TSTP Solution File: SWC014+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC014+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 : n006.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 : Sun May  5 09:51:31 EDT 2024

% Result   : Theorem 25.66s 4.01s
% Output   : Refutation 25.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  108 (  20 unt;   0 def)
%            Number of atoms       :  455 ( 146 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  542 ( 195   ~; 182   |; 129   &)
%                                         (   2 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  193 ( 145   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f56165,plain,
    $false,
    inference(resolution,[],[f56164,f408]) ).

fof(f408,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f56164,plain,
    ~ ssList(nil),
    inference(resolution,[],[f33244,f647]) ).

fof(f647,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f640]) ).

fof(f640,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f587]) ).

fof(f587,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f366]) ).

fof(f366,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).

fof(f33244,plain,
    neq(nil,nil),
    inference(backward_demodulation,[],[f711,f33238]) ).

fof(f33238,plain,
    nil = sK23,
    inference(resolution,[],[f33237,f408]) ).

fof(f33237,plain,
    ( ~ ssList(nil)
    | nil = sK23 ),
    inference(resolution,[],[f33236,f659]) ).

fof(f659,plain,
    ssList(sK23),
    inference(forward_demodulation,[],[f395,f396]) ).

fof(f396,plain,
    sK23 = sK25,
    inference(cnf_transformation,[],[f265]) ).

fof(f265,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])],[f226,f264,f263,f262,f261]) ).

fof(f261,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(f262,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(f263,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(f264,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(f226,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,[],[f100,f225,f224]) ).

fof(f224,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(cons(X4,nil),X5) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f225,plain,
    ! [X2,X3,X1,X0] :
      ( ( sP0(X3,X2)
        & ! [X6] :
            ( ! [X7] :
                ( ~ neq(nil,X1)
                | app(X0,X7) != X6
                | tl(X1) != X7
                | ~ ssList(X7) )
            | X1 != X6
            | ~ ssList(X6) )
        & neq(X1,nil) )
      | ~ sP1(X2,X3,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ~ neq(nil,X1)
                              | app(X0,X7) != X6
                              | tl(X1) != X7
                              | ~ ssList(X7) )
                          | X1 != X6
                          | ~ ssList(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ? [X5] :
                              ( app(cons(X4,nil),X5) = X3
                              & cons(X4,nil) = X2
                              & ssList(X5) )
                          & ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ~ neq(nil,X1)
                              | app(X0,X7) != X6
                              | tl(X1) != X7
                              | ~ ssList(X7) )
                          | X1 != X6
                          | ~ ssList(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] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssItem(X4)
                             => ! [X5] :
                                  ( ssList(X5)
                                 => ( app(cons(X4,nil),X5) != X3
                                    | cons(X4,nil) != X2 ) ) )
                          | ? [X6] :
                              ( ? [X7] :
                                  ( neq(nil,X1)
                                  & app(X0,X7) = X6
                                  & tl(X1) = X7
                                  & ssList(X7) )
                              & X1 = X6
                              & ssList(X6) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

fof(f395,plain,
    ssList(sK25),
    inference(cnf_transformation,[],[f265]) ).

fof(f33236,plain,
    ( ~ ssList(sK23)
    | nil = sK23
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f33235]) ).

fof(f33235,plain,
    ( ~ ssList(sK23)
    | nil = sK23
    | ~ ssList(nil)
    | nil = sK23
    | ~ ssList(sK23) ),
    inference(resolution,[],[f33232,f476]) ).

fof(f476,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f33232,plain,
    ( ~ ssList(tl(sK23))
    | ~ ssList(sK23)
    | nil = sK23
    | ~ ssList(nil) ),
    inference(duplicate_literal_removal,[],[f33230]) ).

fof(f33230,plain,
    ( ~ ssList(tl(sK23))
    | ~ ssList(sK23)
    | nil = sK23
    | ~ ssList(sK23)
    | ~ ssList(nil) ),
    inference(resolution,[],[f33226,f588]) ).

fof(f588,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f366]) ).

fof(f33226,plain,
    ( ~ neq(nil,sK23)
    | ~ ssList(tl(sK23))
    | ~ ssList(sK23) ),
    inference(resolution,[],[f33225,f711]) ).

fof(f33225,plain,
    ( ~ neq(sK23,nil)
    | ~ ssList(sK23)
    | ~ ssList(tl(sK23))
    | ~ neq(nil,sK23) ),
    inference(resolution,[],[f30413,f656]) ).

fof(f656,plain,
    ( sP1(sK22,sK23,sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f655,f397]) ).

fof(f397,plain,
    sK22 = sK24,
    inference(cnf_transformation,[],[f265]) ).

fof(f655,plain,
    ( sP1(sK24,sK23,sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(forward_demodulation,[],[f654,f396]) ).

fof(f654,plain,
    ( ~ neq(sK23,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(forward_demodulation,[],[f399,f396]) ).

fof(f399,plain,
    ( ~ neq(sK25,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(cnf_transformation,[],[f265]) ).

fof(f30413,plain,
    ! [X0,X1] :
      ( ~ sP1(X0,X1,sK23,sK22)
      | ~ neq(nil,sK23)
      | ~ ssList(sK23)
      | ~ ssList(tl(sK23)) ),
    inference(trivial_inequality_removal,[],[f30392]) ).

fof(f30392,plain,
    ! [X0,X1] :
      ( sK23 != sK23
      | ~ ssList(tl(sK23))
      | ~ neq(nil,sK23)
      | ~ ssList(sK23)
      | ~ sP1(X0,X1,sK23,sK22) ),
    inference(superposition,[],[f653,f29664]) ).

fof(f29664,plain,
    sK23 = app(sK22,tl(sK23)),
    inference(backward_demodulation,[],[f1533,f25604]) ).

fof(f25604,plain,
    tl(sK23) = sK21(sK23,sK22),
    inference(backward_demodulation,[],[f19215,f25596]) ).

fof(f25596,plain,
    sK23 = cons(hd(sK22),sK21(sK23,sK22)),
    inference(resolution,[],[f25595,f711]) ).

fof(f25595,plain,
    ( ~ neq(sK23,nil)
    | sK23 = cons(hd(sK22),sK21(sK23,sK22)) ),
    inference(forward_demodulation,[],[f25594,f1533]) ).

fof(f25594,plain,
    ( app(sK22,sK21(sK23,sK22)) = cons(hd(sK22),sK21(sK23,sK22))
    | ~ neq(sK23,nil) ),
    inference(resolution,[],[f16078,f712]) ).

fof(f712,plain,
    ( sP0(sK23,sK22)
    | ~ neq(sK23,nil) ),
    inference(resolution,[],[f387,f656]) ).

fof(f387,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | sP0(X1,X0) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f255,plain,
    ! [X0,X1,X2,X3] :
      ( ( sP0(X1,X0)
        & ! [X4] :
            ( ! [X5] :
                ( ~ neq(nil,X2)
                | app(X3,X5) != X4
                | tl(X2) != X5
                | ~ ssList(X5) )
            | X2 != X4
            | ~ ssList(X4) )
        & neq(X2,nil) )
      | ~ sP1(X0,X1,X2,X3) ),
    inference(rectify,[],[f254]) ).

fof(f254,plain,
    ! [X2,X3,X1,X0] :
      ( ( sP0(X3,X2)
        & ! [X6] :
            ( ! [X7] :
                ( ~ neq(nil,X1)
                | app(X0,X7) != X6
                | tl(X1) != X7
                | ~ ssList(X7) )
            | X1 != X6
            | ~ ssList(X6) )
        & neq(X1,nil) )
      | ~ sP1(X2,X3,X1,X0) ),
    inference(nnf_transformation,[],[f225]) ).

fof(f16078,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | app(sK22,sK21(X0,X1)) = cons(hd(sK22),sK21(X0,X1)) ),
    inference(resolution,[],[f16053,f389]) ).

fof(f389,plain,
    ! [X0,X1] :
      ( ssList(sK21(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( ( app(cons(sK20(X0,X1),nil),sK21(X0,X1)) = 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])],[f257,f259,f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(cons(X2,nil),X3) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( app(cons(sK20(X0,X1),nil),X3) = X0
            & cons(sK20(X0,X1),nil) = X1
            & ssList(X3) )
        & ssItem(sK20(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f259,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( app(cons(sK20(X0,X1),nil),X3) = X0
          & cons(sK20(X0,X1),nil) = X1
          & ssList(X3) )
     => ( app(cons(sK20(X0,X1),nil),sK21(X0,X1)) = X0
        & cons(sK20(X0,X1),nil) = X1
        & ssList(sK21(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( app(cons(X2,nil),X3) = X0
              & cons(X2,nil) = X1
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f256]) ).

fof(f256,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(cons(X4,nil),X5) = X3
              & cons(X4,nil) = X2
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    inference(nnf_transformation,[],[f224]) ).

fof(f16053,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(sK22,X0) = cons(hd(sK22),X0) ),
    inference(resolution,[],[f16018,f711]) ).

fof(f16018,plain,
    ! [X0] :
      ( ~ neq(sK23,nil)
      | ~ ssList(X0)
      | app(sK22,X0) = cons(hd(sK22),X0) ),
    inference(resolution,[],[f15521,f712]) ).

fof(f15521,plain,
    ! [X0] :
      ( ~ sP0(sK23,sK22)
      | app(sK22,X0) = cons(hd(sK22),X0)
      | ~ ssList(X0) ),
    inference(forward_demodulation,[],[f15515,f15185]) ).

fof(f15185,plain,
    sK22 = cons(hd(sK22),nil),
    inference(backward_demodulation,[],[f744,f15184]) ).

fof(f15184,plain,
    sK20(sK23,sK22) = hd(sK22),
    inference(forward_demodulation,[],[f15151,f744]) ).

fof(f15151,plain,
    sK20(sK23,sK22) = hd(cons(sK20(sK23,sK22),nil)),
    inference(resolution,[],[f15128,f408]) ).

fof(f15128,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | sK20(sK23,sK22) = hd(cons(sK20(sK23,sK22),X0)) ),
    inference(resolution,[],[f10916,f711]) ).

fof(f10916,plain,
    ! [X0] :
      ( ~ neq(sK23,nil)
      | sK20(sK23,sK22) = hd(cons(sK20(sK23,sK22),X0))
      | ~ ssList(X0) ),
    inference(resolution,[],[f907,f712]) ).

fof(f907,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ ssList(X2)
      | sK20(X0,X1) = hd(cons(sK20(X0,X1),X2)) ),
    inference(resolution,[],[f574,f388]) ).

fof(f388,plain,
    ! [X0,X1] :
      ( ssItem(sK20(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f260]) ).

fof(f574,plain,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | hd(cons(X1,X0)) = X1
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f183]) ).

fof(f183,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(cons(X1,X0)) = X1
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => hd(cons(X1,X0)) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f744,plain,
    sK22 = cons(sK20(sK23,sK22),nil),
    inference(resolution,[],[f743,f711]) ).

fof(f743,plain,
    ( ~ neq(sK23,nil)
    | sK22 = cons(sK20(sK23,sK22),nil) ),
    inference(resolution,[],[f390,f712]) ).

fof(f390,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK20(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f260]) ).

fof(f15515,plain,
    ! [X0] :
      ( ~ sP0(sK23,sK22)
      | cons(hd(sK22),X0) = app(cons(hd(sK22),nil),X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f15512,f575]) ).

fof(f575,plain,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).

fof(f15512,plain,
    ( ssItem(hd(sK22))
    | ~ sP0(sK23,sK22) ),
    inference(superposition,[],[f388,f15184]) ).

fof(f19215,plain,
    sK21(sK23,sK22) = tl(cons(hd(sK22),sK21(sK23,sK22))),
    inference(resolution,[],[f17828,f711]) ).

fof(f17828,plain,
    ( ~ neq(sK23,nil)
    | sK21(sK23,sK22) = tl(cons(hd(sK22),sK21(sK23,sK22))) ),
    inference(resolution,[],[f15234,f712]) ).

fof(f15234,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sK21(X0,X1) = tl(cons(hd(sK22),sK21(X0,X1))) ),
    inference(backward_demodulation,[],[f9061,f15184]) ).

fof(f9061,plain,
    ! [X0,X1] :
      ( sK21(X0,X1) = tl(cons(sK20(sK23,sK22),sK21(X0,X1)))
      | ~ sP0(X0,X1) ),
    inference(resolution,[],[f9044,f389]) ).

fof(f9044,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | tl(cons(sK20(sK23,sK22),X0)) = X0 ),
    inference(resolution,[],[f9043,f711]) ).

fof(f9043,plain,
    ! [X0] :
      ( ~ neq(sK23,nil)
      | tl(cons(sK20(sK23,sK22),X0)) = X0
      | ~ ssList(X0) ),
    inference(resolution,[],[f854,f712]) ).

fof(f854,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ ssList(X2)
      | tl(cons(sK20(X0,X1),X2)) = X2 ),
    inference(resolution,[],[f573,f388]) ).

fof(f573,plain,
    ! [X0,X1] :
      ( ~ ssItem(X1)
      | tl(cons(X1,X0)) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f182]) ).

fof(f182,plain,
    ! [X0] :
      ( ! [X1] :
          ( tl(cons(X1,X0)) = X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => tl(cons(X1,X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f1533,plain,
    sK23 = app(sK22,sK21(sK23,sK22)),
    inference(resolution,[],[f1532,f711]) ).

fof(f1532,plain,
    ( ~ neq(sK23,nil)
    | sK23 = app(sK22,sK21(sK23,sK22)) ),
    inference(forward_demodulation,[],[f1531,f744]) ).

fof(f1531,plain,
    ( sK23 = app(cons(sK20(sK23,sK22),nil),sK21(sK23,sK22))
    | ~ neq(sK23,nil) ),
    inference(resolution,[],[f391,f712]) ).

fof(f391,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | app(cons(sK20(X0,X1),nil),sK21(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f260]) ).

fof(f653,plain,
    ! [X2,X3,X0,X1] :
      ( app(X3,tl(X2)) != X2
      | ~ ssList(tl(X2))
      | ~ neq(nil,X2)
      | ~ ssList(X2)
      | ~ sP1(X0,X1,X2,X3) ),
    inference(inner_rewriting,[],[f618]) ).

fof(f618,plain,
    ! [X2,X3,X0,X1] :
      ( ~ neq(nil,X2)
      | ~ ssList(tl(X2))
      | app(X3,tl(X2)) != X2
      | ~ ssList(app(X3,tl(X2)))
      | ~ sP1(X0,X1,X2,X3) ),
    inference(equality_resolution,[],[f617]) ).

fof(f617,plain,
    ! [X2,X3,X0,X1,X5] :
      ( ~ neq(nil,X2)
      | tl(X2) != X5
      | ~ ssList(X5)
      | app(X3,X5) != X2
      | ~ ssList(app(X3,X5))
      | ~ sP1(X0,X1,X2,X3) ),
    inference(equality_resolution,[],[f386]) ).

fof(f386,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ neq(nil,X2)
      | app(X3,X5) != X4
      | tl(X2) != X5
      | ~ ssList(X5)
      | X2 != X4
      | ~ ssList(X4)
      | ~ sP1(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f255]) ).

fof(f711,plain,
    neq(sK23,nil),
    inference(duplicate_literal_removal,[],[f709]) ).

fof(f709,plain,
    ( neq(sK23,nil)
    | neq(sK23,nil) ),
    inference(resolution,[],[f385,f658]) ).

fof(f658,plain,
    ( sP1(sK22,sK23,sK23,sK22)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f657,f397]) ).

fof(f657,plain,
    ( sP1(sK24,sK23,sK23,sK22)
    | neq(sK23,nil) ),
    inference(forward_demodulation,[],[f398,f396]) ).

fof(f398,plain,
    ( neq(sK23,nil)
    | sP1(sK24,sK25,sK23,sK22) ),
    inference(cnf_transformation,[],[f265]) ).

fof(f385,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP1(X0,X1,X2,X3)
      | neq(X2,nil) ),
    inference(cnf_transformation,[],[f255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SWC014+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri May  3 20:35:23 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (21672)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (21675)WARNING: value z3 for option sas not known
% 0.12/0.36  % (21674)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36  % (21675)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)
% 0.12/0.36  % (21678)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)
% 0.12/0.36  % (21676)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36  % (21679)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)
% 0.12/0.36  % (21677)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)
% 0.12/0.36  % (21673)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.38  TRYING [1]
% 0.12/0.38  TRYING [2]
% 0.12/0.38  TRYING [1]
% 0.12/0.38  TRYING [2]
% 0.12/0.39  TRYING [3]
% 0.12/0.40  TRYING [3]
% 0.18/0.43  TRYING [4]
% 0.18/0.44  TRYING [4]
% 0.18/0.47  TRYING [1]
% 0.18/0.47  TRYING [2]
% 0.18/0.48  TRYING [3]
% 0.18/0.52  TRYING [5]
% 0.18/0.53  TRYING [4]
% 0.18/0.57  TRYING [5]
% 2.03/0.67  TRYING [5]
% 2.56/0.74  TRYING [6]
% 4.13/0.94  TRYING [6]
% 4.69/1.01  TRYING [6]
% 6.94/1.38  TRYING [7]
% 9.39/1.73  TRYING [7]
% 9.99/1.77  TRYING [7]
% 14.43/2.41  TRYING [8]
% 21.57/3.49  TRYING [8]
% 22.77/3.61  TRYING [8]
% 25.52/3.99  % (21678)First to succeed.
% 25.52/3.99  % (21678)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21672"
% 25.66/4.01  % (21678)Refutation found. Thanks to Tanya!
% 25.66/4.01  % SZS status Theorem for theBenchmark
% 25.66/4.01  % SZS output start Proof for theBenchmark
% See solution above
% 25.66/4.01  % (21678)------------------------------
% 25.66/4.01  % (21678)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 25.66/4.01  % (21678)Termination reason: Refutation
% 25.66/4.01  
% 25.66/4.01  % (21678)Memory used [KB]: 31869
% 25.66/4.01  % (21678)Time elapsed: 3.640 s
% 25.66/4.01  % (21678)Instructions burned: 7127 (million)
% 25.66/4.01  % (21672)Success in time 3.633 s
%------------------------------------------------------------------------------