TSTP Solution File: SWC256+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC256+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_uns --cores 0 -t %d %s

% Computer : n013.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 18:39:55 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   56 (  11 unt;   0 def)
%            Number of atoms       :  284 (  92 equ)
%            Maximal formula atoms :   26 (   5 avg)
%            Number of connectives :  313 (  85   ~;  75   |; 126   &)
%                                         (   8 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   72 (  32   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f320,plain,
    $false,
    inference(avatar_sat_refutation,[],[f233,f238,f260,f270,f319]) ).

fof(f319,plain,
    ( ~ spl12_1
    | ~ spl12_3 ),
    inference(avatar_contradiction_clause,[],[f318]) ).

fof(f318,plain,
    ( $false
    | ~ spl12_1
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f317,f228]) ).

fof(f228,plain,
    ( ssItem(sK8)
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f226,plain,
    ( spl12_1
  <=> ssItem(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f317,plain,
    ( ~ ssItem(sK8)
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f316,f212]) ).

fof(f212,plain,
    ~ singletonP(sK6),
    inference(definition_unfolding,[],[f174,f172]) ).

fof(f172,plain,
    sK4 = sK6,
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ( ssList(sK4)
    & ssList(sK5)
    & ~ singletonP(sK4)
    & ssList(sK7)
    & sK4 = sK6
    & ( ( nil = sK6
        & nil = sK7 )
      | ( cons(sK8,nil) = sK6
        & memberP(sK7,sK8)
        & ssItem(sK8) ) )
    & neq(sK5,nil)
    & sK5 = sK7
    & ssList(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f102,f137,f136,f135,f134,f133]) ).

fof(f133,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ? [X3] :
                    ( ~ singletonP(X0)
                    & ssList(X3)
                    & X0 = X2
                    & ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( cons(X4,nil) = X2
                          & memberP(X3,X4)
                          & ssItem(X4) ) )
                    & neq(X1,nil)
                    & X1 = X3 )
                & ssList(X2) ) ) )
   => ( ssList(sK4)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ~ singletonP(sK4)
                  & ssList(X3)
                  & sK4 = X2
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( cons(X4,nil) = X2
                        & memberP(X3,X4)
                        & ssItem(X4) ) )
                  & neq(X1,nil)
                  & X1 = X3 )
              & ssList(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ? [X3] :
                ( ~ singletonP(sK4)
                & ssList(X3)
                & sK4 = X2
                & ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( cons(X4,nil) = X2
                      & memberP(X3,X4)
                      & ssItem(X4) ) )
                & neq(X1,nil)
                & X1 = X3 )
            & ssList(X2) ) )
   => ( ssList(sK5)
      & ? [X2] :
          ( ? [X3] :
              ( ~ singletonP(sK4)
              & ssList(X3)
              & sK4 = X2
              & ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( cons(X4,nil) = X2
                    & memberP(X3,X4)
                    & ssItem(X4) ) )
              & neq(sK5,nil)
              & sK5 = X3 )
          & ssList(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ singletonP(sK4)
            & ssList(X3)
            & sK4 = X2
            & ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( cons(X4,nil) = X2
                  & memberP(X3,X4)
                  & ssItem(X4) ) )
            & neq(sK5,nil)
            & sK5 = X3 )
        & ssList(X2) )
   => ( ? [X3] :
          ( ~ singletonP(sK4)
          & ssList(X3)
          & sK4 = sK6
          & ( ( nil = sK6
              & nil = X3 )
            | ? [X4] :
                ( cons(X4,nil) = sK6
                & memberP(X3,X4)
                & ssItem(X4) ) )
          & neq(sK5,nil)
          & sK5 = X3 )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ? [X3] :
        ( ~ singletonP(sK4)
        & ssList(X3)
        & sK4 = sK6
        & ( ( nil = sK6
            & nil = X3 )
          | ? [X4] :
              ( cons(X4,nil) = sK6
              & memberP(X3,X4)
              & ssItem(X4) ) )
        & neq(sK5,nil)
        & sK5 = X3 )
   => ( ~ singletonP(sK4)
      & ssList(sK7)
      & sK4 = sK6
      & ( ( nil = sK6
          & nil = sK7 )
        | ? [X4] :
            ( cons(X4,nil) = sK6
            & memberP(sK7,X4)
            & ssItem(X4) ) )
      & neq(sK5,nil)
      & sK5 = sK7 ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ( ? [X4] :
        ( cons(X4,nil) = sK6
        & memberP(sK7,X4)
        & ssItem(X4) )
   => ( cons(sK8,nil) = sK6
      & memberP(sK7,sK8)
      & ssItem(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ? [X3] :
                  ( ~ singletonP(X0)
                  & ssList(X3)
                  & X0 = X2
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( cons(X4,nil) = X2
                        & memberP(X3,X4)
                        & ssItem(X4) ) )
                  & neq(X1,nil)
                  & X1 = X3 )
              & ssList(X2) ) ) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( neq(X1,nil)
                  & ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & X0 = X2
                  & X1 = X3
                  & ~ singletonP(X0)
                  & 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(X1,nil)
                      | ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | X0 != X2
                      | X1 != X3
                      | singletonP(X0) ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f174,plain,
    ~ singletonP(sK4),
    inference(cnf_transformation,[],[f138]) ).

fof(f316,plain,
    ( singletonP(sK6)
    | ~ ssItem(sK8)
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f311,f163]) ).

fof(f163,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f138]) ).

fof(f311,plain,
    ( ~ ssList(sK6)
    | singletonP(sK6)
    | ~ ssItem(sK8)
    | ~ spl12_3 ),
    inference(superposition,[],[f218,f237]) ).

fof(f237,plain,
    ( cons(sK8,nil) = sK6
    | ~ spl12_3 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f235,plain,
    ( spl12_3
  <=> cons(sK8,nil) = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f218,plain,
    ! [X1] :
      ( ~ ssList(cons(X1,nil))
      | singletonP(cons(X1,nil))
      | ~ ssItem(X1) ),
    inference(equality_resolution,[],[f194]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | ~ ssItem(X1)
      | cons(X1,nil) != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( ~ ssItem(X1)
              | cons(X1,nil) != X0 ) )
        & ( ( ssItem(sK11(X0))
            & cons(sK11(X0),nil) = X0 )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f146,f147]) ).

fof(f147,plain,
    ! [X0] :
      ( ? [X2] :
          ( ssItem(X2)
          & cons(X2,nil) = X0 )
     => ( ssItem(sK11(X0))
        & cons(sK11(X0),nil) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( ~ ssItem(X1)
              | cons(X1,nil) != X0 ) )
        & ( ? [X2] :
              ( ssItem(X2)
              & cons(X2,nil) = X0 )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f145]) ).

fof(f145,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( ~ ssItem(X1)
              | cons(X1,nil) != X0 ) )
        & ( ? [X1] :
              ( ssItem(X1)
              & cons(X1,nil) = X0 )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( ssItem(X1)
            & cons(X1,nil) = X0 ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

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

fof(f270,plain,
    ( ~ spl12_2
    | ~ spl12_6 ),
    inference(avatar_contradiction_clause,[],[f269]) ).

fof(f269,plain,
    ( $false
    | ~ spl12_2
    | ~ spl12_6 ),
    inference(subsumption_resolution,[],[f268,f250]) ).

fof(f250,plain,
    ( ssList(nil)
    | ~ spl12_6 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl12_6
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).

fof(f268,plain,
    ( ~ ssList(nil)
    | ~ spl12_2 ),
    inference(resolution,[],[f223,f261]) ).

fof(f261,plain,
    ( neq(nil,nil)
    | ~ spl12_2 ),
    inference(backward_demodulation,[],[f213,f232]) ).

fof(f232,plain,
    ( nil = sK7
    | ~ spl12_2 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f230,plain,
    ( spl12_2
  <=> nil = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f213,plain,
    neq(sK7,nil),
    inference(definition_unfolding,[],[f165,f164]) ).

fof(f164,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f138]) ).

fof(f165,plain,
    neq(sK5,nil),
    inference(cnf_transformation,[],[f138]) ).

fof(f223,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f219]) ).

fof(f219,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f260,plain,
    spl12_6,
    inference(avatar_split_clause,[],[f190,f249]) ).

fof(f190,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

fof(f238,plain,
    ( spl12_3
    | spl12_2 ),
    inference(avatar_split_clause,[],[f168,f230,f235]) ).

fof(f168,plain,
    ( nil = sK7
    | cons(sK8,nil) = sK6 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f233,plain,
    ( spl12_1
    | spl12_2 ),
    inference(avatar_split_clause,[],[f166,f230,f226]) ).

fof(f166,plain,
    ( nil = sK7
    | ssItem(sK8) ),
    inference(cnf_transformation,[],[f138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWC256+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n013.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   : Tue Aug 30 18:36:01 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  % (17821)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.51  % (17813)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.51  % (17813)Instruction limit reached!
% 0.21/0.51  % (17813)------------------------------
% 0.21/0.51  % (17813)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (17813)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (17813)Termination reason: Unknown
% 0.21/0.51  % (17813)Termination phase: shuffling
% 0.21/0.51  
% 0.21/0.51  % (17813)Memory used [KB]: 1535
% 0.21/0.51  % (17813)Time elapsed: 0.005 s
% 0.21/0.51  % (17813)Instructions burned: 3 (million)
% 0.21/0.51  % (17813)------------------------------
% 0.21/0.51  % (17813)------------------------------
% 0.21/0.51  % (17805)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.52  % (17807)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.52  % (17805)First to succeed.
% 0.21/0.52  % (17803)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.52  % (17809)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.21/0.52  % (17821)Also succeeded, but the first one will report.
% 0.21/0.53  % (17805)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (17805)------------------------------
% 0.21/0.53  % (17805)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (17805)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (17805)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (17805)Memory used [KB]: 6140
% 0.21/0.53  % (17805)Time elapsed: 0.078 s
% 0.21/0.53  % (17805)Instructions burned: 6 (million)
% 0.21/0.53  % (17805)------------------------------
% 0.21/0.53  % (17805)------------------------------
% 0.21/0.53  % (17798)Success in time 0.167 s
%------------------------------------------------------------------------------