TSTP Solution File: SWC218-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC218-1 : 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 : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:01:40 EDT 2023

% Result   : Unsatisfiable 38.58s 22.61s
% Output   : CNFRefutation 38.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   98
% Syntax   : Number of formulae    :  192 (  67 unt;  75 typ;   0 def)
%            Number of atoms       :  234 (  53 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  254 ( 137   ~; 117   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   56 (  56 usr;  10 con; 0-2 aty)
%            Number of variables   :   50 (;  50   !;   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_1654,axiom,
    ssItem(sk7),
    file(unknown,unknown) ).

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

tff(f_446,axiom,
    ! [U,V] :
      ( ( cons(U,V) != V )
      | ~ ssItem(U)
      | ~ ssList(V) ),
    file(unknown,unknown) ).

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

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

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

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

tff(f_975,axiom,
    ! [U,V,W] :
      ( ( app(U,V) != W )
      | ~ ssList(V)
      | ~ ssList(U)
      | ~ ssList(W)
      | frontsegP(W,U) ),
    file(unknown,unknown) ).

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

tff(f_1652,axiom,
    ssList(sk6),
    file(unknown,unknown) ).

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

tff(f_961,axiom,
    ! [U,V,W] :
      ( ( app(U,V) != W )
      | ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(W)
      | rearsegP(W,V) ),
    file(unknown,unknown) ).

tff(f_770,axiom,
    ! [U,V] :
      ( ~ rearsegP(U,V)
      | ~ rearsegP(V,U)
      | ~ ssList(U)
      | ~ ssList(V)
      | ( V = U ) ),
    file(unknown,unknown) ).

tff(f_1651,axiom,
    ssList(sk5),
    file(unknown,unknown) ).

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

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

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

tff(f_1657,axiom,
    ~ neq(sk1,nil),
    file(unknown,unknown) ).

tff(f_1655,axiom,
    app(app(sk5,cons(sk7,nil)),sk6) = sk3,
    file(unknown,unknown) ).

tff(f_1653,axiom,
    app(sk5,sk6) = sk4,
    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_1371,axiom,
    ! [U,V,W,X] :
      ( ( app(app(U,V),W) != X )
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(X)
      | segmentP(X,V) ),
    file(unknown,unknown) ).

tff(f_294,axiom,
    ! [U] :
      ( ~ segmentP(nil,U)
      | ~ ssList(U)
      | ( nil = U ) ),
    file(unknown,unknown) ).

tff(c_390,plain,
    ssItem(sk7),
    inference(cnfTransformation,[status(thm)],[f_1654]) ).

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

tff(c_1118,plain,
    ! [V_449,U_450] :
      ( ~ ssList(V_449)
      | ~ ssItem(U_450)
      | ( cons(U_450,V_449) != V_449 ) ),
    inference(cnfTransformation,[status(thm)],[f_446]) ).

tff(c_3084,plain,
    ! [U_607] :
      ( ~ ssItem(U_607)
      | ( cons(U_607,nil) != nil ) ),
    inference(resolution,[status(thm)],[c_16,c_1118]) ).

tff(c_3160,plain,
    cons(sk7,nil) != nil,
    inference(resolution,[status(thm)],[c_390,c_3084]) ).

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_380,plain,
    sk4 = sk2,
    inference(cnfTransformation,[status(thm)],[f_1649]) ).

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_467,plain,
    ! [U_387] :
      ( ( app(nil,U_387) = U_387 )
      | ~ ssList(U_387) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_591,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[c_16,c_467]) ).

tff(c_29297,plain,
    ! [U_2187,V_2188] :
      ( frontsegP(app(U_2187,V_2188),U_2187)
      | ~ ssList(app(U_2187,V_2188))
      | ~ ssList(U_2187)
      | ~ ssList(V_2188) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_29431,plain,
    ( frontsegP(nil,nil)
    | ~ ssList(app(nil,nil))
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_591,c_29297]) ).

tff(c_29521,plain,
    frontsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_29431]) ).

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_386,plain,
    ssList(sk6),
    inference(cnfTransformation,[status(thm)],[f_1652]) ).

tff(c_755,plain,
    ! [U_397] :
      ( ( app(U_397,nil) = U_397 )
      | ~ ssList(U_397) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_884,plain,
    app(sk6,nil) = sk6,
    inference(resolution,[status(thm)],[c_386,c_755]) ).

tff(c_29043,plain,
    ! [U_2185,V_2186] :
      ( rearsegP(app(U_2185,V_2186),V_2186)
      | ~ ssList(app(U_2185,V_2186))
      | ~ ssList(V_2186)
      | ~ ssList(U_2185) ),
    inference(cnfTransformation,[status(thm)],[f_961]) ).

tff(c_29165,plain,
    ( rearsegP(sk6,nil)
    | ~ ssList(app(sk6,nil))
    | ~ ssList(nil)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_884,c_29043]) ).

tff(c_29259,plain,
    rearsegP(sk6,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_884,c_29165]) ).

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_29287,plain,
    ( ( sk6 = nil )
    | ~ ssList(sk6)
    | ~ ssList(nil)
    | ~ rearsegP(nil,sk6) ),
    inference(resolution,[status(thm)],[c_29259,c_256]) ).

tff(c_29290,plain,
    ( ( sk6 = nil )
    | ~ rearsegP(nil,sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_29287]) ).

tff(c_39131,plain,
    ~ rearsegP(nil,sk6),
    inference(splitLeft,[status(thm)],[c_29290]) ).

tff(c_883,plain,
    app(sk2,nil) = sk2,
    inference(resolution,[status(thm)],[c_397,c_755]) ).

tff(c_29413,plain,
    ( frontsegP(sk2,sk2)
    | ~ ssList(app(sk2,nil))
    | ~ ssList(sk2)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_883,c_29297]) ).

tff(c_29509,plain,
    frontsegP(sk2,sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_397,c_397,c_883,c_29413]) ).

tff(c_384,plain,
    ssList(sk5),
    inference(cnfTransformation,[status(thm)],[f_1651]) ).

tff(c_32543,plain,
    ~ rearsegP(nil,sk6),
    inference(splitLeft,[status(thm)],[c_29290]) ).

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_398,plain,
    ssList(sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).

tff(c_2063,plain,
    ! [V_509,U_510] :
      ( ( V_509 = U_510 )
      | neq(V_509,U_510)
      | ~ ssList(V_509)
      | ~ ssList(U_510) ),
    inference(cnfTransformation,[status(thm)],[f_456]) ).

tff(c_394,plain,
    ~ neq(sk1,nil),
    inference(cnfTransformation,[status(thm)],[f_1657]) ).

tff(c_2074,plain,
    ( ( sk1 = nil )
    | ~ ssList(sk1)
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_2063,c_394]) ).

tff(c_2081,plain,
    sk1 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_398,c_2074]) ).

tff(c_392,plain,
    app(app(sk5,cons(sk7,nil)),sk6) = sk3,
    inference(cnfTransformation,[status(thm)],[f_1655]) ).

tff(c_395,plain,
    app(app(sk5,cons(sk7,nil)),sk6) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).

tff(c_2082,plain,
    app(app(sk5,cons(sk7,nil)),sk6) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_2081,c_395]) ).

tff(c_286,plain,
    ! [U_189,V_190] :
      ( rearsegP(app(U_189,V_190),V_190)
      | ~ ssList(app(U_189,V_190))
      | ~ ssList(V_190)
      | ~ ssList(U_189) ),
    inference(cnfTransformation,[status(thm)],[f_961]) ).

tff(c_38201,plain,
    ( rearsegP(nil,sk6)
    | ~ ssList(app(app(sk5,cons(sk7,nil)),sk6))
    | ~ ssList(sk6)
    | ~ ssList(app(sk5,cons(sk7,nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2082,c_286]) ).

tff(c_38240,plain,
    ( rearsegP(nil,sk6)
    | ~ ssList(app(sk5,cons(sk7,nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_2082,c_38201]) ).

tff(c_38241,plain,
    ~ ssList(app(sk5,cons(sk7,nil))),
    inference(negUnitSimplification,[status(thm)],[c_32543,c_38240]) ).

tff(c_38413,plain,
    ( ~ ssList(sk5)
    | ~ ssList(cons(sk7,nil)) ),
    inference(resolution,[status(thm)],[c_170,c_38241]) ).

tff(c_38416,plain,
    ~ ssList(cons(sk7,nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_38413]) ).

tff(c_38419,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk7) ),
    inference(resolution,[status(thm)],[c_172,c_38416]) ).

tff(c_38423,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_16,c_38419]) ).

tff(c_38424,plain,
    sk6 = nil,
    inference(splitRight,[status(thm)],[c_29290]) ).

tff(c_388,plain,
    app(sk5,sk6) = sk4,
    inference(cnfTransformation,[status(thm)],[f_1653]) ).

tff(c_396,plain,
    app(sk5,sk6) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_388]) ).

tff(c_38477,plain,
    app(sk5,nil) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_38424,c_396]) ).

tff(c_881,plain,
    app(sk5,nil) = sk5,
    inference(resolution,[status(thm)],[c_384,c_755]) ).

tff(c_38493,plain,
    sk5 = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_38477,c_881]) ).

tff(c_29434,plain,
    ( frontsegP(sk2,sk5)
    | ~ ssList(app(sk5,sk6))
    | ~ ssList(sk5)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_396,c_29297]) ).

tff(c_29523,plain,
    frontsegP(sk2,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_384,c_397,c_396,c_29434]) ).

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_29525,plain,
    ( ( sk5 = sk2 )
    | ~ ssList(sk2)
    | ~ ssList(sk5)
    | ~ frontsegP(sk5,sk2) ),
    inference(resolution,[status(thm)],[c_29523,c_258]) ).

tff(c_29528,plain,
    ( ( sk5 = sk2 )
    | ~ frontsegP(sk5,sk2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_397,c_29525]) ).

tff(c_32231,plain,
    ~ frontsegP(sk5,sk2),
    inference(splitLeft,[status(thm)],[c_29528]) ).

tff(c_38599,plain,
    ~ frontsegP(sk2,sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_38493,c_32231]) ).

tff(c_38656,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29509,c_38599]) ).

tff(c_38657,plain,
    sk5 = sk2,
    inference(splitRight,[status(thm)],[c_29528]) ).

tff(c_46149,plain,
    app(app(sk2,cons(sk7,nil)),sk6) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_38657,c_2082]) ).

tff(c_46192,plain,
    ( rearsegP(nil,sk6)
    | ~ ssList(app(app(sk2,cons(sk7,nil)),sk6))
    | ~ ssList(sk6)
    | ~ ssList(app(sk2,cons(sk7,nil))) ),
    inference(superposition,[status(thm),theory(equality)],[c_46149,c_286]) ).

tff(c_46231,plain,
    ( rearsegP(nil,sk6)
    | ~ ssList(app(sk2,cons(sk7,nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_46149,c_46192]) ).

tff(c_46232,plain,
    ~ ssList(app(sk2,cons(sk7,nil))),
    inference(negUnitSimplification,[status(thm)],[c_39131,c_46231]) ).

tff(c_46242,plain,
    ( ~ ssList(sk2)
    | ~ ssList(cons(sk7,nil)) ),
    inference(resolution,[status(thm)],[c_170,c_46232]) ).

tff(c_46245,plain,
    ~ ssList(cons(sk7,nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_46242]) ).

tff(c_46249,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk7) ),
    inference(resolution,[status(thm)],[c_172,c_46245]) ).

tff(c_46253,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_16,c_46249]) ).

tff(c_46254,plain,
    sk6 = nil,
    inference(splitRight,[status(thm)],[c_29290]) ).

tff(c_595,plain,
    app(nil,sk6) = sk6,
    inference(resolution,[status(thm)],[c_386,c_467]) ).

tff(c_29422,plain,
    ( frontsegP(sk6,nil)
    | ~ ssList(app(nil,sk6))
    | ~ ssList(nil)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_595,c_29297]) ).

tff(c_29515,plain,
    frontsegP(sk6,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_16,c_386,c_595,c_29422]) ).

tff(c_29597,plain,
    ( ( sk6 = nil )
    | ~ ssList(sk6)
    | ~ ssList(nil)
    | ~ frontsegP(nil,sk6) ),
    inference(resolution,[status(thm)],[c_29515,c_258]) ).

tff(c_29600,plain,
    ( ( sk6 = nil )
    | ~ frontsegP(nil,sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_386,c_29597]) ).

tff(c_39076,plain,
    ~ frontsegP(nil,sk6),
    inference(splitLeft,[status(thm)],[c_29600]) ).

tff(c_46256,plain,
    ~ frontsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_46254,c_39076]) ).

tff(c_46312,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_29521,c_46256]) ).

tff(c_46313,plain,
    sk6 = nil,
    inference(splitRight,[status(thm)],[c_29600]) ).

tff(c_51365,plain,
    app(app(sk2,cons(sk7,nil)),nil) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_46313,c_38657,c_2082]) ).

tff(c_346,plain,
    ! [U_265,V_266,W_267] :
      ( segmentP(app(app(U_265,V_266),W_267),V_266)
      | ~ ssList(app(app(U_265,V_266),W_267))
      | ~ ssList(V_266)
      | ~ ssList(U_265)
      | ~ ssList(W_267) ),
    inference(cnfTransformation,[status(thm)],[f_1371]) ).

tff(c_51372,plain,
    ( segmentP(nil,cons(sk7,nil))
    | ~ ssList(app(app(sk2,cons(sk7,nil)),nil))
    | ~ ssList(cons(sk7,nil))
    | ~ ssList(sk2)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_51365,c_346]) ).

tff(c_51423,plain,
    ( segmentP(nil,cons(sk7,nil))
    | ~ ssList(cons(sk7,nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_397,c_16,c_51365,c_51372]) ).

tff(c_66965,plain,
    ~ ssList(cons(sk7,nil)),
    inference(splitLeft,[status(thm)],[c_51423]) ).

tff(c_66968,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk7) ),
    inference(resolution,[status(thm)],[c_172,c_66965]) ).

tff(c_66972,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_16,c_66968]) ).

tff(c_66974,plain,
    ssList(cons(sk7,nil)),
    inference(splitRight,[status(thm)],[c_51423]) ).

tff(c_66973,plain,
    segmentP(nil,cons(sk7,nil)),
    inference(splitRight,[status(thm)],[c_51423]) ).

tff(c_160,plain,
    ! [U_75] :
      ( ( nil = U_75 )
      | ~ ssList(U_75)
      | ~ segmentP(nil,U_75) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_67106,plain,
    ( ( cons(sk7,nil) = nil )
    | ~ ssList(cons(sk7,nil)) ),
    inference(resolution,[status(thm)],[c_66973,c_160]) ).

tff(c_67116,plain,
    cons(sk7,nil) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_66974,c_67106]) ).

tff(c_67118,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3160,c_67116]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SWC218-1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.15  % 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 : n015.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 21:43:59 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 38.58/22.61  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.58/22.63  
% 38.58/22.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.58/22.67  
% 38.58/22.67  Inference rules
% 38.58/22.67  ----------------------
% 38.58/22.67  #Ref     : 0
% 38.58/22.67  #Sup     : 14493
% 38.58/22.67  #Fact    : 0
% 38.58/22.67  #Define  : 0
% 38.58/22.67  #Split   : 38
% 38.58/22.67  #Chain   : 0
% 38.58/22.67  #Close   : 0
% 38.58/22.67  
% 38.58/22.67  Ordering : KBO
% 38.58/22.67  
% 38.58/22.67  Simplification rules
% 38.58/22.67  ----------------------
% 38.58/22.67  #Subsume      : 2604
% 38.58/22.67  #Demod        : 18534
% 38.58/22.67  #Tautology    : 4841
% 38.58/22.67  #SimpNegUnit  : 137
% 38.58/22.67  #BackRed      : 526
% 38.58/22.67  
% 38.58/22.67  #Partial instantiations: 0
% 38.58/22.67  #Strategies tried      : 1
% 38.58/22.67  
% 38.58/22.67  Timing (in seconds)
% 38.58/22.67  ----------------------
% 38.58/22.68  Preprocessing        : 0.86
% 38.58/22.68  Parsing              : 0.44
% 38.58/22.68  CNF conversion       : 0.06
% 38.58/22.68  Main loop            : 20.69
% 38.58/22.68  Inferencing          : 4.30
% 38.58/22.68  Reduction            : 10.58
% 38.58/22.68  Demodulation         : 8.33
% 38.58/22.68  BG Simplification    : 0.15
% 38.58/22.68  Subsumption          : 4.39
% 38.58/22.68  Abstraction          : 0.22
% 38.58/22.68  MUC search           : 0.00
% 38.58/22.68  Cooper               : 0.00
% 38.58/22.68  Total                : 21.63
% 38.58/22.68  Index Insertion      : 0.00
% 38.58/22.68  Index Deletion       : 0.00
% 38.58/22.68  Index Matching       : 0.00
% 38.58/22.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------