TSTP Solution File: SWC311-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC311-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n029.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 11:02:04 EDT 2023

% Result   : Unsatisfiable 20.69s 7.92s
% Output   : CNFRefutation 20.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   93
% Syntax   : Number of formulae    :  179 (  47 unt;  72 typ;   0 def)
%            Number of atoms       :  245 (  96 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  274 ( 136   ~; 138   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   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    :   53 (  53 usr;   7 con; 0-2 aty)
%            Number of variables   :   51 (;  51   !;   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_1654,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_271,axiom,
    ! [U] :
      ( ~ ssList(U)
      | ssList(tl(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_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_428,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ( hd(cons(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_420,axiom,
    ! [U,V] :
      ( ~ ssItem(U)
      | ~ ssList(V)
      | ( tl(cons(U,V)) = V ) ),
    file(unknown,unknown) ).

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

tff(f_1692,axiom,
    ( ( nil = sk2 )
    | neq(sk2,nil) ),
    file(unknown,unknown) ).

tff(f_1689,axiom,
    ! [A,B,C,D] :
      ( ~ ssList(A)
      | ( sk3 = A )
      | ~ ssList(B)
      | ~ ssList(C)
      | ( tl(sk4) != B )
      | ( app(B,C) != A )
      | ~ ssItem(D)
      | ( cons(D,nil) != C )
      | ( hd(sk4) != D )
      | ~ neq(nil,sk4)
      | ~ neq(nil,sk4)
      | ~ neq(sk4,nil) ),
    file(unknown,unknown) ).

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

tff(f_1706,axiom,
    ! [A,B] :
      ( ( nil = sk2 )
      | ~ ssItem(A)
      | ~ ssList(B)
      | ( app(cons(A,nil),B) != sk2 )
      | ( app(B,cons(A,nil)) != sk1 ) ),
    file(unknown,unknown) ).

tff(f_1710,axiom,
    ( ( nil != sk1 )
    | 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_384,plain,
    ( ( sk4 != nil )
    | ( sk3 = nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1654]) ).

tff(c_395,plain,
    ( ( sk4 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_384]) ).

tff(c_397,plain,
    ( ( sk2 != nil )
    | ( sk1 = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_395]) ).

tff(c_453,plain,
    sk2 != nil,
    inference(splitLeft,[status(thm)],[c_397]) ).

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_156,plain,
    ! [U_73] :
      ( ( nil = U_73 )
      | ssItem(hd(U_73))
      | ~ ssList(U_73) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

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

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_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_2475,plain,
    ! [U_556] :
      ( ( nil = U_556 )
      | ( cons(skaf83(U_556),skaf82(U_556)) = U_556 )
      | ~ ssList(U_556) ),
    inference(cnfTransformation,[status(thm)],[f_543]) ).

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_2484,plain,
    ! [U_556] :
      ( ( skaf83(U_556) = hd(U_556) )
      | ~ ssList(skaf82(U_556))
      | ~ ssItem(skaf83(U_556))
      | ( nil = U_556 )
      | ~ ssList(U_556) ),
    inference(superposition,[status(thm),theory(equality)],[c_2475,c_194]) ).

tff(c_10920,plain,
    ! [U_1104] :
      ( ( skaf83(U_1104) = hd(U_1104) )
      | ( nil = U_1104 )
      | ~ ssList(U_1104) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2484]) ).

tff(c_11019,plain,
    ( ( skaf83(sk2) = hd(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_399,c_10920]) ).

tff(c_11057,plain,
    skaf83(sk2) = hd(sk2),
    inference(negUnitSimplification,[status(thm)],[c_453,c_11019]) ).

tff(c_11115,plain,
    ssItem(hd(sk2)),
    inference(superposition,[status(thm),theory(equality)],[c_11057,c_24]) ).

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_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_11107,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_11057,c_218]) ).

tff(c_11119,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_11107]) ).

tff(c_11120,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_453,c_11119]) ).

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_11585,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_11120,c_192]) ).

tff(c_11647,plain,
    tl(sk2) = skaf82(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_11115,c_26,c_11585]) ).

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_388,plain,
    ( neq(sk2,nil)
    | ( sk2 = nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1692]) ).

tff(c_459,plain,
    neq(sk2,nil),
    inference(negUnitSimplification,[status(thm)],[c_453,c_388]) ).

tff(c_386,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4))
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk3 )
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(cnfTransformation,[status(thm)],[f_1689]) ).

tff(c_396,plain,
    ( ~ neq(sk4,nil)
    | ~ neq(nil,sk4)
    | ~ ssItem(hd(sk4))
    | ~ ssList(cons(hd(sk4),nil))
    | ~ ssList(tl(sk4))
    | ( app(tl(sk4),cons(hd(sk4),nil)) = sk1 )
    | ~ ssList(app(tl(sk4),cons(hd(sk4),nil))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_386]) ).

tff(c_398,plain,
    ( ~ neq(sk2,nil)
    | ~ 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(demodulation,[status(thm),theory(equality)],[c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_380,c_396]) ).

tff(c_9988,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(demodulation,[status(thm),theory(equality)],[c_459,c_398]) ).

tff(c_9989,plain,
    ~ ssList(app(tl(sk2),cons(hd(sk2),nil))),
    inference(splitLeft,[status(thm)],[c_9988]) ).

tff(c_10126,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil)) ),
    inference(resolution,[status(thm)],[c_170,c_9989]) ).

tff(c_13708,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_11647,c_10126]) ).

tff(c_13711,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_13708]) ).

tff(c_13715,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_11115,c_16,c_13711]) ).

tff(c_13716,plain,
    ( ~ ssList(tl(sk2))
    | ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2))
    | ~ neq(nil,sk2)
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_9988]) ).

tff(c_13918,plain,
    ~ neq(nil,sk2),
    inference(splitLeft,[status(thm)],[c_13716]) ).

tff(c_13921,plain,
    ( ( sk2 = nil )
    | ~ ssList(nil)
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_200,c_13918]) ).

tff(c_13927,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_16,c_13921]) ).

tff(c_13929,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_453,c_13927]) ).

tff(c_13930,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_13716]) ).

tff(c_14057,plain,
    ~ ssList(tl(sk2)),
    inference(splitLeft,[status(thm)],[c_13930]) ).

tff(c_14060,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_154,c_14057]) ).

tff(c_14063,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_14060]) ).

tff(c_14065,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_453,c_14063]) ).

tff(c_14066,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ~ ssItem(hd(sk2))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_13930]) ).

tff(c_14423,plain,
    ~ ssItem(hd(sk2)),
    inference(splitLeft,[status(thm)],[c_14066]) ).

tff(c_14426,plain,
    ( ( sk2 = nil )
    | ~ ssList(sk2) ),
    inference(resolution,[status(thm)],[c_156,c_14423]) ).

tff(c_14429,plain,
    sk2 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_14426]) ).

tff(c_14431,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_453,c_14429]) ).

tff(c_14433,plain,
    ssItem(hd(sk2)),
    inference(splitRight,[status(thm)],[c_14066]) ).

tff(c_15775,plain,
    ! [U_1385] :
      ( ( skaf83(U_1385) = hd(U_1385) )
      | ( nil = U_1385 )
      | ~ ssList(U_1385) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26,c_2484]) ).

tff(c_15880,plain,
    ( ( skaf83(sk2) = hd(sk2) )
    | ( sk2 = nil ) ),
    inference(resolution,[status(thm)],[c_399,c_15775]) ).

tff(c_15922,plain,
    skaf83(sk2) = hd(sk2),
    inference(negUnitSimplification,[status(thm)],[c_453,c_15880]) ).

tff(c_15972,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 )
    | ~ ssList(sk2) ),
    inference(superposition,[status(thm),theory(equality)],[c_15922,c_218]) ).

tff(c_15984,plain,
    ( ( sk2 = nil )
    | ( cons(hd(sk2),skaf82(sk2)) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_399,c_15972]) ).

tff(c_15985,plain,
    cons(hd(sk2),skaf82(sk2)) = sk2,
    inference(negUnitSimplification,[status(thm)],[c_453,c_15984]) ).

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_16090,plain,
    ( ( tl(sk2) = skaf82(sk2) )
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_15985,c_192]) ).

tff(c_16152,plain,
    tl(sk2) = skaf82(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_14433,c_26,c_16090]) ).

tff(c_14067,plain,
    ssList(tl(sk2)),
    inference(splitRight,[status(thm)],[c_13930]) ).

tff(c_14432,plain,
    ( ~ ssList(cons(hd(sk2),nil))
    | ( app(tl(sk2),cons(hd(sk2),nil)) = sk1 ) ),
    inference(splitRight,[status(thm)],[c_14066]) ).

tff(c_14594,plain,
    ~ ssList(cons(hd(sk2),nil)),
    inference(splitLeft,[status(thm)],[c_14432]) ).

tff(c_14597,plain,
    ( ~ ssList(nil)
    | ~ ssItem(hd(sk2)) ),
    inference(resolution,[status(thm)],[c_172,c_14594]) ).

tff(c_14601,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14433,c_16,c_14597]) ).

tff(c_14602,plain,
    app(tl(sk2),cons(hd(sk2),nil)) = sk1,
    inference(splitRight,[status(thm)],[c_14432]) ).

tff(c_390,plain,
    ! [B_332,A_331] :
      ( ( app(B_332,cons(A_331,nil)) != sk1 )
      | ( app(cons(A_331,nil),B_332) != sk2 )
      | ~ ssList(B_332)
      | ~ ssItem(A_331)
      | ( sk2 = nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1706]) ).

tff(c_8817,plain,
    ! [B_332,A_331] :
      ( ( app(B_332,cons(A_331,nil)) != sk1 )
      | ( app(cons(A_331,nil),B_332) != sk2 )
      | ~ ssList(B_332)
      | ~ ssItem(A_331) ),
    inference(negUnitSimplification,[status(thm)],[c_453,c_390]) ).

tff(c_14708,plain,
    ( ( app(cons(hd(sk2),nil),tl(sk2)) != sk2 )
    | ~ ssList(tl(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14602,c_8817]) ).

tff(c_14771,plain,
    app(cons(hd(sk2),nil),tl(sk2)) != sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_14433,c_14067,c_14708]) ).

tff(c_17736,plain,
    app(cons(hd(sk2),nil),skaf82(sk2)) != sk2,
    inference(demodulation,[status(thm),theory(equality)],[c_16152,c_14771]) ).

tff(c_17739,plain,
    ( ( cons(hd(sk2),skaf82(sk2)) != sk2 )
    | ~ ssList(skaf82(sk2))
    | ~ ssItem(hd(sk2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_240,c_17736]) ).

tff(c_17742,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14433,c_26,c_15985,c_17739]) ).

tff(c_17743,plain,
    sk1 = nil,
    inference(splitRight,[status(thm)],[c_397]) ).

tff(c_17744,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_397]) ).

tff(c_392,plain,
    ( neq(sk2,nil)
    | ( sk1 != nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1710]) ).

tff(c_17781,plain,
    neq(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_17743,c_17744,c_392]) ).

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

tff(c_17787,plain,
    ~ ssList(nil),
    inference(resolution,[status(thm)],[c_17781,c_230]) ).

tff(c_17792,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_17787]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC311-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 21:58:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 20.69/7.92  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.69/7.93  
% 20.69/7.93  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.95/7.97  
% 20.95/7.97  Inference rules
% 20.95/7.97  ----------------------
% 20.95/7.97  #Ref     : 0
% 20.95/7.97  #Sup     : 3704
% 20.95/7.97  #Fact    : 0
% 20.95/7.97  #Define  : 0
% 20.95/7.97  #Split   : 18
% 20.95/7.97  #Chain   : 0
% 20.95/7.97  #Close   : 0
% 20.95/7.97  
% 20.95/7.97  Ordering : KBO
% 20.95/7.97  
% 20.95/7.97  Simplification rules
% 20.95/7.97  ----------------------
% 20.95/7.97  #Subsume      : 321
% 20.95/7.97  #Demod        : 4352
% 20.95/7.97  #Tautology    : 972
% 20.95/7.97  #SimpNegUnit  : 70
% 20.95/7.97  #BackRed      : 23
% 20.95/7.97  
% 20.95/7.97  #Partial instantiations: 0
% 20.95/7.97  #Strategies tried      : 1
% 20.95/7.97  
% 20.95/7.97  Timing (in seconds)
% 20.95/7.97  ----------------------
% 20.95/7.98  Preprocessing        : 0.87
% 20.95/7.98  Parsing              : 0.44
% 20.95/7.98  CNF conversion       : 0.07
% 20.95/7.98  Main loop            : 6.04
% 20.95/7.98  Inferencing          : 1.43
% 20.95/7.98  Reduction            : 2.83
% 20.95/7.98  Demodulation         : 2.13
% 20.95/7.98  BG Simplification    : 0.10
% 20.95/7.98  Subsumption          : 1.26
% 20.95/7.98  Abstraction          : 0.09
% 20.95/7.98  MUC search           : 0.00
% 20.95/7.98  Cooper               : 0.00
% 20.95/7.98  Total                : 6.97
% 20.95/7.98  Index Insertion      : 0.00
% 20.95/7.98  Index Deletion       : 0.00
% 20.95/7.98  Index Matching       : 0.00
% 20.95/7.98  BG Taut test         : 0.00
%------------------------------------------------------------------------------