TSTP Solution File: SWC182+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 Apr 30 16:06:02 EDT 2024

% Result   : Theorem 1.98s 0.65s
% Output   : Refutation 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   80 (  20 unt;   0 def)
%            Number of atoms       :  407 ( 125 equ)
%            Maximal formula atoms :   26 (   5 avg)
%            Number of connectives :  448 ( 121   ~; 132   |; 155   &)
%                                         (   6 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  148 (  73   !;  75   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5116,plain,
    $false,
    inference(resolution,[],[f5114,f384]) ).

fof(f384,plain,
    ssItem(sK22),
    inference(cnf_transformation,[],[f257]) ).

fof(f257,plain,
    ( ( memberP(sK24,sK22)
      | memberP(sK23,sK22) )
    & sK18 = app(app(sK23,cons(sK22,nil)),sK24)
    & ssList(sK24)
    & ssList(sK23)
    & ssItem(sK22)
    & sK18 = sK20
    & sK19 = sK21
    & nil = sK20
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23,sK24])],[f99,f256,f255,f254,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ( memberP(X6,X4)
                                  | memberP(X5,X4) )
                                & app(app(X5,cons(X4,nil)),X6) = X0
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    & X0 = X2
                    & X1 = X3
                    & nil = X2
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ( memberP(X6,X4)
                                | memberP(X5,X4) )
                              & app(app(X5,cons(X4,nil)),X6) = sK18
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  & sK18 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ? [X5] :
                        ( ? [X6] :
                            ( ( memberP(X6,X4)
                              | memberP(X5,X4) )
                            & app(app(X5,cons(X4,nil)),X6) = sK18
                            & ssList(X6) )
                        & ssList(X5) )
                    & ssItem(X4) )
                & sK18 = X2
                & X1 = X3
                & nil = X2
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ? [X5] :
                      ( ? [X6] :
                          ( ( memberP(X6,X4)
                            | memberP(X5,X4) )
                          & app(app(X5,cons(X4,nil)),X6) = sK18
                          & ssList(X6) )
                      & ssList(X5) )
                  & ssItem(X4) )
              & sK18 = X2
              & sK19 = X3
              & nil = X2
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ? [X5] :
                    ( ? [X6] :
                        ( ( memberP(X6,X4)
                          | memberP(X5,X4) )
                        & app(app(X5,cons(X4,nil)),X6) = sK18
                        & ssList(X6) )
                    & ssList(X5) )
                & ssItem(X4) )
            & sK18 = X2
            & sK19 = X3
            & nil = X2
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ? [X5] :
                  ( ? [X6] :
                      ( ( memberP(X6,X4)
                        | memberP(X5,X4) )
                      & app(app(X5,cons(X4,nil)),X6) = sK18
                      & ssList(X6) )
                  & ssList(X5) )
              & ssItem(X4) )
          & sK18 = sK20
          & sK19 = X3
          & nil = sK20
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ? [X5] :
                ( ? [X6] :
                    ( ( memberP(X6,X4)
                      | memberP(X5,X4) )
                    & app(app(X5,cons(X4,nil)),X6) = sK18
                    & ssList(X6) )
                & ssList(X5) )
            & ssItem(X4) )
        & sK18 = sK20
        & sK19 = X3
        & nil = sK20
        & ssList(X3) )
   => ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ( memberP(X6,X4)
                    | memberP(X5,X4) )
                  & app(app(X5,cons(X4,nil)),X6) = sK18
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      & sK18 = sK20
      & sK19 = sK21
      & nil = sK20
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f254,plain,
    ( ? [X4] :
        ( ? [X5] :
            ( ? [X6] :
                ( ( memberP(X6,X4)
                  | memberP(X5,X4) )
                & app(app(X5,cons(X4,nil)),X6) = sK18
                & ssList(X6) )
            & ssList(X5) )
        & ssItem(X4) )
   => ( ? [X5] :
          ( ? [X6] :
              ( ( memberP(X6,sK22)
                | memberP(X5,sK22) )
              & sK18 = app(app(X5,cons(sK22,nil)),X6)
              & ssList(X6) )
          & ssList(X5) )
      & ssItem(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f255,plain,
    ( ? [X5] :
        ( ? [X6] :
            ( ( memberP(X6,sK22)
              | memberP(X5,sK22) )
            & sK18 = app(app(X5,cons(sK22,nil)),X6)
            & ssList(X6) )
        & ssList(X5) )
   => ( ? [X6] :
          ( ( memberP(X6,sK22)
            | memberP(sK23,sK22) )
          & sK18 = app(app(sK23,cons(sK22,nil)),X6)
          & ssList(X6) )
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ( ? [X6] :
        ( ( memberP(X6,sK22)
          | memberP(sK23,sK22) )
        & sK18 = app(app(sK23,cons(sK22,nil)),X6)
        & ssList(X6) )
   => ( ( memberP(sK24,sK22)
        | memberP(sK23,sK22) )
      & sK18 = app(app(sK23,cons(sK22,nil)),sK24)
      & ssList(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ( memberP(X6,X4)
                                | memberP(X5,X4) )
                              & app(app(X5,cons(X4,nil)),X6) = X0
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  & X0 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ? [X6] :
                              ( ( memberP(X6,X4)
                                | memberP(X5,X4) )
                              & app(app(X5,cons(X4,nil)),X6) = X0
                              & ssList(X6) )
                          & ssList(X5) )
                      & ssItem(X4) )
                  & X0 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X4] :
                          ( ssItem(X4)
                         => ! [X5] :
                              ( ssList(X5)
                             => ! [X6] :
                                  ( ssList(X6)
                                 => ( ( ~ memberP(X6,X4)
                                      & ~ memberP(X5,X4) )
                                    | app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
                      | X0 != X2
                      | X1 != X3
                      | nil != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ! [X4] :
                        ( ssItem(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ! [X6] :
                                ( ssList(X6)
                               => ( ( ~ memberP(X6,X4)
                                    & ~ memberP(X5,X4) )
                                  | app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
                    | X0 != X2
                    | X1 != X3
                    | nil != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f5114,plain,
    ~ ssItem(sK22),
    inference(resolution,[],[f4544,f398]) ).

fof(f398,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f4544,plain,
    memberP(nil,sK22),
    inference(duplicate_literal_removal,[],[f4263]) ).

fof(f4263,plain,
    ( memberP(nil,sK22)
    | memberP(nil,sK22) ),
    inference(backward_demodulation,[],[f1273,f4247]) ).

fof(f4247,plain,
    nil = sK23,
    inference(backward_demodulation,[],[f647,f4246]) ).

fof(f4246,plain,
    nil = app(sK23,nil),
    inference(forward_demodulation,[],[f4046,f647]) ).

fof(f4046,plain,
    nil = app(app(sK23,nil),nil),
    inference(backward_demodulation,[],[f1274,f4040]) ).

fof(f4040,plain,
    nil = cons(sK22,nil),
    inference(resolution,[],[f4039,f643]) ).

fof(f643,plain,
    ssList(nil),
    inference(forward_demodulation,[],[f379,f381]) ).

fof(f381,plain,
    nil = sK20,
    inference(cnf_transformation,[],[f257]) ).

fof(f379,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f257]) ).

fof(f4039,plain,
    ( ~ ssList(nil)
    | nil = cons(sK22,nil) ),
    inference(resolution,[],[f4038,f385]) ).

fof(f385,plain,
    ssList(sK23),
    inference(cnf_transformation,[],[f257]) ).

fof(f4038,plain,
    ( ~ ssList(sK23)
    | nil = cons(sK22,nil)
    | ~ ssList(nil) ),
    inference(resolution,[],[f4037,f384]) ).

fof(f4037,plain,
    ( ~ ssItem(sK22)
    | ~ ssList(nil)
    | nil = cons(sK22,nil)
    | ~ ssList(sK23) ),
    inference(duplicate_literal_removal,[],[f4036]) ).

fof(f4036,plain,
    ( ~ ssList(sK23)
    | ~ ssList(nil)
    | nil = cons(sK22,nil)
    | ~ ssItem(sK22)
    | ~ ssList(nil) ),
    inference(resolution,[],[f4035,f559]) ).

fof(f559,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

fof(f4035,plain,
    ( ~ ssList(cons(sK22,nil))
    | ~ ssList(sK23)
    | ~ ssList(nil)
    | nil = cons(sK22,nil) ),
    inference(duplicate_literal_removal,[],[f4030]) ).

fof(f4030,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK23)
    | ~ ssList(cons(sK22,nil))
    | nil = cons(sK22,nil)
    | ~ ssList(cons(sK22,nil)) ),
    inference(resolution,[],[f4025,f553]) ).

fof(f553,plain,
    ! [X0] :
      ( ~ segmentP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f350,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).

fof(f4025,plain,
    ( segmentP(nil,cons(sK22,nil))
    | ~ ssList(nil)
    | ~ ssList(sK23)
    | ~ ssList(cons(sK22,nil)) ),
    inference(duplicate_literal_removal,[],[f4024]) ).

fof(f4024,plain,
    ( segmentP(nil,cons(sK22,nil))
    | ~ ssList(nil)
    | ~ ssList(sK23)
    | ~ ssList(cons(sK22,nil))
    | ~ ssList(nil) ),
    inference(superposition,[],[f629,f1274]) ).

fof(f629,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f584]) ).

fof(f584,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f367]) ).

fof(f367,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
                & ssList(sK68(X0,X1))
                & ssList(sK67(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f364,f366,f365]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK67(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK67(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f366,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK67(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
        & ssList(sK68(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f364,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f363]) ).

fof(f363,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f200]) ).

fof(f200,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f1274,plain,
    nil = app(app(sK23,cons(sK22,nil)),nil),
    inference(backward_demodulation,[],[f641,f1271]) ).

fof(f1271,plain,
    nil = sK24,
    inference(resolution,[],[f1270,f643]) ).

fof(f1270,plain,
    ( ~ ssList(nil)
    | nil = sK24 ),
    inference(resolution,[],[f1269,f385]) ).

fof(f1269,plain,
    ( ~ ssList(sK23)
    | nil = sK24
    | ~ ssList(nil) ),
    inference(resolution,[],[f1268,f386]) ).

fof(f386,plain,
    ssList(sK24),
    inference(cnf_transformation,[],[f257]) ).

fof(f1268,plain,
    ( ~ ssList(sK24)
    | ~ ssList(sK23)
    | nil = sK24
    | ~ ssList(nil) ),
    inference(resolution,[],[f1267,f384]) ).

fof(f1267,plain,
    ( ~ ssItem(sK22)
    | ~ ssList(sK24)
    | ~ ssList(sK23)
    | nil = sK24
    | ~ ssList(nil) ),
    inference(resolution,[],[f1266,f559]) ).

fof(f1266,plain,
    ( ~ ssList(cons(sK22,nil))
    | nil = sK24
    | ~ ssList(sK24)
    | ~ ssList(sK23) ),
    inference(resolution,[],[f1265,f569]) ).

fof(f569,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f1265,plain,
    ( ~ ssList(app(sK23,cons(sK22,nil)))
    | ~ ssList(sK24)
    | nil = sK24 ),
    inference(trivial_inequality_removal,[],[f1257]) ).

fof(f1257,plain,
    ( nil != nil
    | nil = sK24
    | ~ ssList(sK24)
    | ~ ssList(app(sK23,cons(sK22,nil))) ),
    inference(superposition,[],[f588,f641]) ).

fof(f588,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f373]) ).

fof(f373,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f372]) ).

fof(f372,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).

fof(f641,plain,
    nil = app(app(sK23,cons(sK22,nil)),sK24),
    inference(forward_demodulation,[],[f387,f640]) ).

fof(f640,plain,
    nil = sK18,
    inference(backward_demodulation,[],[f383,f381]) ).

fof(f383,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f257]) ).

fof(f387,plain,
    sK18 = app(app(sK23,cons(sK22,nil)),sK24),
    inference(cnf_transformation,[],[f257]) ).

fof(f647,plain,
    sK23 = app(sK23,nil),
    inference(resolution,[],[f459,f385]) ).

fof(f459,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).

fof(f1273,plain,
    ( memberP(sK23,sK22)
    | memberP(nil,sK22) ),
    inference(backward_demodulation,[],[f388,f1271]) ).

fof(f388,plain,
    ( memberP(sK24,sK22)
    | memberP(sK23,sK22) ),
    inference(cnf_transformation,[],[f257]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SWC182+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n018.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Tue Apr 30 04:24:43 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  % (24737)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39  % (24738)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39  % (24743)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.16/0.40  % (24741)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.40  % (24740)WARNING: value z3 for option sas not known
% 0.16/0.40  % (24739)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.40  % (24744)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.40  % (24742)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.40  % (24740)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.41  TRYING [1]
% 0.22/0.41  TRYING [2]
% 0.22/0.41  TRYING [1]
% 0.22/0.42  TRYING [2]
% 0.22/0.42  TRYING [3]
% 0.22/0.43  TRYING [3]
% 0.22/0.48  TRYING [1]
% 0.22/0.48  TRYING [2]
% 0.22/0.48  TRYING [4]
% 0.22/0.48  TRYING [4]
% 0.22/0.49  TRYING [3]
% 0.22/0.54  TRYING [4]
% 1.65/0.60  TRYING [5]
% 1.79/0.62  TRYING [5]
% 1.98/0.64  % (24743)First to succeed.
% 1.98/0.65  % (24743)Refutation found. Thanks to Tanya!
% 1.98/0.65  % SZS status Theorem for theBenchmark
% 1.98/0.65  % SZS output start Proof for theBenchmark
% See solution above
% 1.98/0.65  % (24743)------------------------------
% 1.98/0.65  % (24743)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.98/0.65  % (24743)Termination reason: Refutation
% 1.98/0.65  
% 1.98/0.65  % (24743)Memory used [KB]: 4915
% 1.98/0.65  % (24743)Time elapsed: 0.252 s
% 1.98/0.65  % (24743)Instructions burned: 430 (million)
% 1.98/0.65  % (24743)------------------------------
% 1.98/0.65  % (24743)------------------------------
% 1.98/0.65  % (24737)Success in time 0.278 s
%------------------------------------------------------------------------------