TSTP Solution File: SWC378-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC378-1 : 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 : n009.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 90.31s 74.01s
% Output   : CNFRefutation 90.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   94
% Syntax   : Number of formulae    :  170 (  42 unt;  75 typ;   0 def)
%            Number of atoms       :  243 (  24 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  292 ( 144   ~; 148   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   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   :   74 (;  74   !;   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_1658,axiom,
    ( memberP(sk2,sk7)
    | memberP(sk1,sk7) ),
    file(unknown,unknown) ).

tff(f_1663,axiom,
    ( ~ memberP(sk2,sk7)
    | ~ memberP(sk1,sk7) ),
    file(unknown,unknown) ).

tff(f_1655,axiom,
    ssItem(sk7),
    file(unknown,unknown) ).

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

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

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

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

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

tff(f_1653,axiom,
    app(sk5,sk6) = sk4,
    file(unknown,unknown) ).

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

tff(f_1654,axiom,
    app(sk6,sk5) = sk3,
    file(unknown,unknown) ).

tff(f_1051,axiom,
    ! [U,V,W] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(W)
      | ( app(app(W,V),U) = app(W,app(V,U)) ) ),
    file(unknown,unknown) ).

tff(f_334,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | ssList(app(V,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_138,axiom,
    ! [U,V] : ssList(skaf46(U,V)),
    file(unknown,unknown) ).

tff(f_809,axiom,
    ! [U,V] :
      ( ~ rearsegP(U,V)
      | ~ ssList(V)
      | ~ ssList(U)
      | ( app(skaf46(U,V),V) = U ) ),
    file(unknown,unknown) ).

tff(f_940,axiom,
    ! [U,V,W] :
      ( ~ memberP(U,V)
      | ~ ssList(U)
      | ~ ssList(W)
      | ~ ssItem(V)
      | memberP(app(W,U),V) ),
    file(unknown,unknown) ).

tff(f_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_926,axiom,
    ! [U,V,W] :
      ( ~ memberP(U,V)
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssItem(V)
      | memberP(app(U,W),V) ),
    file(unknown,unknown) ).

tff(c_394,plain,
    ( memberP(sk1,sk7)
    | memberP(sk2,sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1658]) ).

tff(c_474,plain,
    memberP(sk2,sk7),
    inference(splitLeft,[status(thm)],[c_394]) ).

tff(c_396,plain,
    ( ~ memberP(sk1,sk7)
    | ~ memberP(sk2,sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1663]) ).

tff(c_477,plain,
    ~ memberP(sk1,sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_474,c_396]) ).

tff(c_392,plain,
    ssItem(sk7),
    inference(cnfTransformation,[status(thm)],[f_1655]) ).

tff(c_386,plain,
    ssList(sk6),
    inference(cnfTransformation,[status(thm)],[f_1652]) ).

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_400,plain,
    ssList(sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).

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_399,plain,
    ssList(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).

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

tff(c_398,plain,
    app(sk5,sk6) = sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_388]) ).

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

tff(c_390,plain,
    app(sk6,sk5) = sk3,
    inference(cnfTransformation,[status(thm)],[f_1654]) ).

tff(c_397,plain,
    app(sk6,sk5) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).

tff(c_6934,plain,
    ! [W_782,V_783,U_784] :
      ( ( app(app(W_782,V_783),U_784) = app(W_782,app(V_783,U_784)) )
      | ~ ssList(W_782)
      | ~ ssList(V_783)
      | ~ ssList(U_784) ),
    inference(cnfTransformation,[status(thm)],[f_1051]) ).

tff(c_7107,plain,
    ! [U_784] :
      ( ( app(sk6,app(sk5,U_784)) = app(sk1,U_784) )
      | ~ ssList(sk6)
      | ~ ssList(sk5)
      | ~ ssList(U_784) ),
    inference(superposition,[status(thm),theory(equality)],[c_397,c_6934]) ).

tff(c_23194,plain,
    ! [U_1642] :
      ( ( app(sk6,app(sk5,U_1642)) = app(sk1,U_1642) )
      | ~ ssList(U_1642) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_386,c_7107]) ).

tff(c_23252,plain,
    ( ( app(sk6,sk2) = app(sk1,sk6) )
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_398,c_23194]) ).

tff(c_23289,plain,
    app(sk6,sk2) = app(sk1,sk6),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_23252]) ).

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_23333,plain,
    ( ssList(app(sk1,sk6))
    | ~ ssList(sk6)
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_23289,c_170]) ).

tff(c_23364,plain,
    ssList(app(sk1,sk6)),
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_386,c_23333]) ).

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_23324,plain,
    ( rearsegP(app(sk1,sk6),sk2)
    | ~ ssList(app(sk6,sk2))
    | ~ ssList(sk2)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_23289,c_286]) ).

tff(c_23357,plain,
    ( rearsegP(app(sk1,sk6),sk2)
    | ~ ssList(app(sk1,sk6)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_399,c_23289,c_23324]) ).

tff(c_39225,plain,
    rearsegP(app(sk1,sk6),sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_23364,c_23357]) ).

tff(c_100,plain,
    ! [U_41,V_42] : ssList(skaf46(U_41,V_42)),
    inference(cnfTransformation,[status(thm)],[f_138]) ).

tff(c_262,plain,
    ! [U_160,V_161] :
      ( ( app(skaf46(U_160,V_161),V_161) = U_160 )
      | ~ ssList(U_160)
      | ~ ssList(V_161)
      | ~ rearsegP(U_160,V_161) ),
    inference(cnfTransformation,[status(thm)],[f_809]) ).

tff(c_4543,plain,
    ! [W_659,U_660,V_661] :
      ( memberP(app(W_659,U_660),V_661)
      | ~ ssItem(V_661)
      | ~ ssList(W_659)
      | ~ ssList(U_660)
      | ~ memberP(U_660,V_661) ),
    inference(cnfTransformation,[status(thm)],[f_940]) ).

tff(c_4546,plain,
    ! [U_160,V_661,V_161] :
      ( memberP(U_160,V_661)
      | ~ ssItem(V_661)
      | ~ ssList(skaf46(U_160,V_161))
      | ~ ssList(V_161)
      | ~ memberP(V_161,V_661)
      | ~ ssList(U_160)
      | ~ ssList(V_161)
      | ~ rearsegP(U_160,V_161) ),
    inference(superposition,[status(thm),theory(equality)],[c_262,c_4543]) ).

tff(c_62024,plain,
    ! [U_3120,V_3121,V_3122] :
      ( memberP(U_3120,V_3121)
      | ~ ssItem(V_3121)
      | ~ memberP(V_3122,V_3121)
      | ~ ssList(U_3120)
      | ~ ssList(V_3122)
      | ~ rearsegP(U_3120,V_3122) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_4546]) ).

tff(c_62104,plain,
    ! [U_3120] :
      ( memberP(U_3120,sk7)
      | ~ ssItem(sk7)
      | ~ ssList(U_3120)
      | ~ ssList(sk2)
      | ~ rearsegP(U_3120,sk2) ),
    inference(resolution,[status(thm)],[c_474,c_62024]) ).

tff(c_62213,plain,
    ! [U_3123] :
      ( memberP(U_3123,sk7)
      | ~ ssList(U_3123)
      | ~ rearsegP(U_3123,sk2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_392,c_62104]) ).

tff(c_62216,plain,
    ( memberP(app(sk1,sk6),sk7)
    | ~ ssList(app(sk1,sk6)) ),
    inference(resolution,[status(thm)],[c_39225,c_62213]) ).

tff(c_62334,plain,
    memberP(app(sk1,sk6),sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_23364,c_62216]) ).

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_62427,plain,
    ( memberP(sk1,sk7)
    | memberP(sk6,sk7)
    | ~ ssItem(sk7)
    | ~ ssList(sk1)
    | ~ ssList(sk6) ),
    inference(resolution,[status(thm)],[c_62334,c_316]) ).

tff(c_62433,plain,
    ( memberP(sk1,sk7)
    | memberP(sk6,sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_400,c_392,c_62427]) ).

tff(c_62434,plain,
    memberP(sk6,sk7),
    inference(negUnitSimplification,[status(thm)],[c_477,c_62433]) ).

tff(c_4300,plain,
    ! [U_648,W_649,V_650] :
      ( memberP(app(U_648,W_649),V_650)
      | ~ ssItem(V_650)
      | ~ ssList(U_648)
      | ~ ssList(W_649)
      | ~ memberP(U_648,V_650) ),
    inference(cnfTransformation,[status(thm)],[f_926]) ).

tff(c_4420,plain,
    ! [V_650] :
      ( memberP(sk1,V_650)
      | ~ ssItem(V_650)
      | ~ ssList(sk6)
      | ~ ssList(sk5)
      | ~ memberP(sk6,V_650) ),
    inference(superposition,[status(thm),theory(equality)],[c_397,c_4300]) ).

tff(c_4498,plain,
    ! [V_650] :
      ( memberP(sk1,V_650)
      | ~ ssItem(V_650)
      | ~ memberP(sk6,V_650) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_386,c_4420]) ).

tff(c_62442,plain,
    ( memberP(sk1,sk7)
    | ~ ssItem(sk7) ),
    inference(resolution,[status(thm)],[c_62434,c_4498]) ).

tff(c_62451,plain,
    memberP(sk1,sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_62442]) ).

tff(c_62453,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_477,c_62451]) ).

tff(c_62455,plain,
    ~ memberP(sk2,sk7),
    inference(splitRight,[status(thm)],[c_394]) ).

tff(c_67995,plain,
    ! [W_3479,V_3480,U_3481] :
      ( ( app(app(W_3479,V_3480),U_3481) = app(W_3479,app(V_3480,U_3481)) )
      | ~ ssList(W_3479)
      | ~ ssList(V_3480)
      | ~ ssList(U_3481) ),
    inference(cnfTransformation,[status(thm)],[f_1051]) ).

tff(c_68159,plain,
    ! [U_3481] :
      ( ( app(sk5,app(sk6,U_3481)) = app(sk2,U_3481) )
      | ~ ssList(sk5)
      | ~ ssList(sk6)
      | ~ ssList(U_3481) ),
    inference(superposition,[status(thm),theory(equality)],[c_398,c_67995]) ).

tff(c_83219,plain,
    ! [U_4364] :
      ( ( app(sk5,app(sk6,U_4364)) = app(sk2,U_4364) )
      | ~ ssList(U_4364) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_384,c_68159]) ).

tff(c_83277,plain,
    ( ( app(sk5,sk1) = app(sk2,sk5) )
    | ~ ssList(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_397,c_83219]) ).

tff(c_83314,plain,
    app(sk5,sk1) = app(sk2,sk5),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_83277]) ).

tff(c_83358,plain,
    ( ssList(app(sk2,sk5))
    | ~ ssList(sk5)
    | ~ ssList(sk1) ),
    inference(superposition,[status(thm),theory(equality)],[c_83314,c_170]) ).

tff(c_83389,plain,
    ssList(app(sk2,sk5)),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_384,c_83358]) ).

tff(c_83349,plain,
    ( rearsegP(app(sk2,sk5),sk1)
    | ~ ssList(app(sk5,sk1))
    | ~ ssList(sk1)
    | ~ ssList(sk5) ),
    inference(superposition,[status(thm),theory(equality)],[c_83314,c_286]) ).

tff(c_83382,plain,
    ( rearsegP(app(sk2,sk5),sk1)
    | ~ ssList(app(sk2,sk5)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_400,c_83314,c_83349]) ).

tff(c_122257,plain,
    rearsegP(app(sk2,sk5),sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_83389,c_83382]) ).

tff(c_62454,plain,
    memberP(sk1,sk7),
    inference(splitRight,[status(thm)],[c_394]) ).

tff(c_66275,plain,
    ! [W_3376,U_3377,V_3378] :
      ( memberP(app(W_3376,U_3377),V_3378)
      | ~ ssItem(V_3378)
      | ~ ssList(W_3376)
      | ~ ssList(U_3377)
      | ~ memberP(U_3377,V_3378) ),
    inference(cnfTransformation,[status(thm)],[f_940]) ).

tff(c_66281,plain,
    ! [U_160,V_3378,V_161] :
      ( memberP(U_160,V_3378)
      | ~ ssItem(V_3378)
      | ~ ssList(skaf46(U_160,V_161))
      | ~ ssList(V_161)
      | ~ memberP(V_161,V_3378)
      | ~ ssList(U_160)
      | ~ ssList(V_161)
      | ~ rearsegP(U_160,V_161) ),
    inference(superposition,[status(thm),theory(equality)],[c_262,c_66275]) ).

tff(c_128829,plain,
    ! [U_5956,V_5957,V_5958] :
      ( memberP(U_5956,V_5957)
      | ~ ssItem(V_5957)
      | ~ memberP(V_5958,V_5957)
      | ~ ssList(U_5956)
      | ~ ssList(V_5958)
      | ~ rearsegP(U_5956,V_5958) ),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_66281]) ).

tff(c_128941,plain,
    ! [U_5956] :
      ( memberP(U_5956,sk7)
      | ~ ssItem(sk7)
      | ~ ssList(U_5956)
      | ~ ssList(sk1)
      | ~ rearsegP(U_5956,sk1) ),
    inference(resolution,[status(thm)],[c_62454,c_128829]) ).

tff(c_129098,plain,
    ! [U_5959] :
      ( memberP(U_5959,sk7)
      | ~ ssList(U_5959)
      | ~ rearsegP(U_5959,sk1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_392,c_128941]) ).

tff(c_129101,plain,
    ( memberP(app(sk2,sk5),sk7)
    | ~ ssList(app(sk2,sk5)) ),
    inference(resolution,[status(thm)],[c_122257,c_129098]) ).

tff(c_129219,plain,
    memberP(app(sk2,sk5),sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_83389,c_129101]) ).

tff(c_129316,plain,
    ( memberP(sk2,sk7)
    | memberP(sk5,sk7)
    | ~ ssItem(sk7)
    | ~ ssList(sk2)
    | ~ ssList(sk5) ),
    inference(resolution,[status(thm)],[c_129219,c_316]) ).

tff(c_129328,plain,
    ( memberP(sk2,sk7)
    | memberP(sk5,sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_399,c_392,c_129316]) ).

tff(c_129329,plain,
    memberP(sk5,sk7),
    inference(negUnitSimplification,[status(thm)],[c_62455,c_129328]) ).

tff(c_66877,plain,
    ! [U_3410,W_3411,V_3412] :
      ( memberP(app(U_3410,W_3411),V_3412)
      | ~ ssItem(V_3412)
      | ~ ssList(U_3410)
      | ~ ssList(W_3411)
      | ~ memberP(U_3410,V_3412) ),
    inference(cnfTransformation,[status(thm)],[f_926]) ).

tff(c_66994,plain,
    ! [V_3412] :
      ( memberP(sk2,V_3412)
      | ~ ssItem(V_3412)
      | ~ ssList(sk5)
      | ~ ssList(sk6)
      | ~ memberP(sk5,V_3412) ),
    inference(superposition,[status(thm),theory(equality)],[c_398,c_66877]) ).

tff(c_67073,plain,
    ! [V_3412] :
      ( memberP(sk2,V_3412)
      | ~ ssItem(V_3412)
      | ~ memberP(sk5,V_3412) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_384,c_66994]) ).

tff(c_129338,plain,
    ( memberP(sk2,sk7)
    | ~ ssItem(sk7) ),
    inference(resolution,[status(thm)],[c_129329,c_67073]) ).

tff(c_129353,plain,
    memberP(sk2,sk7),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_129338]) ).

tff(c_129355,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_62455,c_129353]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC378-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 21:42:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 90.31/74.01  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 90.31/74.02  
% 90.31/74.02  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.38/74.06  
% 90.38/74.06  Inference rules
% 90.38/74.06  ----------------------
% 90.38/74.06  #Ref     : 0
% 90.38/74.06  #Sup     : 29756
% 90.38/74.06  #Fact    : 0
% 90.38/74.06  #Define  : 0
% 90.38/74.06  #Split   : 151
% 90.38/74.06  #Chain   : 0
% 90.38/74.06  #Close   : 0
% 90.38/74.06  
% 90.38/74.06  Ordering : KBO
% 90.38/74.06  
% 90.38/74.06  Simplification rules
% 90.38/74.06  ----------------------
% 90.38/74.06  #Subsume      : 6745
% 90.38/74.06  #Demod        : 26641
% 90.38/74.06  #Tautology    : 6496
% 90.38/74.06  #SimpNegUnit  : 1325
% 90.38/74.06  #BackRed      : 293
% 90.38/74.06  
% 90.38/74.06  #Partial instantiations: 0
% 90.38/74.06  #Strategies tried      : 1
% 90.38/74.06  
% 90.38/74.06  Timing (in seconds)
% 90.38/74.06  ----------------------
% 90.38/74.07  Preprocessing        : 0.85
% 90.38/74.07  Parsing              : 0.44
% 90.38/74.07  CNF conversion       : 0.07
% 90.38/74.07  Main loop            : 72.14
% 90.38/74.07  Inferencing          : 12.65
% 90.38/74.07  Reduction            : 35.75
% 90.38/74.07  Demodulation         : 26.05
% 90.38/74.07  BG Simplification    : 0.23
% 90.38/74.07  Subsumption          : 18.89
% 90.38/74.07  Abstraction          : 0.54
% 90.38/74.07  MUC search           : 0.00
% 90.38/74.07  Cooper               : 0.00
% 90.38/74.07  Total                : 73.06
% 90.38/74.07  Index Insertion      : 0.00
% 90.38/74.07  Index Deletion       : 0.00
% 90.38/74.07  Index Matching       : 0.00
% 90.38/74.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------