TSTP Solution File: SWC204+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWC204+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n008.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 : Wed Aug 31 18:42:23 EDT 2022

% Result   : Theorem 2.09s 0.65s
% Output   : Refutation 2.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   95 (  18 unt;   0 def)
%            Number of atoms       :  444 ( 161 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  560 ( 211   ~; 222   |; 100   &)
%                                         (   2 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   99 (  71   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1160,plain,
    $false,
    inference(subsumption_resolution,[],[f1152,f805]) ).

fof(f805,plain,
    ~ neq(nil,nil),
    inference(subsumption_resolution,[],[f800,f595]) ).

fof(f595,plain,
    neq(sK47,nil),
    inference(duplicate_literal_removal,[],[f518]) ).

fof(f518,plain,
    ( neq(sK47,nil)
    | neq(sK47,nil) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f329,plain,
    ( ssList(sK47)
    & sK48 = sK46
    & ( ( neq(sK47,nil)
        & ! [X4] :
            ( sK49 = X4
            | ~ ssList(X4)
            | ! [X5] :
                ( app(sK48,X5) != X4
                | ~ ssList(X5)
                | ~ neq(nil,sK49)
                | tl(sK49) != X5 ) )
        & ~ neq(sK46,nil) )
      | ( ~ neq(sK49,nil)
        & neq(sK47,nil) ) )
    & sK47 = sK49
    & ssList(sK49)
    & ssList(sK48)
    & ssList(sK46) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48,sK49])],[f149,f328,f327,f326,f325]) ).

fof(f325,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( X0 = X2
                    & ( ( neq(X1,nil)
                        & ! [X4] :
                            ( X3 = X4
                            | ~ ssList(X4)
                            | ! [X5] :
                                ( app(X2,X5) != X4
                                | ~ ssList(X5)
                                | ~ neq(nil,X3)
                                | tl(X3) != X5 ) )
                        & ~ neq(X0,nil) )
                      | ( ~ neq(X3,nil)
                        & neq(X1,nil) ) )
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) ) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( sK46 = X2
                  & ( ( neq(X1,nil)
                      & ! [X4] :
                          ( X3 = X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | ~ ssList(X5)
                              | ~ neq(nil,X3)
                              | tl(X3) != X5 ) )
                      & ~ neq(sK46,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) ) )
      & ssList(sK46) ) ),
    introduced(choice_axiom,[]) ).

fof(f326,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( sK46 = X2
                & ( ( neq(X1,nil)
                    & ! [X4] :
                        ( X3 = X4
                        | ~ ssList(X4)
                        | ! [X5] :
                            ( app(X2,X5) != X4
                            | ~ ssList(X5)
                            | ~ neq(nil,X3)
                            | tl(X3) != X5 ) )
                    & ~ neq(sK46,nil) )
                  | ( ~ neq(X3,nil)
                    & neq(X1,nil) ) )
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) ) )
   => ( ssList(sK47)
      & ? [X2] :
          ( ? [X3] :
              ( sK46 = X2
              & ( ( neq(sK47,nil)
                  & ! [X4] :
                      ( X3 = X4
                      | ~ ssList(X4)
                      | ! [X5] :
                          ( app(X2,X5) != X4
                          | ~ ssList(X5)
                          | ~ neq(nil,X3)
                          | tl(X3) != X5 ) )
                  & ~ neq(sK46,nil) )
                | ( ~ neq(X3,nil)
                  & neq(sK47,nil) ) )
              & sK47 = X3
              & ssList(X3) )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f327,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( sK46 = X2
            & ( ( neq(sK47,nil)
                & ! [X4] :
                    ( X3 = X4
                    | ~ ssList(X4)
                    | ! [X5] :
                        ( app(X2,X5) != X4
                        | ~ ssList(X5)
                        | ~ neq(nil,X3)
                        | tl(X3) != X5 ) )
                & ~ neq(sK46,nil) )
              | ( ~ neq(X3,nil)
                & neq(sK47,nil) ) )
            & sK47 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( sK48 = sK46
          & ( ( neq(sK47,nil)
              & ! [X4] :
                  ( X3 = X4
                  | ~ ssList(X4)
                  | ! [X5] :
                      ( app(sK48,X5) != X4
                      | ~ ssList(X5)
                      | ~ neq(nil,X3)
                      | tl(X3) != X5 ) )
              & ~ neq(sK46,nil) )
            | ( ~ neq(X3,nil)
              & neq(sK47,nil) ) )
          & sK47 = X3
          & ssList(X3) )
      & ssList(sK48) ) ),
    introduced(choice_axiom,[]) ).

fof(f328,plain,
    ( ? [X3] :
        ( sK48 = sK46
        & ( ( neq(sK47,nil)
            & ! [X4] :
                ( X3 = X4
                | ~ ssList(X4)
                | ! [X5] :
                    ( app(sK48,X5) != X4
                    | ~ ssList(X5)
                    | ~ neq(nil,X3)
                    | tl(X3) != X5 ) )
            & ~ neq(sK46,nil) )
          | ( ~ neq(X3,nil)
            & neq(sK47,nil) ) )
        & sK47 = X3
        & ssList(X3) )
   => ( sK48 = sK46
      & ( ( neq(sK47,nil)
          & ! [X4] :
              ( sK49 = X4
              | ~ ssList(X4)
              | ! [X5] :
                  ( app(sK48,X5) != X4
                  | ~ ssList(X5)
                  | ~ neq(nil,sK49)
                  | tl(sK49) != X5 ) )
          & ~ neq(sK46,nil) )
        | ( ~ neq(sK49,nil)
          & neq(sK47,nil) ) )
      & sK47 = sK49
      & ssList(sK49) ) ),
    introduced(choice_axiom,[]) ).

fof(f149,plain,
    ? [X0] :
      ( ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( X0 = X2
                  & ( ( neq(X1,nil)
                      & ! [X4] :
                          ( X3 = X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | ~ ssList(X5)
                              | ~ neq(nil,X3)
                              | tl(X3) != X5 ) )
                      & ~ neq(X0,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) ) )
      & ssList(X0) ),
    inference(flattening,[],[f148]) ).

fof(f148,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( neq(X1,nil)
                      & ! [X4] :
                          ( X3 = X4
                          | ~ ssList(X4)
                          | ! [X5] :
                              ( app(X2,X5) != X4
                              | ~ ssList(X5)
                              | ~ neq(nil,X3)
                              | tl(X3) != X5 ) )
                      & ~ neq(X0,nil) )
                    | ( ~ neq(X3,nil)
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & 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)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( neq(X0,nil)
                          | ? [X4] :
                              ( X3 != X4
                              & ssList(X4)
                              & ? [X5] :
                                  ( ssList(X5)
                                  & app(X2,X5) = X4
                                  & tl(X3) = X5
                                  & neq(nil,X3) ) )
                          | ~ 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) )
                      & ( neq(X0,nil)
                        | ? [X4] :
                            ( X3 != X4
                            & ssList(X4)
                            & ? [X5] :
                                ( ssList(X5)
                                & app(X2,X5) = X4
                                & tl(X3) = X5
                                & neq(nil,X3) ) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f800,plain,
    ( ~ neq(nil,nil)
    | ~ neq(sK47,nil) ),
    inference(backward_demodulation,[],[f607,f796]) ).

fof(f796,plain,
    nil = sK46,
    inference(subsumption_resolution,[],[f795,f510]) ).

fof(f510,plain,
    ssList(sK46),
    inference(cnf_transformation,[],[f329]) ).

fof(f795,plain,
    ( nil = sK46
    | ~ ssList(sK46) ),
    inference(subsumption_resolution,[],[f794,f595]) ).

fof(f794,plain,
    ( nil = sK46
    | ~ neq(sK47,nil)
    | ~ ssList(sK46) ),
    inference(subsumption_resolution,[],[f787,f485]) ).

fof(f485,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f787,plain,
    ( nil = sK46
    | ~ ssList(nil)
    | ~ neq(sK47,nil)
    | ~ ssList(sK46) ),
    inference(resolution,[],[f386,f607]) ).

fof(f386,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X0)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f256]) ).

fof(f256,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f167]) ).

fof(f167,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ssList(X1)
          | ( X0 != X1
          <=> neq(X0,X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f607,plain,
    ( ~ neq(sK46,nil)
    | ~ neq(sK47,nil) ),
    inference(backward_demodulation,[],[f515,f513]) ).

fof(f513,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f329]) ).

fof(f515,plain,
    ( ~ neq(sK49,nil)
    | ~ neq(sK46,nil) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f1152,plain,
    neq(nil,nil),
    inference(backward_demodulation,[],[f595,f1150]) ).

fof(f1150,plain,
    nil = sK47,
    inference(subsumption_resolution,[],[f1149,f606]) ).

fof(f606,plain,
    ssList(sK47),
    inference(backward_demodulation,[],[f512,f513]) ).

fof(f512,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f329]) ).

fof(f1149,plain,
    ( ~ ssList(sK47)
    | nil = sK47 ),
    inference(duplicate_literal_removal,[],[f1148]) ).

fof(f1148,plain,
    ( nil = sK47
    | ~ ssList(sK47)
    | nil = sK47 ),
    inference(resolution,[],[f1147,f508]) ).

fof(f508,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssItem(hd(X0))
      | nil = X0 ),
    inference(flattening,[],[f164]) ).

fof(f164,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f1147,plain,
    ( ~ ssItem(hd(sK47))
    | nil = sK47 ),
    inference(subsumption_resolution,[],[f1146,f844]) ).

fof(f844,plain,
    ( sF57 = sK47
    | nil = sK47 ),
    inference(duplicate_literal_removal,[],[f831]) ).

fof(f831,plain,
    ( nil = sK47
    | nil = sK47
    | sF57 = sK47 ),
    inference(superposition,[],[f807,f812]) ).

fof(f812,plain,
    ( sF57 = sF58
    | nil = sK47 ),
    inference(superposition,[],[f799,f708]) ).

fof(f708,plain,
    ( app(nil,sF57) = sF57
    | nil = sK47 ),
    inference(resolution,[],[f706,f541]) ).

fof(f541,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f706,plain,
    ( ssList(sF57)
    | nil = sK47 ),
    inference(subsumption_resolution,[],[f705,f606]) ).

fof(f705,plain,
    ( ~ ssList(sK47)
    | nil = sK47
    | ssList(sF57) ),
    inference(superposition,[],[f526,f612]) ).

fof(f612,plain,
    tl(sK47) = sF57,
    inference(forward_demodulation,[],[f590,f513]) ).

fof(f590,plain,
    tl(sK49) = sF57,
    introduced(function_definition,[]) ).

fof(f526,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | ~ ssList(X0)
      | nil = X0 ),
    inference(cnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ssList(tl(X0))
      | nil = X0 ),
    inference(flattening,[],[f209]) ).

fof(f209,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(f799,plain,
    app(nil,sF57) = sF58,
    inference(backward_demodulation,[],[f605,f796]) ).

fof(f605,plain,
    app(sK46,sF57) = sF58,
    inference(backward_demodulation,[],[f591,f520]) ).

fof(f520,plain,
    sK48 = sK46,
    inference(cnf_transformation,[],[f329]) ).

fof(f591,plain,
    app(sK48,sF57) = sF58,
    introduced(function_definition,[]) ).

fof(f807,plain,
    ( sK47 = sF58
    | nil = sK47 ),
    inference(subsumption_resolution,[],[f806,f485]) ).

fof(f806,plain,
    ( nil = sK47
    | ~ ssList(nil)
    | sK47 = sF58 ),
    inference(subsumption_resolution,[],[f792,f606]) ).

fof(f792,plain,
    ( ~ ssList(sK47)
    | nil = sK47
    | ~ ssList(nil)
    | sK47 = sF58 ),
    inference(duplicate_literal_removal,[],[f790]) ).

fof(f790,plain,
    ( ~ ssList(sK47)
    | ~ ssList(nil)
    | nil = sK47
    | nil = sK47
    | sK47 = sF58 ),
    inference(resolution,[],[f386,f714]) ).

fof(f714,plain,
    ( ~ neq(nil,sK47)
    | nil = sK47
    | sK47 = sF58 ),
    inference(subsumption_resolution,[],[f711,f706]) ).

fof(f711,plain,
    ( ~ ssList(sF57)
    | nil = sK47
    | ~ neq(nil,sK47)
    | sK47 = sF58 ),
    inference(resolution,[],[f707,f615]) ).

fof(f615,plain,
    ( ~ ssList(sF58)
    | ~ ssList(sF57)
    | sK47 = sF58
    | ~ neq(nil,sK47) ),
    inference(subsumption_resolution,[],[f614,f610]) ).

fof(f610,plain,
    ( ~ ssList(sF58)
    | ~ neq(sK47,nil)
    | ~ neq(nil,sK47)
    | sK47 = sF58
    | ~ ssList(sF57) ),
    inference(forward_demodulation,[],[f609,f513]) ).

fof(f609,plain,
    ( ~ ssList(sF58)
    | ~ neq(sK47,nil)
    | ~ ssList(sF57)
    | sK49 = sF58
    | ~ neq(nil,sK47) ),
    inference(forward_demodulation,[],[f608,f513]) ).

fof(f608,plain,
    ( ~ neq(nil,sK49)
    | ~ neq(sK47,nil)
    | ~ ssList(sF58)
    | sK49 = sF58
    | ~ ssList(sF57) ),
    inference(backward_demodulation,[],[f592,f513]) ).

fof(f592,plain,
    ( ~ ssList(sF57)
    | ~ neq(nil,sK49)
    | sK49 = sF58
    | ~ neq(sK49,nil)
    | ~ ssList(sF58) ),
    inference(definition_folding,[],[f584,f590,f591,f590,f591,f590]) ).

fof(f584,plain,
    ( app(sK48,tl(sK49)) = sK49
    | ~ ssList(app(sK48,tl(sK49)))
    | ~ ssList(tl(sK49))
    | ~ neq(nil,sK49)
    | ~ neq(sK49,nil) ),
    inference(equality_resolution,[],[f583]) ).

fof(f583,plain,
    ! [X5] :
      ( app(sK48,X5) = sK49
      | ~ ssList(app(sK48,X5))
      | ~ ssList(X5)
      | ~ neq(nil,sK49)
      | tl(sK49) != X5
      | ~ neq(sK49,nil) ),
    inference(equality_resolution,[],[f517]) ).

fof(f517,plain,
    ! [X4,X5] :
      ( sK49 = X4
      | ~ ssList(X4)
      | app(sK48,X5) != X4
      | ~ ssList(X5)
      | ~ neq(nil,sK49)
      | tl(sK49) != X5
      | ~ neq(sK49,nil) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f614,plain,
    ( ~ ssList(sF57)
    | ~ ssList(sF58)
    | sK47 = sF58
    | neq(sK47,nil)
    | ~ neq(nil,sK47) ),
    inference(forward_demodulation,[],[f613,f513]) ).

fof(f613,plain,
    ( ~ neq(nil,sK47)
    | ~ ssList(sF58)
    | sK49 = sF58
    | ~ ssList(sF57)
    | neq(sK47,nil) ),
    inference(forward_demodulation,[],[f593,f513]) ).

fof(f593,plain,
    ( ~ neq(nil,sK49)
    | neq(sK47,nil)
    | sK49 = sF58
    | ~ ssList(sF58)
    | ~ ssList(sF57) ),
    inference(definition_folding,[],[f586,f590,f591,f590,f591,f590]) ).

fof(f586,plain,
    ( app(sK48,tl(sK49)) = sK49
    | ~ ssList(app(sK48,tl(sK49)))
    | ~ ssList(tl(sK49))
    | ~ neq(nil,sK49)
    | neq(sK47,nil) ),
    inference(equality_resolution,[],[f585]) ).

fof(f585,plain,
    ! [X5] :
      ( app(sK48,X5) = sK49
      | ~ ssList(app(sK48,X5))
      | ~ ssList(X5)
      | ~ neq(nil,sK49)
      | tl(sK49) != X5
      | neq(sK47,nil) ),
    inference(equality_resolution,[],[f516]) ).

fof(f516,plain,
    ! [X4,X5] :
      ( sK49 = X4
      | ~ ssList(X4)
      | app(sK48,X5) != X4
      | ~ ssList(X5)
      | ~ neq(nil,sK49)
      | tl(sK49) != X5
      | neq(sK47,nil) ),
    inference(cnf_transformation,[],[f329]) ).

fof(f707,plain,
    ( ssList(sF58)
    | nil = sK47 ),
    inference(resolution,[],[f706,f702]) ).

fof(f702,plain,
    ( ~ ssList(sF57)
    | ssList(sF58) ),
    inference(subsumption_resolution,[],[f695,f510]) ).

fof(f695,plain,
    ( ssList(sF58)
    | ~ ssList(sF57)
    | ~ ssList(sK46) ),
    inference(superposition,[],[f494,f605]) ).

fof(f494,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,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(f1146,plain,
    ( ~ ssItem(hd(sK47))
    | sF57 != sK47
    | nil = sK47 ),
    inference(subsumption_resolution,[],[f1141,f706]) ).

fof(f1141,plain,
    ( ~ ssList(sF57)
    | nil = sK47
    | ~ ssItem(hd(sK47))
    | sF57 != sK47 ),
    inference(superposition,[],[f544,f1137]) ).

fof(f1137,plain,
    ( cons(hd(sK47),sF57) = sK47
    | nil = sK47 ),
    inference(forward_demodulation,[],[f1131,f612]) ).

fof(f1131,plain,
    ( nil = sK47
    | cons(hd(sK47),tl(sK47)) = sK47 ),
    inference(resolution,[],[f440,f606]) ).

fof(f440,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(hd(X0),tl(X0)) = X0
      | nil = X0 ),
    inference(cnf_transformation,[],[f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | cons(hd(X0),tl(X0)) = X0
      | nil = X0 ),
    inference(flattening,[],[f176]) ).

fof(f176,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).

fof(f544,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f172,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC204+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 18:37:55 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.52  % (13223)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (13225)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53  % (13225)Instruction limit reached!
% 0.20/0.53  % (13225)------------------------------
% 0.20/0.53  % (13225)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (13225)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (13225)Termination reason: Unknown
% 0.20/0.53  % (13225)Termination phase: Preprocessing 1
% 0.20/0.53  
% 0.20/0.53  % (13225)Memory used [KB]: 895
% 0.20/0.53  % (13225)Time elapsed: 0.002 s
% 0.20/0.53  % (13225)Instructions burned: 2 (million)
% 0.20/0.53  % (13225)------------------------------
% 0.20/0.53  % (13225)------------------------------
% 0.20/0.53  % (13231)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53  % (13239)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53  % (13233)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54  % (13241)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.44/0.54  % (13222)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.44/0.54  % (13220)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.44/0.54  % (13224)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.44/0.55  % (13236)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.55  TRYING [1]
% 1.44/0.55  % (13219)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.44/0.55  % (13234)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.55  % (13221)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.44/0.56  TRYING [2]
% 1.44/0.56  % (13244)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.44/0.56  % (13232)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.44/0.56  % (13238)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.44/0.56  % (13235)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.58/0.56  % (13237)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.58/0.56  % (13217)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.58/0.56  % (13226)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.58/0.56  % (13243)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.58/0.57  % (13245)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.58/0.57  % (13224)Instruction limit reached!
% 1.58/0.57  % (13224)------------------------------
% 1.58/0.57  % (13224)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.57  % (13224)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.57  % (13224)Termination reason: Unknown
% 1.58/0.57  % (13224)Termination phase: Property scanning
% 1.58/0.57  
% 1.58/0.57  % (13224)Memory used [KB]: 1279
% 1.58/0.57  % (13224)Time elapsed: 0.005 s
% 1.58/0.57  % (13224)Instructions burned: 7 (million)
% 1.58/0.57  % (13224)------------------------------
% 1.58/0.57  % (13224)------------------------------
% 1.58/0.57  % (13240)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.58/0.57  % (13246)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.58/0.57  % (13228)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.58/0.57  % (13218)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.58/0.57  % (13227)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.58/0.57  % (13230)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.58/0.57  % (13229)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.58/0.57  % (13242)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.58/0.58  TRYING [3]
% 1.58/0.59  % (13223)Instruction limit reached!
% 1.58/0.59  % (13223)------------------------------
% 1.58/0.59  % (13223)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.59  % (13223)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.59  % (13223)Termination reason: Unknown
% 1.58/0.59  % (13223)Termination phase: Finite model building constraint generation
% 1.58/0.59  
% 1.58/0.59  % (13223)Memory used [KB]: 7675
% 1.58/0.59  % (13223)Time elapsed: 0.153 s
% 1.58/0.59  % (13223)Instructions burned: 54 (million)
% 1.58/0.59  % (13223)------------------------------
% 1.58/0.59  % (13223)------------------------------
% 1.58/0.60  TRYING [1]
% 1.58/0.60  % (13218)Refutation not found, incomplete strategy% (13218)------------------------------
% 1.58/0.60  % (13218)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.60  % (13218)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.60  % (13218)Termination reason: Refutation not found, incomplete strategy
% 1.58/0.60  
% 1.58/0.60  % (13218)Memory used [KB]: 6012
% 1.58/0.60  % (13218)Time elapsed: 0.168 s
% 1.58/0.60  % (13218)Instructions burned: 20 (million)
% 1.58/0.60  % (13218)------------------------------
% 1.58/0.60  % (13218)------------------------------
% 1.58/0.60  TRYING [2]
% 1.58/0.61  TRYING [1]
% 1.58/0.62  % (13231)Instruction limit reached!
% 1.58/0.62  % (13231)------------------------------
% 1.58/0.62  % (13231)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.62  % (13231)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.62  % (13231)Termination reason: Unknown
% 1.58/0.62  % (13231)Termination phase: Saturation
% 1.58/0.62  
% 1.58/0.62  % (13231)Memory used [KB]: 7036
% 1.58/0.62  % (13231)Time elapsed: 0.048 s
% 1.58/0.62  % (13231)Instructions burned: 68 (million)
% 1.58/0.62  % (13231)------------------------------
% 1.58/0.62  % (13231)------------------------------
% 1.58/0.62  TRYING [2]
% 1.58/0.62  % (13222)Instruction limit reached!
% 1.58/0.62  % (13222)------------------------------
% 1.58/0.62  % (13222)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.58/0.62  % (13222)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.58/0.62  % (13222)Termination reason: Unknown
% 1.58/0.62  % (13222)Termination phase: Saturation
% 1.58/0.62  
% 1.58/0.62  % (13222)Memory used [KB]: 6396
% 1.58/0.62  % (13222)Time elapsed: 0.199 s
% 1.58/0.62  % (13222)Instructions burned: 49 (million)
% 1.58/0.62  % (13222)------------------------------
% 1.58/0.62  % (13222)------------------------------
% 2.09/0.63  % (13232)First to succeed.
% 2.09/0.63  TRYING [3]
% 2.09/0.63  % (13220)Instruction limit reached!
% 2.09/0.63  % (13220)------------------------------
% 2.09/0.63  % (13220)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.63  TRYING [3]
% 2.09/0.63  % (13219)Instruction limit reached!
% 2.09/0.63  % (13219)------------------------------
% 2.09/0.63  % (13219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.63  % (13219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.63  % (13219)Termination reason: Unknown
% 2.09/0.63  % (13219)Termination phase: Saturation
% 2.09/0.63  
% 2.09/0.63  % (13219)Memory used [KB]: 1663
% 2.09/0.63  % (13219)Time elapsed: 0.212 s
% 2.09/0.63  % (13219)Instructions burned: 37 (million)
% 2.09/0.63  % (13219)------------------------------
% 2.09/0.63  % (13219)------------------------------
% 2.09/0.64  % (13226)Instruction limit reached!
% 2.09/0.64  % (13226)------------------------------
% 2.09/0.64  % (13226)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.64  % (13226)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.64  % (13226)Termination reason: Unknown
% 2.09/0.64  % (13226)Termination phase: Saturation
% 2.09/0.64  
% 2.09/0.64  % (13226)Memory used [KB]: 2174
% 2.09/0.64  % (13226)Time elapsed: 0.205 s
% 2.09/0.64  % (13226)Instructions burned: 52 (million)
% 2.09/0.64  % (13226)------------------------------
% 2.09/0.64  % (13226)------------------------------
% 2.09/0.64  TRYING [3]
% 2.09/0.64  % (13234)Instruction limit reached!
% 2.09/0.64  % (13234)------------------------------
% 2.09/0.64  % (13234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.64  % (13234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.64  % (13234)Termination reason: Unknown
% 2.09/0.64  % (13234)Termination phase: Finite model building constraint generation
% 2.09/0.64  
% 2.09/0.64  % (13234)Memory used [KB]: 7803
% 2.09/0.64  % (13234)Time elapsed: 0.190 s
% 2.09/0.64  % (13234)Instructions burned: 60 (million)
% 2.09/0.64  % (13234)------------------------------
% 2.09/0.64  % (13234)------------------------------
% 2.09/0.65  % (13227)Instruction limit reached!
% 2.09/0.65  % (13227)------------------------------
% 2.09/0.65  % (13227)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.65  % (13220)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.65  % (13220)Termination reason: Unknown
% 2.09/0.65  % (13220)Termination phase: Saturation
% 2.09/0.65  
% 2.09/0.65  % (13220)Memory used [KB]: 6396
% 2.09/0.65  % (13220)Time elapsed: 0.227 s
% 2.09/0.65  % (13220)Instructions burned: 52 (million)
% 2.09/0.65  % (13220)------------------------------
% 2.09/0.65  % (13220)------------------------------
% 2.09/0.65  % (13227)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.65  % (13227)Termination reason: Unknown
% 2.09/0.65  % (13227)Termination phase: Saturation
% 2.09/0.65  
% 2.09/0.65  % (13227)Memory used [KB]: 6652
% 2.09/0.65  % (13227)Time elapsed: 0.218 s
% 2.09/0.65  % (13227)Instructions burned: 51 (million)
% 2.09/0.65  % (13227)------------------------------
% 2.09/0.65  % (13227)------------------------------
% 2.09/0.65  % (13232)Refutation found. Thanks to Tanya!
% 2.09/0.65  % SZS status Theorem for theBenchmark
% 2.09/0.65  % SZS output start Proof for theBenchmark
% See solution above
% 2.09/0.65  % (13232)------------------------------
% 2.09/0.65  % (13232)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.65  % (13232)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.65  % (13232)Termination reason: Refutation
% 2.09/0.65  
% 2.09/0.65  % (13232)Memory used [KB]: 1918
% 2.09/0.65  % (13232)Time elapsed: 0.229 s
% 2.09/0.65  % (13232)Instructions burned: 47 (million)
% 2.09/0.65  % (13232)------------------------------
% 2.09/0.65  % (13232)------------------------------
% 2.09/0.65  % (13216)Success in time 0.297 s
%------------------------------------------------------------------------------