TSTP Solution File: SWC408+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC408+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 : n003.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 18:41:01 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  11 unt;   0 def)
%            Number of atoms       :  184 (  43 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  207 (  53   ~;  39   |;  95   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   63 (  28   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f271,plain,
    $false,
    inference(subsumption_resolution,[],[f270,f191]) ).

fof(f191,plain,
    ~ memberP(sK2,sK4),
    inference(definition_unfolding,[],[f154,f151]) ).

fof(f151,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ( ssList(sK0)
    & ssList(sK1)
    & ssList(sK2)
    & app(sK3,sK3) = sK2
    & ~ memberP(sK0,sK4)
    & memberP(sK1,sK4)
    & ssItem(sK4)
    & sK0 = sK2
    & ssList(sK3)
    & sK3 = sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f113,f128,f127,f126,f125,f124]) ).

fof(f124,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( app(X3,X3) = X2
                    & ? [X4] :
                        ( ~ memberP(X0,X4)
                        & memberP(X1,X4)
                        & ssItem(X4) )
                    & X0 = X2
                    & ssList(X3)
                    & X1 = X3 ) ) ) )
   => ( ssList(sK0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( app(X3,X3) = X2
                  & ? [X4] :
                      ( ~ memberP(sK0,X4)
                      & memberP(X1,X4)
                      & ssItem(X4) )
                  & sK0 = X2
                  & ssList(X3)
                  & X1 = X3 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( app(X3,X3) = X2
                & ? [X4] :
                    ( ~ memberP(sK0,X4)
                    & memberP(X1,X4)
                    & ssItem(X4) )
                & sK0 = X2
                & ssList(X3)
                & X1 = X3 ) ) )
   => ( ssList(sK1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( app(X3,X3) = X2
              & ? [X4] :
                  ( ~ memberP(sK0,X4)
                  & memberP(sK1,X4)
                  & ssItem(X4) )
              & sK0 = X2
              & ssList(X3)
              & sK1 = X3 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( app(X3,X3) = X2
            & ? [X4] :
                ( ~ memberP(sK0,X4)
                & memberP(sK1,X4)
                & ssItem(X4) )
            & sK0 = X2
            & ssList(X3)
            & sK1 = X3 ) )
   => ( ssList(sK2)
      & ? [X3] :
          ( app(X3,X3) = sK2
          & ? [X4] :
              ( ~ memberP(sK0,X4)
              & memberP(sK1,X4)
              & ssItem(X4) )
          & sK0 = sK2
          & ssList(X3)
          & sK1 = X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ? [X3] :
        ( app(X3,X3) = sK2
        & ? [X4] :
            ( ~ memberP(sK0,X4)
            & memberP(sK1,X4)
            & ssItem(X4) )
        & sK0 = sK2
        & ssList(X3)
        & sK1 = X3 )
   => ( app(sK3,sK3) = sK2
      & ? [X4] :
          ( ~ memberP(sK0,X4)
          & memberP(sK1,X4)
          & ssItem(X4) )
      & sK0 = sK2
      & ssList(sK3)
      & sK3 = sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ? [X4] :
        ( ~ memberP(sK0,X4)
        & memberP(sK1,X4)
        & ssItem(X4) )
   => ( ~ memberP(sK0,sK4)
      & memberP(sK1,sK4)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( app(X3,X3) = X2
                  & ? [X4] :
                      ( ~ memberP(X0,X4)
                      & memberP(X1,X4)
                      & ssItem(X4) )
                  & X0 = X2
                  & ssList(X3)
                  & X1 = X3 ) ) ) ),
    inference(flattening,[],[f112]) ).

fof(f112,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( app(X3,X3) = X2
                  & X0 = X2
                  & ? [X4] :
                      ( memberP(X1,X4)
                      & ~ memberP(X0,X4)
                      & ssItem(X4) )
                  & 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)
                   => ( app(X3,X3) != X2
                      | X0 != X2
                      | ! [X4] :
                          ( ssItem(X4)
                         => ( ~ memberP(X1,X4)
                            | memberP(X0,X4) ) )
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

fof(f154,plain,
    ~ memberP(sK0,sK4),
    inference(cnf_transformation,[],[f129]) ).

fof(f270,plain,
    memberP(sK2,sK4),
    inference(subsumption_resolution,[],[f268,f152]) ).

fof(f152,plain,
    ssItem(sK4),
    inference(cnf_transformation,[],[f129]) ).

fof(f268,plain,
    ( ~ ssItem(sK4)
    | memberP(sK2,sK4) ),
    inference(resolution,[],[f267,f153]) ).

fof(f153,plain,
    memberP(sK1,sK4),
    inference(cnf_transformation,[],[f129]) ).

fof(f267,plain,
    ! [X8] :
      ( ~ memberP(sK1,X8)
      | memberP(sK2,X8)
      | ~ ssItem(X8) ),
    inference(subsumption_resolution,[],[f266,f157]) ).

fof(f157,plain,
    ssList(sK1),
    inference(cnf_transformation,[],[f129]) ).

fof(f266,plain,
    ! [X8] :
      ( ~ ssList(sK1)
      | memberP(sK2,X8)
      | ~ ssItem(X8)
      | ~ memberP(sK1,X8) ),
    inference(duplicate_literal_removal,[],[f261]) ).

fof(f261,plain,
    ! [X8] :
      ( ~ ssItem(X8)
      | memberP(sK2,X8)
      | ~ ssList(sK1)
      | ~ ssList(sK1)
      | ~ memberP(sK1,X8) ),
    inference(superposition,[],[f163,f190]) ).

fof(f190,plain,
    app(sK1,sK1) = sK2,
    inference(definition_unfolding,[],[f155,f149,f149]) ).

fof(f149,plain,
    sK3 = sK1,
    inference(cnf_transformation,[],[f129]) ).

fof(f155,plain,
    app(sK3,sK3) = sK2,
    inference(cnf_transformation,[],[f129]) ).

fof(f163,plain,
    ! [X2,X0,X1] :
      ( memberP(app(X1,X2),X0)
      | ~ memberP(X2,X0)
      | ~ ssItem(X0)
      | ~ ssList(X2)
      | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X1,X0)
                    & ~ memberP(X2,X0) ) )
                & ( memberP(X1,X0)
                  | memberP(X2,X0)
                  | ~ memberP(app(X1,X2),X0) ) ) ) ) ),
    inference(flattening,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ( ( memberP(app(X1,X2),X0)
                  | ( ~ memberP(X1,X0)
                    & ~ memberP(X2,X0) ) )
                & ( memberP(X1,X0)
                  | memberP(X2,X0)
                  | ~ memberP(app(X1,X2),X0) ) ) ) ) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ! [X1] :
          ( ~ ssList(X1)
          | ! [X2] :
              ( ~ ssList(X2)
              | ( memberP(app(X1,X2),X0)
              <=> ( memberP(X1,X0)
                  | memberP(X2,X0) ) ) ) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(app(X1,X2),X0)
              <=> ( memberP(X1,X0)
                  | memberP(X2,X0) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWC408+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 18:54:37 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (21287)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)
% 0.20/0.52  % (21295)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (21284)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.53  % (21279)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.54  % (21285)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)
% 0.20/0.54  % (21282)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (21301)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)
% 0.20/0.54  % (21298)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.54  % (21288)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.54  % (21302)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.54  % (21308)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.20/0.54  % (21294)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54  % (21285)First to succeed.
% 0.20/0.54  % (21293)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)
% 0.20/0.54  % (21293)Instruction limit reached!
% 0.20/0.54  % (21293)------------------------------
% 0.20/0.54  % (21293)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (21293)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (21293)Termination reason: Unknown
% 0.20/0.54  % (21293)Termination phase: Preprocessing 3
% 0.20/0.54  
% 0.20/0.54  % (21293)Memory used [KB]: 1535
% 0.20/0.54  % (21293)Time elapsed: 0.003 s
% 0.20/0.54  % (21293)Instructions burned: 3 (million)
% 0.20/0.54  % (21293)------------------------------
% 0.20/0.54  % (21293)------------------------------
% 0.20/0.54  % (21299)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.54  % (21284)Also succeeded, but the first one will report.
% 0.20/0.55  % (21306)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.55  % (21285)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (21285)------------------------------
% 0.20/0.55  % (21285)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (21285)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (21285)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (21285)Memory used [KB]: 6140
% 0.20/0.55  % (21285)Time elapsed: 0.121 s
% 0.20/0.55  % (21285)Instructions burned: 6 (million)
% 0.20/0.55  % (21285)------------------------------
% 0.20/0.55  % (21285)------------------------------
% 0.20/0.55  % (21278)Success in time 0.19 s
%------------------------------------------------------------------------------