TSTP Solution File: SWC013-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC013-1 : 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 : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:00:44 EDT 2023

% Result   : Unsatisfiable 13.34s 4.52s
% Output   : CNFRefutation 13.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  164 (  46 unt;  72 typ;   0 def)
%            Number of atoms       :  213 (  53 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  260 ( 139   ~; 121   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 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    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :   39 (;  39   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_56,axiom,
    ssList(nil),
    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_961,axiom,
    ! [U,V,W] :
      ( ( app(U,V) != W )
      | ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(W)
      | rearsegP(W,V) ),
    file(unknown,unknown) ).

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

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

tff(f_278,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ssItem(hd(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_342,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    file(unknown,unknown) ).

tff(f_1653,axiom,
    ( neq(sk2,nil)
    | neq(sk2,nil) ),
    file(unknown,unknown) ).

tff(f_1737,axiom,
    ! [A,B] :
      ( ~ ssList(A)
      | ( sk1 != A )
      | ~ ssItem(B)
      | ( cons(B,nil) != A )
      | ( hd(sk2) != B )
      | ~ neq(nil,sk2)
      | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

tff(f_245,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( app(U,nil) = U ) ),
    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_1650,axiom,
    sk1 = sk3,
    file(unknown,unknown) ).

tff(f_1716,axiom,
    ! [A,B] :
      ( ~ ssList(A)
      | ( sk3 = A )
      | ~ ssItem(B)
      | ( cons(B,nil) != A )
      | ( hd(sk4) != B )
      | ~ neq(nil,sk4)
      | ~ neq(sk4,nil) ),
    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_613,axiom,
    ! [U,V] :
      ( ( U != V )
      | ~ neq(U,V)
      | ~ ssList(V)
      | ~ ssList(U) ),
    file(unknown,unknown) ).

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

tff(c_471,plain,
    ! [U_395] :
      ( ( app(nil,U_395) = U_395 )
      | ~ ssList(U_395) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_591,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[c_16,c_471]) ).

tff(c_3664,plain,
    ! [U_672,V_673] :
      ( frontsegP(app(U_672,V_673),U_672)
      | ~ ssList(app(U_672,V_673))
      | ~ ssList(U_672)
      | ~ ssList(V_673) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_3810,plain,
    ( frontsegP(nil,nil)
    | ~ ssList(app(nil,nil))
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_591,c_3664]) ).

tff(c_3911,plain,
    frontsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_3810]) ).

tff(c_3951,plain,
    ! [U_674,V_675] :
      ( rearsegP(app(U_674,V_675),V_675)
      | ~ ssList(app(U_674,V_675))
      | ~ ssList(V_675)
      | ~ ssList(U_674) ),
    inference(cnfTransformation,[status(thm)],[f_961]) ).

tff(c_4097,plain,
    ( rearsegP(nil,nil)
    | ~ ssList(app(nil,nil))
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_591,c_3951]) ).

tff(c_4198,plain,
    rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_591,c_4097]) ).

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

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

tff(c_405,plain,
    ssList(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).

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

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_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_384,plain,
    neq(sk2,nil),
    inference(cnfTransformation,[status(thm)],[f_1653]) ).

tff(c_394,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) != sk1 )
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(cnfTransformation,[status(thm)],[f_1737]) ).

tff(c_399,plain,
    ( ~ neq(sk2,nil)
    | ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) != sk1 )
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).

tff(c_402,plain,
    ( ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) != sk1 )
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_399]) ).

tff(c_7610,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(splitLeft,[status(thm)],[c_402]) ).

tff(c_7613,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_7610]) ).

tff(c_7616,plain,
    ~ ssItem(hd(sk2)),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_7613]) ).

tff(c_7619,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_7616]) ).

tff(c_7622,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_7619]) ).

tff(c_608,plain,
    ! [U_400] :
      ( ( app(U_400,nil) = U_400 )
      | ~ ssList(U_400) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_726,plain,
    app(sk2,nil) = sk2,
    inference(resolution,[status(thm)],[c_405,c_608]) ).

tff(c_4094,plain,
    ( rearsegP(sk2,nil)
    | ~ ssList(app(sk2,nil))
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_726,c_3951]) ).

tff(c_4196,plain,
    rearsegP(sk2,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_726,c_4094]) ).

tff(c_256,plain,
    ! [V_155,U_154] :
      ( ( V_155 = U_154 )
      | ~ ssList(V_155)
      | ~ ssList(U_154)
      | ~ rearsegP(V_155,U_154)
      | ~ rearsegP(U_154,V_155) ),
    inference(cnfTransformation,[status(thm)],[f_770]) ).

tff(c_4209,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2)
    | ~ ssList(nil)
    | ~ rearsegP(nil,sk2) ),
    inference(resolution,[status(thm)],[c_4196,c_256]) ).

tff(c_4212,plain,
    ( ( sk2 = nil )
    | ~ rearsegP(nil,sk2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_4209]) ).

tff(c_7230,plain,
    ~ rearsegP(nil,sk2),
    inference(splitLeft,[status(thm)],[c_4212]) ).

tff(c_7625,plain,
    ~ rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_7622,c_7230]) ).

tff(c_7677,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4198,c_7625]) ).

tff(c_7678,plain,
    ( ( cons(hd(sk2),nil) != sk1 )
    | ~ ssItem(hd(sk2))
    | ~ neq(nil,sk2) ),
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_7912,plain,
    ~ neq(nil,sk2),
    inference(splitLeft,[status(thm)],[c_7678]) ).

tff(c_7915,plain,
    ( ( sk2 = nil )
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_200,c_7912]) ).

tff(c_7921,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_7915]) ).

tff(c_7926,plain,
    ~ rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_7921,c_7230]) ).

tff(c_7978,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4198,c_7926]) ).

tff(c_7979,plain,
    ( ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) != sk1 ) ),
    inference(splitRight,[status(thm)],[c_7678]) ).

tff(c_8254,plain,
    cons(hd(sk2),nil) != sk1,
    inference(splitLeft,[status(thm)],[c_7979]) ).

tff(c_7679,plain,
    ssList(cons(hd(sk2),nil)),
    inference(splitRight,[status(thm)],[c_402]) ).

tff(c_7980,plain,
    neq(nil,sk2),
    inference(splitRight,[status(thm)],[c_7678]) ).

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

tff(c_392,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ( cons(hd(sk4),nil) = sk3 )
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(cnfTransformation,[status(thm)],[f_1716]) ).

tff(c_398,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ( cons(hd(sk4),nil) = sk1 )
    | ~ ssList(cons(hd(sk4),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_392]) ).

tff(c_400,plain,
    ( ~ neq(sk2,nil)
    | ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) = sk1 )
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_398]) ).

tff(c_404,plain,
    ( ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) = sk1 )
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_400]) ).

tff(c_8338,plain,
    ( ~ ssItem(hd(sk2))
    | ( cons(hd(sk2),nil) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7679,c_7980,c_404]) ).

tff(c_8339,plain,
    ~ ssItem(hd(sk2)),
    inference(negUnitSimplification,[status(thm)],[c_8254,c_8338]) ).

tff(c_8342,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_8339]) ).

tff(c_8345,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_8342]) ).

tff(c_8351,plain,
    ~ rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_8345,c_7230]) ).

tff(c_8403,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4198,c_8351]) ).

tff(c_8404,plain,
    ~ ssItem(hd(sk2)),
    inference(splitRight,[status(thm)],[c_7979]) ).

tff(c_8408,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_8404]) ).

tff(c_8411,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_8408]) ).

tff(c_8416,plain,
    ~ rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_8411,c_7230]) ).

tff(c_8468,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4198,c_8416]) ).

tff(c_8469,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_4212]) ).

tff(c_589,plain,
    app(nil,sk2) = sk2,
    inference(resolution,[status(thm)],[c_405,c_471]) ).

tff(c_3816,plain,
    ( frontsegP(sk2,nil)
    | ~ ssList(app(nil,sk2))
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_589,c_3664]) ).

tff(c_3915,plain,
    frontsegP(sk2,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_405,c_16,c_405,c_589,c_3816]) ).

tff(c_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_3947,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2)
    | ~ ssList(nil)
    | ~ frontsegP(nil,sk2) ),
    inference(resolution,[status(thm)],[c_3915,c_258]) ).

tff(c_3950,plain,
    ( ( sk2 = nil )
    | ~ frontsegP(nil,sk2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_405,c_3947]) ).

tff(c_7229,plain,
    ~ frontsegP(nil,sk2),
    inference(splitLeft,[status(thm)],[c_3950]) ).

tff(c_8492,plain,
    ~ frontsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_8469,c_7229]) ).

tff(c_8543,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3911,c_8492]) ).

tff(c_8544,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_3950]) ).

tff(c_8591,plain,
    neq(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_8544,c_384]) ).

tff(c_230,plain,
    ! [V_129] :
      ( ~ ssList(V_129)
      | ~ neq(V_129,V_129) ),
    inference(cnfTransformation,[status(thm)],[f_613]) ).

tff(c_8613,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_8591,c_230]) ).

tff(c_8620,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_8613]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWC013-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 21:24:22 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 13.34/4.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.34/4.53  
% 13.34/4.53  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.34/4.57  
% 13.34/4.57  Inference rules
% 13.34/4.57  ----------------------
% 13.34/4.57  #Ref     : 0
% 13.34/4.57  #Sup     : 1703
% 13.34/4.57  #Fact    : 0
% 13.34/4.57  #Define  : 0
% 13.34/4.57  #Split   : 12
% 13.34/4.57  #Chain   : 0
% 13.34/4.57  #Close   : 0
% 13.34/4.57  
% 13.34/4.57  Ordering : KBO
% 13.34/4.57  
% 13.34/4.57  Simplification rules
% 13.34/4.57  ----------------------
% 13.34/4.57  #Subsume      : 166
% 13.34/4.57  #Demod        : 2254
% 13.34/4.57  #Tautology    : 529
% 13.34/4.57  #SimpNegUnit  : 1
% 13.34/4.57  #BackRed      : 311
% 13.34/4.57  
% 13.34/4.57  #Partial instantiations: 0
% 13.34/4.57  #Strategies tried      : 1
% 13.34/4.57  
% 13.34/4.57  Timing (in seconds)
% 13.34/4.57  ----------------------
% 13.34/4.57  Preprocessing        : 0.88
% 13.34/4.57  Parsing              : 0.45
% 13.34/4.57  CNF conversion       : 0.07
% 13.34/4.57  Main loop            : 2.58
% 13.34/4.57  Inferencing          : 0.73
% 13.34/4.57  Reduction            : 1.10
% 13.34/4.57  Demodulation         : 0.82
% 13.34/4.57  BG Simplification    : 0.09
% 13.34/4.57  Subsumption          : 0.50
% 13.34/4.57  Abstraction          : 0.06
% 13.34/4.57  MUC search           : 0.00
% 13.34/4.57  Cooper               : 0.00
% 13.34/4.57  Total                : 3.53
% 13.34/4.57  Index Insertion      : 0.00
% 13.34/4.57  Index Deletion       : 0.00
% 13.34/4.57  Index Matching       : 0.00
% 13.34/4.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------