TSTP Solution File: SWC096+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC096+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 May 21 04:47:10 EDT 2024

% Result   : Theorem 0.22s 0.46s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   78 (  10 unt;   0 def)
%            Number of atoms       :  356 (  96 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  432 ( 154   ~; 136   |; 120   &)
%                                         (   2 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  147 ( 100   !;  47   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2193,plain,
    $false,
    inference(resolution,[],[f2190,f658]) ).

fof(f658,plain,
    ssList(sK22),
    inference(forward_demodulation,[],[f393,f396]) ).

fof(f396,plain,
    sK22 = sK24,
    inference(cnf_transformation,[],[f264]) ).

fof(f264,plain,
    ( ( ( ~ neq(sK25,nil)
        & neq(sK23,nil) )
      | sP1(sK24,sK25,sK23,sK22) )
    & sK22 = sK24
    & sK23 = sK25
    & ssList(sK25)
    & ssList(sK24)
    & ssList(sK23)
    & ssList(sK22) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f225,f263,f262,f261,f260]) ).

fof(f260,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | sP1(X2,X3,X1,X0) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP1(X2,X3,X1,sK22) )
                  & sK22 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK22) ) ),
    introduced(choice_axiom,[]) ).

fof(f261,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | sP1(X2,X3,X1,sK22) )
                & sK22 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK23,nil) )
                | sP1(X2,X3,sK23,sK22) )
              & sK22 = X2
              & sK23 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK23) ) ),
    introduced(choice_axiom,[]) ).

fof(f262,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK23,nil) )
              | sP1(X2,X3,sK23,sK22) )
            & sK22 = X2
            & sK23 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK23,nil) )
            | sP1(sK24,X3,sK23,sK22) )
          & sK22 = sK24
          & sK23 = X3
          & ssList(X3) )
      & ssList(sK24) ) ),
    introduced(choice_axiom,[]) ).

fof(f263,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK23,nil) )
          | sP1(sK24,X3,sK23,sK22) )
        & sK22 = sK24
        & sK23 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK25,nil)
          & neq(sK23,nil) )
        | sP1(sK24,sK25,sK23,sK22) )
      & sK22 = sK24
      & sK23 = sK25
      & ssList(sK25) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP1(X2,X3,X1,X0) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f99,f224,f223]) ).

fof(f223,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X5,cons(X4,nil)) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f224,plain,
    ! [X2,X3,X1,X0] :
      ( ( sP0(X3,X2)
        & ! [X6] :
            ( ! [X7] :
                ( app(X7,cons(X6,nil)) != X1
                | cons(X6,nil) != X0
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & neq(X1,nil) )
      | ~ sP1(X2,X3,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( app(X7,cons(X6,nil)) != X1
                              | cons(X6,nil) != X0
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ! [X4] :
                            ( ssItem(X4)
                           => ! [X5] :
                                ( app(X5,cons(X4,nil)) != X3
                                | cons(X4,nil) != X2
                                | ~ ssList(X5) ) )
                        | ? [X6] :
                            ( ? [X7] :
                                ( app(X7,cons(X6,nil)) = X1
                                & cons(X6,nil) = X0
                                & ssList(X7) )
                            & ssItem(X6) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ! [X6] :
                            ( ssItem(X6)
                           => ! [X7] :
                                ( app(X7,cons(X6,nil)) != X3
                                | cons(X6,nil) != X2
                                | ~ ssList(X7) ) )
                        | ? [X4] :
                            ( ? [X5] :
                                ( app(X5,cons(X4,nil)) = X1
                                & cons(X4,nil) = X0
                                & ssList(X5) )
                            & ssItem(X4) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3
                    | ~ ssList(X3) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( neq(X3,nil)
                      | ~ neq(X1,nil) )
                    & ( ! [X6] :
                          ( ssItem(X6)
                         => ! [X7] :
                              ( app(X7,cons(X6,nil)) != X3
                              | cons(X6,nil) != X2
                              | ~ ssList(X7) ) )
                      | ? [X4] :
                          ( ? [X5] :
                              ( app(X5,cons(X4,nil)) = X1
                              & cons(X4,nil) = X0
                              & ssList(X5) )
                          & ssItem(X4) )
                      | ~ neq(X1,nil) ) )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f393,plain,
    ssList(sK24),
    inference(cnf_transformation,[],[f264]) ).

fof(f2190,plain,
    ~ ssList(sK22),
    inference(resolution,[],[f2189,f709]) ).

fof(f709,plain,
    neq(sK23,nil),
    inference(duplicate_literal_removal,[],[f707]) ).

fof(f707,plain,
    ( neq(sK23,nil)
    | neq(sK23,nil) ),
    inference(resolution,[],[f384,f656]) ).

fof(f656,plain,
    ( sP1(sK22,sK23,sK23,sK22)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f655,f396]) ).

fof(f655,plain,
    ( sP1(sK24,sK23,sK23,sK22)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f397,f395]) ).

fof(f395,plain,
    sK23 = sK25,
    inference(cnf_transformation,[],[f264]) ).

fof(f397,plain,
    ( neq(sK23,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f384,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | neq(X2,nil) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP0(X1,X0)
        & ! [X4] :
            ( ! [X5] :
                ( app(X5,cons(X4,nil)) != X2
                | cons(X4,nil) != X3
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & neq(X2,nil) )
      | ~ sP1(X0,X1,X2,X3) ),
    inference(rectify,[],[f253]) ).

fof(f253,plain,
    ! [X2,X3,X1,X0] :
      ( ( sP0(X3,X2)
        & ! [X6] :
            ( ! [X7] :
                ( app(X7,cons(X6,nil)) != X1
                | cons(X6,nil) != X0
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & neq(X1,nil) )
      | ~ sP1(X2,X3,X1,X0) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f2189,plain,
    ( ~ neq(sK23,nil)
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2188,f710]) ).

fof(f710,plain,
    ( sP0(sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(resolution,[],[f386,f654]) ).

fof(f654,plain,
    ( sP1(sK22,sK23,sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f653,f396]) ).

fof(f653,plain,
    ( sP1(sK24,sK23,sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f652,f395]) ).

fof(f652,plain,
    ( ~ neq(sK23,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(forward_demodulation,[],[f398,f395]) ).

fof(f398,plain,
    ( ~ neq(sK25,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f386,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | sP0(X1,X0) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f2188,plain,
    ( ~ sP0(sK23,sK22)
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2185,f388]) ).

fof(f388,plain,
    ! [X0,X1] :
      ( ssList(sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ( app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0
        & cons(sK20(X0,X1),nil) = X1
        & ssList(sK21(X0,X1))
        & ssItem(sK20(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f256,f258,f257]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(X3,cons(X2,nil)) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( app(X3,cons(sK20(X0,X1),nil)) = X0
            & cons(sK20(X0,X1),nil) = X1
            & ssList(X3) )
        & ssItem(sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(X3,cons(sK20(X0,X1),nil)) = X0
          & cons(sK20(X0,X1),nil) = X1
          & ssList(X3) )
     => ( app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0
        & cons(sK20(X0,X1),nil) = X1
        & ssList(sK21(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(X3,cons(X2,nil)) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f255]) ).

fof(f255,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X5,cons(X4,nil)) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f2185,plain,
    ( ~ ssList(sK21(sK23,sK22))
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2107,f709]) ).

fof(f2107,plain,
    ( ~ neq(sK23,nil)
    | ~ ssList(sK22)
    | ~ ssList(sK21(sK23,sK22)) ),
    inference(resolution,[],[f2106,f710]) ).

fof(f2106,plain,
    ( ~ sP0(sK23,sK22)
    | ~ ssList(sK21(sK23,sK22))
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2104,f387]) ).

fof(f387,plain,
    ! [X0,X1] :
      ( ssItem(sK20(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f259]) ).

fof(f2104,plain,
    ( ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(sK22)
    | ~ ssList(sK21(sK23,sK22)) ),
    inference(duplicate_literal_removal,[],[f2103]) ).

fof(f2103,plain,
    ( ~ ssList(sK21(sK23,sK22))
    | ~ ssList(sK22)
    | ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2101,f1042]) ).

fof(f1042,plain,
    ( singletonP(sK22)
    | ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(sK22) ),
    inference(superposition,[],[f626,f742]) ).

fof(f742,plain,
    sK22 = cons(sK20(sK23,sK22),nil),
    inference(resolution,[],[f741,f709]) ).

fof(f741,plain,
    ( ~ neq(sK23,nil)
    | sK22 = cons(sK20(sK23,sK22),nil) ),
    inference(resolution,[],[f389,f710]) ).

fof(f389,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK20(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f259]) ).

fof(f626,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f483]) ).

fof(f483,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f294,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK30(X0),nil) = X0
            & ssItem(sK30(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f292,f293]) ).

fof(f293,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK30(X0),nil) = X0
        & ssItem(sK30(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f292,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f291]) ).

fof(f291,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f2101,plain,
    ( ~ singletonP(sK22)
    | ~ ssList(sK21(sK23,sK22))
    | ~ ssList(sK22) ),
    inference(resolution,[],[f2098,f481]) ).

fof(f481,plain,
    ! [X0] :
      ( ssItem(sK30(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f2098,plain,
    ( ~ ssItem(sK30(sK22))
    | ~ ssList(sK21(sK23,sK22)) ),
    inference(resolution,[],[f2097,f709]) ).

fof(f2097,plain,
    ( ~ neq(sK23,nil)
    | ~ ssList(sK21(sK23,sK22))
    | ~ ssItem(sK30(sK22)) ),
    inference(resolution,[],[f2096,f654]) ).

fof(f2096,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,X1,sK23,sK22)
      | ~ ssItem(sK30(sK22))
      | ~ ssList(sK21(sK23,sK22)) ),
    inference(superposition,[],[f2093,f1531]) ).

fof(f1531,plain,
    sK23 = app(sK21(sK23,sK22),sK22),
    inference(resolution,[],[f1530,f709]) ).

fof(f1530,plain,
    ( ~ neq(sK23,nil)
    | sK23 = app(sK21(sK23,sK22),sK22) ),
    inference(forward_demodulation,[],[f1529,f742]) ).

fof(f1529,plain,
    ( sK23 = app(sK21(sK23,sK22),cons(sK20(sK23,sK22),nil))
    | ~ neq(sK23,nil) ),
    inference(resolution,[],[f390,f710]) ).

fof(f390,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | app(sK21(X0,X1),cons(sK20(X0,X1),nil)) = X0 ),
    inference(cnf_transformation,[],[f259]) ).

fof(f2093,plain,
    ! [X2,X0,X1] :
      ( ~ sP1(X0,X1,app(X2,sK22),sK22)
      | ~ ssItem(sK30(sK22))
      | ~ ssList(X2) ),
    inference(superposition,[],[f617,f1051]) ).

fof(f1051,plain,
    sK22 = cons(sK30(sK22),nil),
    inference(resolution,[],[f1048,f658]) ).

fof(f1048,plain,
    ( ~ ssList(sK22)
    | sK22 = cons(sK30(sK22),nil) ),
    inference(resolution,[],[f1047,f709]) ).

fof(f1047,plain,
    ( ~ neq(sK23,nil)
    | ~ ssList(sK22)
    | sK22 = cons(sK30(sK22),nil) ),
    inference(resolution,[],[f1046,f710]) ).

fof(f1046,plain,
    ( ~ sP0(sK23,sK22)
    | sK22 = cons(sK30(sK22),nil)
    | ~ ssList(sK22) ),
    inference(resolution,[],[f1045,f387]) ).

fof(f1045,plain,
    ( ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(sK22)
    | sK22 = cons(sK30(sK22),nil) ),
    inference(duplicate_literal_removal,[],[f1044]) ).

fof(f1044,plain,
    ( ~ ssItem(sK20(sK23,sK22))
    | ~ ssList(sK22)
    | sK22 = cons(sK30(sK22),nil)
    | ~ ssList(sK22) ),
    inference(resolution,[],[f1042,f482]) ).

fof(f482,plain,
    ! [X0] :
      ( ~ singletonP(X0)
      | cons(sK30(X0),nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f294]) ).

fof(f617,plain,
    ! [X0,X1,X4,X5] :
      ( ~ sP1(X0,X1,app(X5,cons(X4,nil)),cons(X4,nil))
      | ~ ssItem(X4)
      | ~ ssList(X5) ),
    inference(equality_resolution,[],[f616]) ).

fof(f616,plain,
    ! [X3,X0,X1,X4,X5] :
      ( cons(X4,nil) != X3
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ sP1(X0,X1,app(X5,cons(X4,nil)),X3) ),
    inference(equality_resolution,[],[f385]) ).

fof(f385,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( app(X5,cons(X4,nil)) != X2
      | cons(X4,nil) != X3
      | ~ ssList(X5)
      | ~ ssItem(X4)
      | ~ sP1(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC096+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 02:52:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (29038)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (29039)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (29041)WARNING: value z3 for option sas not known
% 0.14/0.37  % (29041)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)
% 0.14/0.37  % (29042)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (29043)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)
% 0.14/0.38  % (29040)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (29044)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)
% 0.14/0.38  % (29045)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)
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [3]
% 0.22/0.41  TRYING [3]
% 0.22/0.43  TRYING [1]
% 0.22/0.43  TRYING [2]
% 0.22/0.43  TRYING [4]
% 0.22/0.44  TRYING [3]
% 0.22/0.46  % (29044)First to succeed.
% 0.22/0.46  % (29044)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29038"
% 0.22/0.46  % (29044)Refutation found. Thanks to Tanya!
% 0.22/0.46  % SZS status Theorem for theBenchmark
% 0.22/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.46  % (29044)------------------------------
% 0.22/0.46  % (29044)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.46  % (29044)Termination reason: Refutation
% 0.22/0.46  
% 0.22/0.46  % (29044)Memory used [KB]: 2764
% 0.22/0.46  % (29044)Time elapsed: 0.085 s
% 0.22/0.46  % (29044)Instructions burned: 148 (million)
% 0.22/0.46  % (29038)Success in time 0.106 s
%------------------------------------------------------------------------------