TSTP Solution File: SWC308-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC308-1 : 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 : n014.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 11:02:03 EDT 2023

% Result   : Unsatisfiable 70.96s 53.86s
% Output   : CNFRefutation 71.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   96
% Syntax   : Number of formulae    :  193 (  56 unt;  72 typ;   0 def)
%            Number of atoms       :  263 ( 104 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  283 ( 141   ~; 142   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  65   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :   67 (;  67   !;   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_1649,axiom,
    sk2 = sk4,
    file(unknown,unknown) ).

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

tff(f_1699,axiom,
    ( ( nil = sk3 )
    | ( nil != 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_62,axiom,
    ! [U] : ssItem(skaf83(U)),
    file(unknown,unknown) ).

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

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

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

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

tff(f_492,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( cons(hd(U),tl(U)) = U )
      | ( nil = U ) ),
    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(f_342,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ssList(cons(U,V)) ),
    file(unknown,unknown) ).

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

tff(f_1684,axiom,
    ! [A,B,C,D] :
      ( ~ ssList(A)
      | ( sk1 != A )
      | ~ ssList(B)
      | ~ ssList(C)
      | ( tl(sk2) != B )
      | ( app(B,C) != A )
      | ~ ssItem(D)
      | ( cons(D,nil) != C )
      | ( hd(sk2) != D )
      | ~ neq(nil,sk2)
      | ~ neq(nil,sk2) ),
    file(unknown,unknown) ).

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

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

tff(f_250,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ( app(nil,U) = U ) ),
    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_1695,axiom,
    ! [A,B] :
      ( ~ ssItem(A)
      | ~ ssList(B)
      | ( app(B,cons(A,nil)) = sk3 )
      | ( app(cons(A,nil),B) != sk4 ) ),
    file(unknown,unknown) ).

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

tff(f_1651,axiom,
    neq(sk2,nil),
    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_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_1699]) ).

tff(c_391,plain,
    ( ( sk4 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).

tff(c_393,plain,
    ( ( sk2 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_391]) ).

tff(c_446,plain,
    sk2 != nil,
    inference(splitLeft,[status(thm)],[c_393]) ).

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

tff(c_395,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_24,plain,
    ! [U_1] : ssItem(skaf83(U_1)),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

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

tff(c_2177,plain,
    ! [U_557] :
      ( ( nil = U_557 )
      | ( cons(skaf83(U_557),skaf82(U_557)) = U_557 )
      | ~ ssList(U_557) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

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

tff(c_2189,plain,
    ! [U_557] :
      ( ( tl(U_557) = skaf82(U_557) )
      | ~ ssList(skaf82(U_557))
      | ~ ssItem(skaf83(U_557))
      | ( nil = U_557 )
      | ~ ssList(U_557) ),
    inference(superposition,[status(thm),theory(equality)],[c_2177,c_192]) ).

tff(c_14893,plain,
    ! [U_1416] :
      ( ( tl(U_1416) = skaf82(U_1416) )
      | ( nil = U_1416 )
      | ~ ssList(U_1416) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2189]) ).

tff(c_14992,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_395,c_14893]) ).

tff(c_15031,plain,
    tl(sk2) = skaf82(sk2),
    inference(negUnitSimplification,[status(thm)],[c_446,c_14992]) ).

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_10719,plain,
    ! [U_1071] :
      ( ( tl(U_1071) = skaf82(U_1071) )
      | ( nil = U_1071 )
      | ~ ssList(U_1071) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2189]) ).

tff(c_10815,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_395,c_10719]) ).

tff(c_10853,plain,
    tl(sk2) = skaf82(sk2),
    inference(negUnitSimplification,[status(thm)],[c_446,c_10815]) ).

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

tff(c_10865,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_10853,c_208]) ).

tff(c_10878,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_10865]) ).

tff(c_10879,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_446,c_10878]) ).

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_11052,plain,
    ( memberP(sk2,hd(sk2))
    | ~ ssItem(hd(sk2))
    | ~ ssList(skaf82(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_10879,c_276]) ).

tff(c_11113,plain,
    ( memberP(sk2,hd(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_11052]) ).

tff(c_11918,plain,
    ~ ssItem(hd(sk2)),
    inference(splitLeft,[status(thm)],[c_11113]) ).

tff(c_11922,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_11918]) ).

tff(c_11925,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_11922]) ).

tff(c_11927,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_446,c_11925]) ).

tff(c_11929,plain,
    ssItem(hd(sk2)),
    inference(splitRight,[status(thm)],[c_11113]) ).

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_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,
    ( ~ neq(nil,sk2)
    | ~ ssItem(hd(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) != sk1 )
    | ~ ssList(app(tl(sk2),cons(hd(sk2),nil))) ),
    inference(cnfTransformation,[status(thm)],[f_1684]) ).

tff(c_9813,plain,
    ~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
    inference(splitLeft,[status(thm)],[c_386]) ).

tff(c_9833,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(resolution,[status(thm)],[c_170,c_9813]) ).

tff(c_13253,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_10853,c_9833]) ).

tff(c_13256,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_13253]) ).

tff(c_13260,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_11929,c_16,c_13256]) ).

tff(c_13261,plain,
    ( ( app(tl(sk2),cons(hd(sk2),nil)) != sk1 )
    | ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2))
    | ~ neq(nil,sk2) ),
    inference(splitRight,[status(thm)],[c_386]) ).

tff(c_13464,plain,
    ~ neq(nil,sk2),
    inference(splitLeft,[status(thm)],[c_13261]) ).

tff(c_13470,plain,
    ( ( sk2 = nil )
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_200,c_13464]) ).

tff(c_13476,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_16,c_13470]) ).

tff(c_13478,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_446,c_13476]) ).

tff(c_13479,plain,
    ( ~ ssItem(hd(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) != sk1 ) ),
    inference(splitRight,[status(thm)],[c_13261]) ).

tff(c_13609,plain,
    app(tl(sk2),cons(hd(sk2),nil)) != sk1,
    inference(splitLeft,[status(thm)],[c_13479]) ).

tff(c_15082,plain,
    app(skaf82(sk2),cons(hd(sk2),nil)) != sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_15031,c_13609]) ).

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

tff(c_2186,plain,
    ! [U_557] :
      ( ( skaf83(U_557) = hd(U_557) )
      | ~ ssList(skaf82(U_557))
      | ~ ssItem(skaf83(U_557))
      | ( nil = U_557 )
      | ~ ssList(U_557) ),
    inference(superposition,[status(thm),theory(equality)],[c_2177,c_194]) ).

tff(c_14642,plain,
    ! [U_1411] :
      ( ( skaf83(U_1411) = hd(U_1411) )
      | ( nil = U_1411 )
      | ~ ssList(U_1411) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2186]) ).

tff(c_14741,plain,
    ( ( skaf83(sk2) = hd(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_395,c_14642]) ).

tff(c_14780,plain,
    skaf83(sk2) = hd(sk2),
    inference(negUnitSimplification,[status(thm)],[c_446,c_14741]) ).

tff(c_14800,plain,
    ssItem(hd(sk2)),
    inference(superposition,[status(thm),theory(equality)],[c_14780,c_24]) ).

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

tff(c_14790,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_14780,c_218]) ).

tff(c_14807,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_14790]) ).

tff(c_14808,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_446,c_14807]) ).

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

tff(c_396,plain,
    ssList(sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).

tff(c_462,plain,
    ! [U_393] :
      ( ( app(nil,U_393) = U_393 )
      | ~ ssList(U_393) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_582,plain,
    app(nil,sk1) = sk1,
    inference(resolution,[status(thm)],[c_396,c_462]) ).

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_388,plain,
    ! [A_331,B_332] :
      ( ( app(cons(A_331,nil),B_332) != sk4 )
      | ( app(B_332,cons(A_331,nil)) = sk3 )
      | ~ ssList(B_332)
      | ~ ssItem(A_331) ),
    inference(cnfTransformation,[status(thm)],[f_1695]) ).

tff(c_392,plain,
    ! [A_331,B_332] :
      ( ( app(cons(A_331,nil),B_332) != sk4 )
      | ( app(B_332,cons(A_331,nil)) = sk1 )
      | ~ ssList(B_332)
      | ~ ssItem(A_331) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_388]) ).

tff(c_6656,plain,
    ! [A_785,B_786] :
      ( ( app(cons(A_785,nil),B_786) != sk2 )
      | ( app(B_786,cons(A_785,nil)) = sk1 )
      | ~ ssList(B_786)
      | ~ ssItem(A_785) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_392]) ).

tff(c_87846,plain,
    ! [U_4861,V_4862] :
      ( ( cons(U_4861,V_4862) != sk2 )
      | ( app(V_4862,cons(U_4861,nil)) = sk1 )
      | ~ ssList(V_4862)
      | ~ ssItem(U_4861)
      | ~ ssList(V_4862)
      | ~ ssItem(U_4861) ),
    inference(superposition,[status(thm),theory(equality)],[c_240,c_6656]) ).

tff(c_13262,plain,
    ssList(app(tl(sk2),cons(hd(sk2),nil))),
    inference(splitRight,[status(thm)],[c_386]) ).

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

tff(c_13328,plain,
    app(nil,app(tl(sk2),cons(hd(sk2),nil))) = app(tl(sk2),cons(hd(sk2),nil)),
    inference(resolution,[status(thm)],[c_13262,c_148]) ).

tff(c_79225,plain,
    app(nil,app(skaf82(sk2),cons(hd(sk2),nil))) = app(skaf82(sk2),cons(hd(sk2),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_15031,c_15031,c_13328]) ).

tff(c_87874,plain,
    ( ( app(skaf82(sk2),cons(hd(sk2),nil)) = app(nil,sk1) )
    | ( cons(hd(sk2),skaf82(sk2)) != sk2 )
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2))
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_87846,c_79225]) ).

tff(c_88489,plain,
    app(skaf82(sk2),cons(hd(sk2),nil)) = sk1,
    inference(demodulation,[status(thm),theory(equality)],[c_14800,c_26,c_14800,c_26,c_14808,c_582,c_87874]) ).

tff(c_88491,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_15082,c_88489]) ).

tff(c_88492,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2)) ),
    inference(splitRight,[status(thm)],[c_13479]) ).

tff(c_88841,plain,
    ~ ssItem(hd(sk2)),
    inference(splitLeft,[status(thm)],[c_88492]) ).

tff(c_88844,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_88841]) ).

tff(c_88847,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_88844]) ).

tff(c_88849,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_446,c_88847]) ).

tff(c_88851,plain,
    ssItem(hd(sk2)),
    inference(splitRight,[status(thm)],[c_88492]) ).

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

tff(c_88850,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ~ ssList(tl(sk2)) ),
    inference(splitRight,[status(thm)],[c_88492]) ).

tff(c_88997,plain,
    ~ ssList(tl(sk2)),
    inference(splitLeft,[status(thm)],[c_88850]) ).

tff(c_89000,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_154,c_88997]) ).

tff(c_89003,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_395,c_89000]) ).

tff(c_89005,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_446,c_89003]) ).

tff(c_89006,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(splitRight,[status(thm)],[c_88850]) ).

tff(c_89165,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_89006]) ).

tff(c_89169,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_88851,c_16,c_89165]) ).

tff(c_89171,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_393]) ).

tff(c_384,plain,
    neq(sk2,nil),
    inference(cnfTransformation,[status(thm)],[f_1651]) ).

tff(c_89179,plain,
    neq(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_89171,c_384]) ).

tff(c_89201,plain,
    ! [V_4904] :
      ( ~ ssList(V_4904)
      | ~ neq(V_4904,V_4904) ),
    inference(cnfTransformation,[status(thm)],[f_613]) ).

tff(c_89204,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_89179,c_89201]) ).

tff(c_89208,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_89204]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC308-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n014.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 21:19:48 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 70.96/53.86  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.96/53.88  
% 70.96/53.88  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 71.16/53.92  
% 71.16/53.92  Inference rules
% 71.16/53.92  ----------------------
% 71.16/53.92  #Ref     : 34
% 71.16/53.92  #Sup     : 22035
% 71.16/53.92  #Fact    : 0
% 71.16/53.92  #Define  : 0
% 71.16/53.92  #Split   : 41
% 71.16/53.92  #Chain   : 0
% 71.16/53.92  #Close   : 0
% 71.16/53.92  
% 71.16/53.92  Ordering : KBO
% 71.16/53.92  
% 71.16/53.92  Simplification rules
% 71.16/53.92  ----------------------
% 71.16/53.92  #Subsume      : 4239
% 71.16/53.92  #Demod        : 16551
% 71.16/53.92  #Tautology    : 3648
% 71.16/53.92  #SimpNegUnit  : 387
% 71.16/53.92  #BackRed      : 159
% 71.16/53.92  
% 71.16/53.92  #Partial instantiations: 0
% 71.16/53.92  #Strategies tried      : 1
% 71.16/53.92  
% 71.16/53.92  Timing (in seconds)
% 71.16/53.92  ----------------------
% 71.16/53.92  Preprocessing        : 0.89
% 71.16/53.92  Parsing              : 0.47
% 71.16/53.92  CNF conversion       : 0.07
% 71.16/53.92  Main loop            : 51.94
% 71.16/53.92  Inferencing          : 8.37
% 71.16/53.92  Reduction            : 23.71
% 71.16/53.92  Demodulation         : 17.33
% 71.16/53.92  BG Simplification    : 0.22
% 71.16/53.92  Subsumption          : 16.28
% 71.16/53.92  Abstraction          : 0.44
% 71.16/53.92  MUC search           : 0.00
% 71.16/53.92  Cooper               : 0.00
% 71.16/53.92  Total                : 52.91
% 71.16/53.92  Index Insertion      : 0.00
% 71.16/53.92  Index Deletion       : 0.00
% 71.16/53.92  Index Matching       : 0.00
% 71.16/53.92  BG Taut test         : 0.00
%------------------------------------------------------------------------------