TSTP Solution File: SWC071-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC071-1 : 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 : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Aug 22 11:01:02 EDT 2023

% Result   : Unsatisfiable 21.56s 8.35s
% Output   : CNFRefutation 21.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  103
% Syntax   : Number of formulae    :  227 (  71 unt;  75 typ;   0 def)
%            Number of atoms       :  305 ( 107 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  303 ( 150   ~; 153   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   56 (  56 usr;  10 con; 0-2 aty)
%            Number of variables   :   55 (;  55   !;   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_1650,axiom,
    sk1 = sk3,
    file(unknown,unknown) ).

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

tff(f_161,axiom,
    ! [U] :
      ( ~ ssList(U)
      | segmentP(U,U) ),
    file(unknown,unknown) ).

tff(f_1716,axiom,
    ( ( cons(sk5,nil) = sk3 )
    | ( nil = sk3 ) ),
    file(unknown,unknown) ).

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

tff(f_1670,axiom,
    ( ssItem(sk5)
    | ( nil = sk4 ) ),
    file(unknown,unknown) ).

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

tff(f_437,axiom,
    ! [U,V] :
      ( ( cons(U,V) != nil )
      | ~ ssItem(U)
      | ~ ssList(V) ),
    file(unknown,unknown) ).

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

tff(f_1713,axiom,
    ( ssList(sk7)
    | ( nil = sk3 ) ),
    file(unknown,unknown) ).

tff(f_1676,axiom,
    ( ssList(sk6)
    | ( nil = sk4 ) ),
    file(unknown,unknown) ).

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

tff(f_1719,axiom,
    ( ( app(app(sk6,sk3),sk7) = sk4 )
    | ( nil = sk3 ) ),
    file(unknown,unknown) ).

tff(f_1371,axiom,
    ! [U,V,W,X] :
      ( ( app(app(U,V),W) != X )
      | ~ ssList(W)
      | ~ ssList(U)
      | ~ ssList(V)
      | ~ ssList(X)
      | segmentP(X,V) ),
    file(unknown,unknown) ).

tff(f_1662,axiom,
    ! [A] :
      ( ~ ssList(A)
      | ~ neq(A,nil)
      | ~ segmentP(sk2,A)
      | ~ segmentP(sk1,A) ),
    file(unknown,unknown) ).

tff(f_1667,axiom,
    ( ( nil != sk2 )
    | ( nil != sk1 ) ),
    file(unknown,unknown) ).

tff(f_1682,axiom,
    ( ( cons(sk5,nil) = sk3 )
    | ( nil = sk4 ) ),
    file(unknown,unknown) ).

tff(f_1679,axiom,
    ( ssList(sk7)
    | ( nil = sk4 ) ),
    file(unknown,unknown) ).

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

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

tff(f_784,axiom,
    ! [U,V] :
      ( ~ frontsegP(U,V)
      | ~ frontsegP(V,U)
      | ~ ssList(U)
      | ~ ssList(V)
      | ( 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_334,axiom,
    ! [U,V] :
      ( ~ ssList(U)
      | ~ ssList(V)
      | ssList(app(V,U)) ),
    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_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_1710,axiom,
    ( ssList(sk6)
    | ( nil = sk3 ) ),
    file(unknown,unknown) ).

tff(f_1673,axiom,
    ( ssItem(sk5)
    | ( nil = sk3 ) ),
    file(unknown,unknown) ).

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_433,plain,
    ssList(sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_376]) ).

tff(c_114,plain,
    ! [U_51] :
      ( segmentP(U_51,U_51)
      | ~ ssList(U_51) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_408,plain,
    ( ( sk3 = nil )
    | ( cons(sk5,nil) = sk3 ) ),
    inference(cnfTransformation,[status(thm)],[f_1716]) ).

tff(c_418,plain,
    ( ( sk1 = nil )
    | ( cons(sk5,nil) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_408]) ).

tff(c_508,plain,
    cons(sk5,nil) = sk1,
    inference(splitLeft,[status(thm)],[c_418]) ).

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

tff(c_388,plain,
    ( ( sk4 = nil )
    | ssItem(sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1670]) ).

tff(c_425,plain,
    ( ( sk2 = nil )
    | ssItem(sk5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_388]) ).

tff(c_480,plain,
    ssItem(sk5),
    inference(splitLeft,[status(thm)],[c_425]) ).

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

tff(c_1207,plain,
    ! [V_437,U_438] :
      ( ~ ssList(V_437)
      | ~ ssItem(U_438)
      | ( cons(U_438,V_437) != nil ) ),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_1709,plain,
    ! [U_474] :
      ( ~ ssItem(U_474)
      | ( cons(U_474,nil) != nil ) ),
    inference(resolution,[status(thm)],[c_16,c_1207]) ).

tff(c_1715,plain,
    cons(sk5,nil) != nil,
    inference(resolution,[status(thm)],[c_480,c_1709]) ).

tff(c_1769,plain,
    sk1 != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_508,c_1715]) ).

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_406,plain,
    ( ( sk3 = nil )
    | ssList(sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1713]) ).

tff(c_415,plain,
    ( ( sk1 = nil )
    | ssList(sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_406]) ).

tff(c_486,plain,
    ssList(sk7),
    inference(splitLeft,[status(thm)],[c_415]) ).

tff(c_392,plain,
    ( ( sk4 = nil )
    | ssList(sk6) ),
    inference(cnfTransformation,[status(thm)],[f_1676]) ).

tff(c_426,plain,
    ( ( sk2 = nil )
    | ssList(sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_392]) ).

tff(c_482,plain,
    ssList(sk6),
    inference(splitLeft,[status(thm)],[c_426]) ).

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

tff(c_432,plain,
    ssList(sk2),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_378]) ).

tff(c_410,plain,
    ( ( sk3 = nil )
    | ( app(app(sk6,sk3),sk7) = sk4 ) ),
    inference(cnfTransformation,[status(thm)],[f_1719]) ).

tff(c_420,plain,
    ( ( sk1 = nil )
    | ( app(app(sk6,sk1),sk7) = sk4 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_382,c_410]) ).

tff(c_430,plain,
    ( ( sk1 = nil )
    | ( app(app(sk6,sk1),sk7) = sk2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_420]) ).

tff(c_1618,plain,
    app(app(sk6,sk1),sk7) = sk2,
    inference(splitLeft,[status(thm)],[c_430]) ).

tff(c_10046,plain,
    ! [U_907,V_908,W_909] :
      ( segmentP(app(app(U_907,V_908),W_909),V_908)
      | ~ ssList(app(app(U_907,V_908),W_909))
      | ~ ssList(V_908)
      | ~ ssList(U_907)
      | ~ ssList(W_909) ),
    inference(cnfTransformation,[status(thm)],[f_1371]) ).

tff(c_10234,plain,
    ( segmentP(sk2,sk1)
    | ~ ssList(app(app(sk6,sk1),sk7))
    | ~ ssList(sk1)
    | ~ ssList(sk6)
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_1618,c_10046]) ).

tff(c_10375,plain,
    segmentP(sk2,sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_486,c_482,c_433,c_432,c_1618,c_10234]) ).

tff(c_384,plain,
    ! [A_327] :
      ( ~ segmentP(sk1,A_327)
      | ~ segmentP(sk2,A_327)
      | ~ neq(A_327,nil)
      | ~ ssList(A_327) ),
    inference(cnfTransformation,[status(thm)],[f_1662]) ).

tff(c_10404,plain,
    ( ~ segmentP(sk1,sk1)
    | ~ neq(sk1,nil)
    | ~ ssList(sk1) ),
    inference(resolution,[status(thm)],[c_10375,c_384]) ).

tff(c_10413,plain,
    ( ~ segmentP(sk1,sk1)
    | ~ neq(sk1,nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_10404]) ).

tff(c_11686,plain,
    ~ neq(sk1,nil),
    inference(splitLeft,[status(thm)],[c_10413]) ).

tff(c_11689,plain,
    ( ( sk1 = nil )
    | ~ ssList(sk1)
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_200,c_11686]) ).

tff(c_11695,plain,
    sk1 = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_433,c_11689]) ).

tff(c_11697,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1769,c_11695]) ).

tff(c_11698,plain,
    ~ segmentP(sk1,sk1),
    inference(splitRight,[status(thm)],[c_10413]) ).

tff(c_11702,plain,
    ~ ssList(sk1),
    inference(resolution,[status(thm)],[c_114,c_11698]) ).

tff(c_11706,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_11702]) ).

tff(c_11707,plain,
    sk1 = nil,
    inference(splitRight,[status(thm)],[c_430]) ).

tff(c_11718,plain,
    cons(sk5,nil) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_11707,c_508]) ).

tff(c_11875,plain,
    ! [U_1075] :
      ( ~ ssItem(U_1075)
      | ( cons(U_1075,nil) != nil ) ),
    inference(resolution,[status(thm)],[c_16,c_1207]) ).

tff(c_11881,plain,
    cons(sk5,nil) != nil,
    inference(resolution,[status(thm)],[c_480,c_11875]) ).

tff(c_11937,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_11718,c_11881]) ).

tff(c_11938,plain,
    sk1 = nil,
    inference(splitRight,[status(thm)],[c_418]) ).

tff(c_11939,plain,
    cons(sk5,nil) != sk1,
    inference(splitRight,[status(thm)],[c_418]) ).

tff(c_11951,plain,
    cons(sk5,nil) != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_11938,c_11939]) ).

tff(c_386,plain,
    ( ( sk1 != nil )
    | ( sk2 != nil ) ),
    inference(cnfTransformation,[status(thm)],[f_1667]) ).

tff(c_484,plain,
    sk2 != nil,
    inference(splitLeft,[status(thm)],[c_386]) ).

tff(c_396,plain,
    ( ( sk4 = nil )
    | ( cons(sk5,nil) = sk3 ) ),
    inference(cnfTransformation,[status(thm)],[f_1682]) ).

tff(c_421,plain,
    ( ( sk4 = nil )
    | ( cons(sk5,nil) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_396]) ).

tff(c_427,plain,
    ( ( sk2 = nil )
    | ( cons(sk5,nil) = sk1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_421]) ).

tff(c_12369,plain,
    ( ( sk2 = nil )
    | ( cons(sk5,nil) = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11938,c_427]) ).

tff(c_12370,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_11951,c_484,c_12369]) ).

tff(c_12372,plain,
    ~ ssList(sk7),
    inference(splitRight,[status(thm)],[c_415]) ).

tff(c_394,plain,
    ( ( sk4 = nil )
    | ssList(sk7) ),
    inference(cnfTransformation,[status(thm)],[f_1679]) ).

tff(c_424,plain,
    ( ( sk2 = nil )
    | ssList(sk7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_380,c_394]) ).

tff(c_12389,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12372,c_484,c_424]) ).

tff(c_12390,plain,
    sk1 != nil,
    inference(splitRight,[status(thm)],[c_386]) ).

tff(c_12687,plain,
    ! [U_1149] :
      ( ( app(nil,U_1149) = U_1149 )
      | ~ ssList(U_1149) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_12811,plain,
    app(nil,sk1) = sk1,
    inference(resolution,[status(thm)],[c_433,c_12687]) ).

tff(c_16025,plain,
    ! [U_1417,V_1418] :
      ( frontsegP(app(U_1417,V_1418),U_1417)
      | ~ ssList(app(U_1417,V_1418))
      | ~ ssList(U_1417)
      | ~ ssList(V_1418) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_16180,plain,
    ( frontsegP(sk1,nil)
    | ~ ssList(app(nil,sk1))
    | ~ ssList(nil)
    | ~ ssList(sk1) ),
    inference(superposition,[status(thm),theory(equality)],[c_12811,c_16025]) ).

tff(c_16281,plain,
    frontsegP(sk1,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_433,c_16,c_433,c_12811,c_16180]) ).

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_16302,plain,
    ( ( sk1 = nil )
    | ~ ssList(sk1)
    | ~ ssList(nil)
    | ~ frontsegP(nil,sk1) ),
    inference(resolution,[status(thm)],[c_16281,c_258]) ).

tff(c_16305,plain,
    ( ( sk1 = nil )
    | ~ frontsegP(nil,sk1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_433,c_16302]) ).

tff(c_16306,plain,
    ~ frontsegP(nil,sk1),
    inference(negUnitSimplification,[status(thm)],[c_12390,c_16305]) ).

tff(c_12403,plain,
    ssList(sk7),
    inference(negUnitSimplification,[status(thm)],[c_12390,c_415]) ).

tff(c_12810,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[c_16,c_12687]) ).

tff(c_16307,plain,
    ! [U_1419,V_1420] :
      ( rearsegP(app(U_1419,V_1420),V_1420)
      | ~ ssList(app(U_1419,V_1420))
      | ~ ssList(V_1420)
      | ~ ssList(U_1419) ),
    inference(cnfTransformation,[status(thm)],[f_961]) ).

tff(c_16459,plain,
    ( rearsegP(nil,nil)
    | ~ ssList(app(nil,nil))
    | ~ ssList(nil)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_12810,c_16307]) ).

tff(c_16561,plain,
    rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_16,c_16,c_12810,c_16459]) ).

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_12788,plain,
    app(nil,sk6) = sk6,
    inference(resolution,[status(thm)],[c_482,c_12687]) ).

tff(c_16171,plain,
    ( frontsegP(sk6,nil)
    | ~ ssList(app(nil,sk6))
    | ~ ssList(nil)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_12788,c_16025]) ).

tff(c_16275,plain,
    frontsegP(sk6,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_482,c_16,c_482,c_12788,c_16171]) ).

tff(c_16596,plain,
    ( ( sk6 = nil )
    | ~ ssList(sk6)
    | ~ ssList(nil)
    | ~ frontsegP(nil,sk6) ),
    inference(resolution,[status(thm)],[c_16275,c_258]) ).

tff(c_16599,plain,
    ( ( sk6 = nil )
    | ~ frontsegP(nil,sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_482,c_16596]) ).

tff(c_19542,plain,
    ~ frontsegP(nil,sk6),
    inference(splitLeft,[status(thm)],[c_16599]) ).

tff(c_20053,plain,
    ! [W_1591,V_1592,U_1593] :
      ( ( app(app(W_1591,V_1592),U_1593) = app(W_1591,app(V_1592,U_1593)) )
      | ~ ssList(W_1591)
      | ~ ssList(V_1592)
      | ~ ssList(U_1593) ),
    inference(cnfTransformation,[status(thm)],[f_1051]) ).

tff(c_12391,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_386]) ).

tff(c_13653,plain,
    ( ( sk1 = nil )
    | ( app(app(sk6,sk1),sk7) = nil ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12391,c_430]) ).

tff(c_13654,plain,
    app(app(sk6,sk1),sk7) = nil,
    inference(negUnitSimplification,[status(thm)],[c_12390,c_13653]) ).

tff(c_20090,plain,
    ( ( app(sk6,app(sk1,sk7)) = nil )
    | ~ ssList(sk6)
    | ~ ssList(sk1)
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_20053,c_13654]) ).

tff(c_20276,plain,
    app(sk6,app(sk1,sk7)) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_12403,c_433,c_482,c_20090]) ).

tff(c_288,plain,
    ! [U_192,V_193] :
      ( frontsegP(app(U_192,V_193),U_192)
      | ~ ssList(app(U_192,V_193))
      | ~ ssList(U_192)
      | ~ ssList(V_193) ),
    inference(cnfTransformation,[status(thm)],[f_975]) ).

tff(c_20907,plain,
    ( frontsegP(nil,sk6)
    | ~ ssList(app(sk6,app(sk1,sk7)))
    | ~ ssList(sk6)
    | ~ ssList(app(sk1,sk7)) ),
    inference(superposition,[status(thm),theory(equality)],[c_20276,c_288]) ).

tff(c_20933,plain,
    ( frontsegP(nil,sk6)
    | ~ ssList(app(sk1,sk7)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_482,c_16,c_20276,c_20907]) ).

tff(c_20934,plain,
    ~ ssList(app(sk1,sk7)),
    inference(negUnitSimplification,[status(thm)],[c_19542,c_20933]) ).

tff(c_20942,plain,
    ( ~ ssList(sk1)
    | ~ ssList(sk7) ),
    inference(resolution,[status(thm)],[c_170,c_20934]) ).

tff(c_20946,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12403,c_433,c_20942]) ).

tff(c_20947,plain,
    sk6 = nil,
    inference(splitRight,[status(thm)],[c_16599]) ).

tff(c_12557,plain,
    ! [U_1143] :
      ( ( app(U_1143,nil) = U_1143 )
      | ~ ssList(U_1143) ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_12658,plain,
    app(sk6,nil) = sk6,
    inference(resolution,[status(thm)],[c_482,c_12557]) ).

tff(c_16450,plain,
    ( rearsegP(sk6,nil)
    | ~ ssList(app(sk6,nil))
    | ~ ssList(nil)
    | ~ ssList(sk6) ),
    inference(superposition,[status(thm),theory(equality)],[c_12658,c_16307]) ).

tff(c_16555,plain,
    rearsegP(sk6,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_482,c_16,c_482,c_12658,c_16450]) ).

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_16642,plain,
    ( ( sk6 = nil )
    | ~ ssList(sk6)
    | ~ ssList(nil)
    | ~ rearsegP(nil,sk6) ),
    inference(resolution,[status(thm)],[c_16555,c_256]) ).

tff(c_16645,plain,
    ( ( sk6 = nil )
    | ~ rearsegP(nil,sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_482,c_16642]) ).

tff(c_19498,plain,
    ~ rearsegP(nil,sk6),
    inference(splitLeft,[status(thm)],[c_16645]) ).

tff(c_20949,plain,
    ~ rearsegP(nil,nil),
    inference(demodulation,[status(thm),theory(equality)],[c_20947,c_19498]) ).

tff(c_21002,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16561,c_20949]) ).

tff(c_21003,plain,
    sk6 = nil,
    inference(splitRight,[status(thm)],[c_16645]) ).

tff(c_21093,plain,
    app(app(nil,sk1),sk7) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_21003,c_13654]) ).

tff(c_21104,plain,
    app(sk1,sk7) = nil,
    inference(demodulation,[status(thm),theory(equality)],[c_12811,c_21093]) ).

tff(c_21132,plain,
    ( frontsegP(nil,sk1)
    | ~ ssList(app(sk1,sk7))
    | ~ ssList(sk1)
    | ~ ssList(sk7) ),
    inference(superposition,[status(thm),theory(equality)],[c_21104,c_288]) ).

tff(c_21152,plain,
    frontsegP(nil,sk1),
    inference(demodulation,[status(thm),theory(equality)],[c_12403,c_433,c_16,c_21104,c_21132]) ).

tff(c_21154,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16306,c_21152]) ).

tff(c_21156,plain,
    ~ ssList(sk6),
    inference(splitRight,[status(thm)],[c_426]) ).

tff(c_21155,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_426]) ).

tff(c_21171,plain,
    sk1 != nil,
    inference(demodulation,[status(thm),theory(equality)],[c_21155,c_386]) ).

tff(c_404,plain,
    ( ( sk3 = nil )
    | ssList(sk6) ),
    inference(cnfTransformation,[status(thm)],[f_1710]) ).

tff(c_416,plain,
    ( ( sk1 = nil )
    | ssList(sk6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_404]) ).

tff(c_21173,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_21156,c_21171,c_416]) ).

tff(c_21174,plain,
    sk2 = nil,
    inference(splitRight,[status(thm)],[c_425]) ).

tff(c_21175,plain,
    ~ ssItem(sk5),
    inference(splitRight,[status(thm)],[c_425]) ).

tff(c_390,plain,
    ( ( sk3 = nil )
    | ssItem(sk5) ),
    inference(cnfTransformation,[status(thm)],[f_1673]) ).

tff(c_423,plain,
    ( ( sk1 = nil )
    | ssItem(sk5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_382,c_390]) ).

tff(c_21187,plain,
    sk1 = nil,
    inference(negUnitSimplification,[status(thm)],[c_21175,c_423]) ).

tff(c_21210,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_21174,c_21187,c_386]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWC071-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % 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
% 0.14/0.36  % Computer : n031.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 22:04:59 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 21.56/8.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.56/8.36  
% 21.56/8.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.74/8.40  
% 21.74/8.40  Inference rules
% 21.74/8.40  ----------------------
% 21.74/8.40  #Ref     : 0
% 21.74/8.40  #Sup     : 4490
% 21.74/8.40  #Fact    : 0
% 21.74/8.40  #Define  : 0
% 21.74/8.40  #Split   : 32
% 21.74/8.40  #Chain   : 0
% 21.74/8.40  #Close   : 0
% 21.74/8.40  
% 21.74/8.40  Ordering : KBO
% 21.74/8.40  
% 21.74/8.40  Simplification rules
% 21.74/8.40  ----------------------
% 21.74/8.40  #Subsume      : 340
% 21.74/8.40  #Demod        : 4973
% 21.74/8.40  #Tautology    : 1263
% 21.74/8.40  #SimpNegUnit  : 55
% 21.74/8.40  #BackRed      : 125
% 21.74/8.40  
% 21.74/8.40  #Partial instantiations: 0
% 21.74/8.40  #Strategies tried      : 1
% 21.74/8.40  
% 21.74/8.40  Timing (in seconds)
% 21.74/8.40  ----------------------
% 21.74/8.41  Preprocessing        : 0.91
% 21.74/8.41  Parsing              : 0.45
% 21.74/8.41  CNF conversion       : 0.07
% 21.74/8.41  Main loop            : 6.39
% 21.74/8.41  Inferencing          : 1.44
% 21.74/8.41  Reduction            : 3.23
% 21.74/8.41  Demodulation         : 2.46
% 21.74/8.41  BG Simplification    : 0.11
% 21.74/8.41  Subsumption          : 1.21
% 21.74/8.41  Abstraction          : 0.10
% 21.74/8.41  MUC search           : 0.00
% 21.74/8.41  Cooper               : 0.00
% 21.74/8.41  Total                : 7.37
% 21.74/8.41  Index Insertion      : 0.00
% 21.74/8.41  Index Deletion       : 0.00
% 21.74/8.41  Index Matching       : 0.00
% 21.74/8.41  BG Taut test         : 0.00
%------------------------------------------------------------------------------