(resolution,[status(thm)],[c_2325,c_58907]) ).

tff(c_58914,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_406,c_58910]) ).

tff(c_58915,plain,
    ~ ssList(app(sk2,sk1)),
    inference(splitRight,[status(thm)],[c_58903]) ).

tff(c_58920,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk1) ),
    inference(resolution,[status(thm)],[c_170,c_58915]) ).

tff(c_58924,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_406,c_58920]) ).

tff(c_58925,plain,
    ! [V_67] : ssItem(V_67),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_240,plain,
    ! [U_138,V_139] :
      ( ( app(cons(U_138,nil),V_139) = cons(U_138,V_139) )
      | ~ ssList(V_139)
      | ~ ssItem(U_138) ),
    inference(cnfTransformation,[status(thm)],[f_666]) ).

tff(c_61196,plain,
    ! [U_3398,V_3399] :
      ( ( app(cons(U_3398,nil),V_3399) = cons(U_3398,V_3399) )
      | ~ ssList(V_3399) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58925,c_240]) ).

tff(c_60612,plain,
    app(cons(sk6,nil),sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_405]) ).

tff(c_61202,plain,
    ( ( cons(sk6,sk7) = sk1 )
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_61196,c_60612]) ).

tff(c_61217,plain,
    cons(sk6,sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_61202]) ).

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_66178,plain,
    ! [W_3623,U_3624,V_3625] :
      ( ( W_3623 = U_3624 )
      | memberP(V_3625,W_3623)
      | ~ ssList(V_3625)
      | ~ memberP(cons(U_3624,V_3625),W_3623) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58925,c_58925,c_322]) ).

tff(c_66187,plain,
    ! [W_3623] :
      ( ( sk6 = W_3623 )
      | memberP(sk7,W_3623)
      | ~ ssList(sk7)
      | ~ memberP(sk1,W_3623) ),
    inference(superposition,[status(thm),theory(equality)],[c_61217,c_66178]) ).

tff(c_66202,plain,
    ! [W_3623] :
      ( ( sk6 = W_3623 )
      | memberP(sk7,W_3623)
      | ~ memberP(sk1,W_3623) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_66187]) ).

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_59686,plain,
    ! [U_82,V_83] :
      ( ssList(cons(U_82,V_83))
      | ~ ssList(V_83) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58925,c_172]) ).

tff(c_60076,plain,
    app(sk7,cons(sk6,nil)) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_403]) ).

tff(c_62303,plain,
    ! [U_3461,V_3462] :
      ( frontsegP(app(U_3461,V_3462),U_3461)
      | ~ ssList(app(U_3461,V_3462))
      | ~ ssList(U_3461)
      | ~ ssList(V_3462) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_62329,plain,
    ( frontsegP(sk2,sk7)
    | ~ ssList(app(sk7,cons(sk6,nil)))
    | ~ ssList(sk7)
    | ~ ssList(cons(sk6,nil)) ),
    inference(superposition,[status(thm),theory(equality)],[c_60076,c_62303]) ).

tff(c_62482,plain,
    ( frontsegP(sk2,sk7)
    | ~ ssList(cons(sk6,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_406,c_60076,c_62329]) ).

tff(c_67484,plain,
    ~ ssList(cons(sk6,nil)),
    inference(splitLeft,[status(thm)],[c_62482]) ).

tff(c_67487,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_59686,c_67484]) ).

tff(c_67491,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_67487]) ).

tff(c_67493,plain,
    ssList(cons(sk6,nil)),
    inference(splitRight,[status(thm)],[c_62482]) ).

tff(c_280,plain,
    ! [U_182,W_184,V_183] :
      ( memberP(app(U_182,W_184),V_183)
      | ~ ssItem(V_183)
      | ~ ssList(U_182)
      | ~ ssList(W_184)
      | ~ memberP(U_182,V_183) ),
    inference(cnfTransformation,[status(thm)],[f_926]) ).

tff(c_62902,plain,
    ! [U_3466,W_3467,V_3468] :
      ( memberP(app(U_3466,W_3467),V_3468)
      | ~ ssList(U_3466)
      | ~ ssList(W_3467)
      | ~ memberP(U_3466,V_3468) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58925,c_280]) ).

tff(c_62926,plain,
    ! [V_3468] :
      ( memberP(sk2,V_3468)
      | ~ ssList(sk7)
      | ~ ssList(cons(sk6,nil))
      | ~ memberP(sk7,V_3468) ),
    inference(superposition,[status(thm),theory(equality)],[c_60076,c_62902]) ).

tff(c_63078,plain,
    ! [V_3468] :
      ( memberP(sk2,V_3468)
      | ~ ssList(cons(sk6,nil))
      | ~ memberP(sk7,V_3468) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_62926]) ).

tff(c_85875,plain,
    ! [V_4523] :
      ( memberP(sk2,V_4523)
      | ~ memberP(sk7,V_4523) ),
    inference(demodulation,[status(thm),theory(equality)],[c_67493,c_63078]) ).

tff(c_85996,plain,
    ! [W_4528] :
      ( memberP(sk2,W_4528)
      | ( sk6 = W_4528 )
      | ~ memberP(sk1,W_4528) ),
    inference(resolution,[status(thm)],[c_66202,c_85875]) ).

tff(c_85999,plain,
    ( ( sk6 = sk5 )
    | ~ memberP(sk1,sk5) ),
    inference(resolution,[status(thm)],[c_85996,c_1747]) ).

tff(c_86002,plain,
    sk6 = sk5,
    inference(demodulation,[status(thm),theory(equality)],[c_58973,c_85999]) ).

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_68099,plain,
    ! [U_3706,V_3707,W_3708] :
      ( memberP(app(U_3706,cons(V_3707,W_3708)),V_3707)
      | ~ ssList(app(U_3706,cons(V_3707,W_3708)))
      | ~ ssList(U_3706)
      | ~ ssList(W_3708) ),
    inference(demodulation,[status(thm),theory(equality)],[c_58925,c_350]) ).

tff(c_68157,plain,
    ( memberP(sk2,sk6)
    | ~ ssList(app(sk7,cons(sk6,nil)))
    | ~ ssList(sk7)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_60076,c_68099]) ).

tff(c_68185,plain,
    memberP(sk2,sk6),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_1587,c_406,c_60076,c_68157]) ).

tff(c_86458,plain,
    memberP(sk2,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_86002,c_68185]) ).

tff(c_86469,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1747,c_86458]) ).

tff(c_86470,plain,
    ~ memberP(sk1,sk5),
    inference(splitRight,[status(thm)],[c_388]) ).

tff(c_86474,plain,
    ! [U_4534] :
      ( ( app(U_4534,nil) = U_4534 )
      | ~ ssList(U_4534) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_86598,plain,
    app(sk2,nil) = sk2,
    inference(resolution,[status(thm)],[c_406,c_86474]) ).

tff(c_147164,plain,
    ! [U_7463,V_7464] :
      ( frontsegP(app(U_7463,V_7464),U_7463)
      | ~ ssList(app(U_7463,V_7464))
      | ~ ssList(U_7463)
      | ~ ssList(V_7464) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_147313,plain,
    ( frontsegP(sk2,sk2)
    | ~ ssList(app(sk2,nil))
    | ~ ssList(sk2)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_86598,c_147164]) ).

tff(c_147422,plain,
    frontsegP(sk2,sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_406,c_406,c_86598,c_147313]) ).

tff(c_86471,plain,
    memberP(sk2,sk5),
    inference(splitRight,[status(thm)],[c_388]) ).

tff(c_102,plain,
    ! [U_43,V_44] : ssList(skaf45(U_43,V_44)),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_264,plain,
    ! [V_163,U_162] :
      ( ( app(V_163,skaf45(U_162,V_163)) = U_162 )
      | ~ ssList(U_162)
      | ~ ssList(V_163)
      | ~ frontsegP(U_162,V_163) ),
    inference(cnfTransformation,[status(thm)],[f_820]) ).

tff(c_86871,plain,
    ! [V_4580,U_4581] :
      ( ssList(app(V_4580,U_4581))
      | ~ ssList(V_4580)
      | ~ ssList(U_4581) ),
    inference(cnfTransformation,[status(thm)],[f_334]) ).

tff(c_86612,plain,
    ! [U_66] :
      ( duplicatefreeP(U_66)
      | ~ ssList(U_66) ),
    inference(splitLeft,[status(thm)],[c_144]) ).

tff(c_86914,plain,
    ! [V_4580,U_4581] :
      ( duplicatefreeP(app(V_4580,U_4581))
      | ~ ssList(V_4580)
      | ~ ssList(U_4581) ),
    inference(resolution,[status(thm)],[c_86871,c_86612]) ).

tff(c_88977,plain,
    ! [U_4735,V_4736] :
      ( ( app(cons(U_4735,nil),V_4736) = cons(U_4735,V_4736) )
      | ~ ssList(V_4736)
      | ~ ssItem(U_4735) ),
    inference(cnfTransformation,[status(thm)],[f_666]) ).

tff(c_88251,plain,
    app(cons(sk6,nil),sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_405]) ).

tff(c_88983,plain,
    ( ( cons(sk6,sk7) = sk1 )
    | ~ ssList(sk7)
    | ~ ssItem(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_88977,c_88251]) ).

tff(c_88998,plain,
    cons(sk6,sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1596,c_1587,c_88983]) ).

tff(c_87934,plain,
    app(sk7,cons(sk6,nil)) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_403]) ).

tff(c_96022,plain,
    ! [U_5057,V_5058,W_5059,X_5060] :
      ( ~ ssList(app(app(U_5057,cons(V_5058,W_5059)),cons(V_5058,X_5060)))
      | ~ duplicatefreeP(app(app(U_5057,cons(V_5058,W_5059)),cons(V_5058,X_5060)))
      | ~ ssItem(V_5058)
      | ~ ssList(U_5057)
      | ~ ssList(W_5059)
      | ~ ssList(X_5060) ),
    inference(cnfTransformation,[status(thm)],[f_1481]) ).

tff(c_96090,plain,
    ! [X_5060] :
      ( ~ ssList(app(sk2,cons(sk6,X_5060)))
      | ~ duplicatefreeP(app(app(sk7,cons(sk6,nil)),cons(sk6,X_5060)))
      | ~ ssItem(sk6)
      | ~ ssList(sk7)
      | ~ ssList(nil)
      | ~ ssList(X_5060) ),
    inference(superposition,[status(thm),theory(equality)],[c_87934,c_96022]) ).

tff(c_143775,plain,
    ! [X_7152] :
      ( ~ ssList(app(sk2,cons(sk6,X_7152)))
      | ~ duplicatefreeP(app(sk2,cons(sk6,X_7152)))
      | ~ ssList(X_7152) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_1587,c_1596,c_87934,c_96090]) ).

tff(c_143782,plain,
    ( ~ ssList(app(sk2,sk1))
    | ~ duplicatefreeP(app(sk2,cons(sk6,sk7)))
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_88998,c_143775]) ).

tff(c_143789,plain,
    ( ~ ssList(app(sk2,sk1))
    | ~ duplicatefreeP(app(sk2,sk1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_88998,c_143782]) ).

tff(c_143793,plain,
    ~ duplicatefreeP(app(sk2,sk1)),
    inference(splitLeft,[status(thm)],[c_143789]) ).

tff(c_143796,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk1) ),
    inference(resolution,[status(thm)],[c_86914,c_143793]) ).

tff(c_143800,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_406,c_143796]) ).

tff(c_143801,plain,
    ~ ssList(app(sk2,sk1)),
    inference(splitRight,[status(thm)],[c_143789]) ).

tff(c_143806,plain,
    ( ~ ssList(sk2)
    | ~ ssList(sk1) ),
    inference(resolution,[status(thm)],[c_170,c_143801]) ).

tff(c_143810,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_406,c_143806]) ).

tff(c_143811,plain,
    ! [V_67] : ssItem(V_67),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_148012,plain,
    ! [U_7492,W_7493,V_7494] :
      ( memberP(app(U_7492,W_7493),V_7494)
      | ~ ssList(U_7492)
      | ~ ssList(W_7493)
      | ~ memberP(U_7492,V_7494) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_280]) ).

tff(c_148018,plain,
    ! [U_162,V_7494,V_163] :
      ( memberP(U_162,V_7494)
      | ~ ssList(V_163)
      | ~ ssList(skaf45(U_162,V_163))
      | ~ memberP(V_163,V_7494)
      | ~ ssList(U_162)
      | ~ ssList(V_163)
      | ~ frontsegP(U_162,V_163) ),
    inference(superposition,[status(thm),theory(equality)],[c_264,c_148012]) ).

tff(c_208591,plain,
    ! [U_10704,V_10705,V_10706] :
      ( memberP(U_10704,V_10705)
      | ~ memberP(V_10706,V_10705)
      | ~ ssList(U_10704)
      | ~ ssList(V_10706)
      | ~ frontsegP(U_10704,V_10706) ),
    inference(demodulation,[status(thm),theory(equality)],[c_102,c_148018]) ).

tff(c_208683,plain,
    ! [U_10704] :
      ( memberP(U_10704,sk5)
      | ~ ssList(U_10704)
      | ~ ssList(sk2)
      | ~ frontsegP(U_10704,sk2) ),
    inference(resolution,[status(thm)],[c_86471,c_208591]) ).

tff(c_208805,plain,
    ! [U_10704] :
      ( memberP(U_10704,sk5)
      | ~ ssList(U_10704)
      | ~ frontsegP(U_10704,sk2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_208683]) ).

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

tff(c_143829,plain,
    ! [U_65] : ~ memberP(nil,U_65),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_142]) ).

tff(c_1605,plain,
    ! [U_487] :
      ( ( app(nil,U_487) = U_487 )
      | ~ ssList(U_487) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_1727,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[c_16,c_1605]) ).

tff(c_314,plain,
    ! [U_230,V_231,W_232] :
      ( ( cons(U_230,app(V_231,W_232)) = app(cons(U_230,V_231),W_232) )
      | ~ ssList(W_232)
      | ~ ssList(V_231)
      | ~ ssItem(U_230) ),
    inference(cnfTransformation,[status(thm)],[f_1175]) ).

tff(c_150628,plain,
    ! [U_7616,V_7617,W_7618] :
      ( ( cons(U_7616,app(V_7617,W_7618)) = app(cons(U_7616,V_7617),W_7618) )
      | ~ ssList(W_7618)
      | ~ ssList(V_7617) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_314]) ).

tff(c_150832,plain,
    ! [U_7616] :
      ( ( app(cons(U_7616,nil),nil) = cons(U_7616,nil) )
      | ~ ssList(nil)
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_1727,c_150628]) ).

tff(c_150942,plain,
    ! [U_7616] : ( app(cons(U_7616,nil),nil) = cons(U_7616,nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_150832]) ).

tff(c_144511,plain,
    ! [U_82,V_83] :
      ( ssList(cons(U_82,V_83))
      | ~ ssList(V_83) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_172]) ).

tff(c_222139,plain,
    ! [U_11243,V_11244,W_11245] :
      ( ssList(app(cons(U_11243,V_11244),W_11245))
      | ~ ssList(app(V_11244,W_11245))
      | ~ ssList(W_11245)
      | ~ ssList(V_11244) ),
    inference(superposition,[status(thm),theory(equality)],[c_150628,c_144511]) ).

tff(c_222628,plain,
    ! [U_7616] :
      ( ssList(cons(U_7616,nil))
      | ~ ssList(app(nil,nil))
      | ~ ssList(nil)
      | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_150942,c_222139]) ).

tff(c_222887,plain,
    ! [U_7616] : ssList(cons(U_7616,nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_1727,c_222628]) ).

tff(c_145357,plain,
    app(sk7,cons(sk6,nil)) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_403]) ).

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_151135,plain,
    ! [U_7647,W_7648,V_7649] :
      ( memberP(U_7647,W_7648)
      | memberP(V_7649,W_7648)
      | ~ ssList(U_7647)
      | ~ ssList(V_7649)
      | ~ memberP(app(U_7647,V_7649),W_7648) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_316]) ).

tff(c_151162,plain,
    ! [W_7648] :
      ( memberP(sk7,W_7648)
      | memberP(cons(sk6,nil),W_7648)
      | ~ ssList(sk7)
      | ~ ssList(cons(sk6,nil))
      | ~ memberP(sk2,W_7648) ),
    inference(superposition,[status(thm),theory(equality)],[c_145357,c_151135]) ).

tff(c_151322,plain,
    ! [W_7648] :
      ( memberP(sk7,W_7648)
      | memberP(cons(sk6,nil),W_7648)
      | ~ ssList(cons(sk6,nil))
      | ~ memberP(sk2,W_7648) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_151162]) ).

tff(c_244881,plain,
    ! [W_11733] :
      ( memberP(sk7,W_11733)
      | memberP(cons(sk6,nil),W_11733)
      | ~ memberP(sk2,W_11733) ),
    inference(demodulation,[status(thm),theory(equality)],[c_222887,c_151322]) ).

tff(c_151097,plain,
    ! [W_242,U_240,V_241] :
      ( ( W_242 = U_240 )
      | memberP(V_241,W_242)
      | ~ ssList(V_241)
      | ~ memberP(cons(U_240,V_241),W_242) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_143811,c_322]) ).

tff(c_244900,plain,
    ! [W_11733] :
      ( ( sk6 = W_11733 )
      | memberP(nil,W_11733)
      | ~ ssList(nil)
      | memberP(sk7,W_11733)
      | ~ memberP(sk2,W_11733) ),
    inference(resolution,[status(thm)],[c_244881,c_151097]) ).

tff(c_244915,plain,
    ! [W_11733] :
      ( ( sk6 = W_11733 )
      | memberP(nil,W_11733)
      | memberP(sk7,W_11733)
      | ~ memberP(sk2,W_11733) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_244900]) ).

tff(c_252441,plain,
    ! [W_12002] :
      ( ( sk6 = W_12002 )
      | memberP(sk7,W_12002)
      | ~ memberP(sk2,W_12002) ),
    inference(negUnitSimplification,[status(thm)],[c_143829,c_244915]) ).

tff(c_146546,plain,
    ! [U_7424,V_7425] :
      ( ( app(cons(U_7424,nil),V_7425) = cons(U_7424,V_7425) )
      | ~ ssList(V_7425) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_240]) ).

tff(c_144747,plain,
    app(cons(sk6,nil),sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1588,c_405]) ).

tff(c_146555,plain,
    ( ( cons(sk6,sk7) = sk1 )
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_146546,c_144747]) ).

tff(c_146571,plain,
    cons(sk6,sk7) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_146555]) ).

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_147671,plain,
    ! [W_7478,U_7479,V_7480] :
      ( memberP(cons(W_7478,U_7479),V_7480)
      | ~ ssList(U_7479)
      | ~ memberP(U_7479,V_7480) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_143811,c_278]) ).

tff(c_147674,plain,
    ! [V_7480] :
      ( memberP(sk1,V_7480)
      | ~ ssList(sk7)
      | ~ memberP(sk7,V_7480) ),
    inference(superposition,[status(thm),theory(equality)],[c_146571,c_147671]) ).

tff(c_147685,plain,
    ! [V_7480] :
      ( memberP(sk1,V_7480)
      | ~ memberP(sk7,V_7480) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_147674]) ).

tff(c_291697,plain,
    ! [W_12396] :
      ( memberP(sk1,W_12396)
      | ( sk6 = W_12396 )
      | ~ memberP(sk2,W_12396) ),
    inference(resolution,[status(thm)],[c_252441,c_147685]) ).

tff(c_291709,plain,
    ( memberP(sk1,sk5)
    | ( sk6 = sk5 )
    | ~ ssList(sk2)
    | ~ frontsegP(sk2,sk2) ),
    inference(resolution,[status(thm)],[c_208805,c_291697]) ).

tff(c_291755,plain,
    ( memberP(sk1,sk5)
    | ( sk6 = sk5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_147422,c_406,c_291709]) ).

tff(c_291756,plain,
    sk6 = sk5,
    inference(negUnitSimplification,[status(thm)],[c_86470,c_291755]) ).

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_144678,plain,
    ! [V_177,W_178] :
      ( memberP(cons(V_177,W_178),V_177)
      | ~ ssList(W_178) ),
    inference(demodulation,[status(thm),theory(equality)],[c_143811,c_276]) ).

tff(c_146584,plain,
    ( memberP(sk1,sk6)
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_146571,c_144678]) ).

tff(c_146599,plain,
    memberP(sk1,sk6),
    inference(demodulation,[status(thm),theory(equality)],[c_1587,c_146584]) ).

tff(c_291845,plain,
    memberP(sk1,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_291756,c_146599]) ).

tff(c_291853,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_86470,c_291845]) ).

tff(c_291855,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_401]) ).

tff(c_291854,plain,
    sk1 = nil,
    inference(splitRight,[status(thm)],[c_401]) ).

tff(c_291896,plain,
    ( ~ memberP(nil,sk5)
    | ~ memberP(nil,sk5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_291855,c_291854,c_388]) ).

tff(c_291897,plain,
    ~ memberP(nil,sk5),
    inference(splitLeft,[status(thm)],[c_291896]) ).

tff(c_291898,plain,
    ( memberP(nil,sk5)
    | memberP(nil,sk5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_291855,c_291854,c_386]) ).

tff(c_291899,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_291897,c_291897,c_291898]) ).

tff(c_291900,plain,
    ~ memberP(nil,sk5),
    inference(splitRight,[status(thm)],[c_291896]) ).

tff(c_291901,plain,
    memberP(nil,sk5),
    inference(splitRight,[status(thm)],[c_291896]) ).

tff(c_291902,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_291900,c_291901]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC377-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 21:16:13 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 171.72/151.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 171.91/151.42  
% 171.91/151.42  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 172.19/151.47  
% 172.19/151.47  Inference rules
% 172.19/151.47  ----------------------
% 172.19/151.47  #Ref     : 20
% 172.19/151.47  #Sup     : 67492
% 172.19/151.47  #Fact    : 0
% 172.19/151.47  #Define  : 0
% 172.19/151.47  #Split   : 164
% 172.19/151.47  #Chain   : 0
% 172.19/151.47  #Close   : 0
% 172.19/151.47  
% 172.19/151.47  Ordering : KBO
% 172.19/151.47  
% 172.19/151.47  Simplification rules
% 172.19/151.47  ----------------------
% 172.19/151.47  #Subsume      : 15613
% 172.19/151.47  #Demod        : 57989
% 172.19/151.47  #Tautology    : 13439
% 172.19/151.47  #SimpNegUnit  : 3573
% 172.19/151.47  #BackRed      : 457
% 172.19/151.47  
% 172.19/151.47  #Partial instantiations: 0
% 172.19/151.47  #Strategies tried      : 1
% 172.19/151.47  
% 172.19/151.47  Timing (in seconds)
% 172.19/151.47  ----------------------
% 172.19/151.47  Preprocessing        : 0.85
% 172.19/151.47  Parsing              : 0.45
% 172.19/151.47  CNF conversion       : 0.06
% 172.19/151.47  Main loop            : 149.46
% 172.19/151.47  Inferencing          : 23.09
% 172.19/151.47  Reduction            : 69.18
% 172.19/151.47  Demodulation         : 50.91
% 172.19/151.47  BG Simplification    : 0.43
% 172.19/151.47  Subsumption          : 45.19
% 172.19/151.47  Abstraction          : 1.14
% 172.19/151.47  MUC search           : 0.00
% 172.19/151.47  Cooper               : 0.00
% 172.19/151.47  Total                : 150.40
% 172.19/151.47  Index Insertion      : 0.00
% 172.19/151.47  Index Deletion       : 0.00
% 172.19/151.47  Index Matching       : 0.00
% 172.19/151.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------