TSTP Solution File: SWC129+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SWC129+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 : n020.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 18:39:00 EDT 2022

% Result   : Theorem 1.48s 0.57s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (  12 unt;   0 def)
%            Number of atoms       :  137 (  35 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  154 (  49   ~;  22   |;  66   &)
%                                         (   3 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   40 (  16   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f296,plain,
    $false,
    inference(avatar_sat_refutation,[],[f227,f295]) ).

fof(f295,plain,
    ~ spl15_1,
    inference(avatar_contradiction_clause,[],[f294]) ).

fof(f294,plain,
    ( $false
    | ~ spl15_1 ),
    inference(subsumption_resolution,[],[f291,f156]) ).

fof(f156,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).

fof(f291,plain,
    ( ~ cyclefreeP(nil)
    | ~ spl15_1 ),
    inference(backward_demodulation,[],[f165,f286]) ).

fof(f286,plain,
    ( nil = sK3
    | ~ spl15_1 ),
    inference(subsumption_resolution,[],[f285,f220]) ).

fof(f220,plain,
    ( ssList(nil)
    | ~ spl15_1 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f219,plain,
    ( spl15_1
  <=> ssList(nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f285,plain,
    ( nil = sK3
    | ~ ssList(nil) ),
    inference(subsumption_resolution,[],[f280,f168]) ).

fof(f168,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ( ssList(sK2)
    & ssList(sK3)
    & ssList(sK4)
    & sK5 = sK3
    & ~ cyclefreeP(sK3)
    & ssList(sK5)
    & sK2 = sK4
    & ~ neq(sK5,nil) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f124,f134,f133,f132,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ssList(X0)
        & ? [X1] :
            ( ssList(X1)
            & ? [X2] :
                ( ssList(X2)
                & ? [X3] :
                    ( X1 = X3
                    & ~ cyclefreeP(X1)
                    & ssList(X3)
                    & X0 = X2
                    & ~ neq(X3,nil) ) ) ) )
   => ( ssList(sK2)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ~ cyclefreeP(X1)
                  & ssList(X3)
                  & sK2 = X2
                  & ~ neq(X3,nil) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X1] :
        ( ssList(X1)
        & ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( X1 = X3
                & ~ cyclefreeP(X1)
                & ssList(X3)
                & sK2 = X2
                & ~ neq(X3,nil) ) ) )
   => ( ssList(sK3)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( sK3 = X3
              & ~ cyclefreeP(sK3)
              & ssList(X3)
              & sK2 = X2
              & ~ neq(X3,nil) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( ? [X2] :
        ( ssList(X2)
        & ? [X3] :
            ( sK3 = X3
            & ~ cyclefreeP(sK3)
            & ssList(X3)
            & sK2 = X2
            & ~ neq(X3,nil) ) )
   => ( ssList(sK4)
      & ? [X3] :
          ( sK3 = X3
          & ~ cyclefreeP(sK3)
          & ssList(X3)
          & sK2 = sK4
          & ~ neq(X3,nil) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X3] :
        ( sK3 = X3
        & ~ cyclefreeP(sK3)
        & ssList(X3)
        & sK2 = sK4
        & ~ neq(X3,nil) )
   => ( sK5 = sK3
      & ~ cyclefreeP(sK3)
      & ssList(sK5)
      & sK2 = sK4
      & ~ neq(sK5,nil) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ? [X0] :
      ( ssList(X0)
      & ? [X1] :
          ( ssList(X1)
          & ? [X2] :
              ( ssList(X2)
              & ? [X3] :
                  ( X1 = X3
                  & ~ cyclefreeP(X1)
                  & ssList(X3)
                  & X0 = X2
                  & ~ neq(X3,nil) ) ) ) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ cyclefreeP(X1)
                  & X1 = X3
                  & ~ neq(X3,nil)
                  & X0 = X2
                  & 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)
                   => ( cyclefreeP(X1)
                      | X1 != X3
                      | neq(X3,nil)
                      | X0 != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( cyclefreeP(X1)
                    | X1 != X3
                    | neq(X3,nil)
                    | X0 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f280,plain,
    ( ~ ssList(sK3)
    | ~ ssList(nil)
    | nil = sK3 ),
    inference(resolution,[],[f170,f209]) ).

fof(f209,plain,
    ~ neq(sK3,nil),
    inference(definition_unfolding,[],[f162,f166]) ).

fof(f166,plain,
    sK5 = sK3,
    inference(cnf_transformation,[],[f135]) ).

fof(f162,plain,
    ~ neq(sK5,nil),
    inference(cnf_transformation,[],[f135]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | ~ ssList(X0)
      | ~ ssList(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( ( X0 != X1
              | ~ neq(X0,X1) )
            & ( neq(X0,X1)
              | X0 = X1 ) )
          | ~ ssList(X1) ) ),
    inference(nnf_transformation,[],[f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ! [X1] :
          ( ( X0 != X1
          <=> neq(X0,X1) )
          | ~ ssList(X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

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

fof(f165,plain,
    ~ cyclefreeP(sK3),
    inference(cnf_transformation,[],[f135]) ).

fof(f227,plain,
    spl15_1,
    inference(avatar_split_clause,[],[f196,f219]) ).

fof(f196,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWC129+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_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n020.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 18:23:00 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.54  % (2901)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)
% 0.20/0.56  % (2901)First to succeed.
% 0.20/0.56  % (2917)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)
% 1.48/0.56  % (2909)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)
% 1.48/0.57  % (2901)Refutation found. Thanks to Tanya!
% 1.48/0.57  % SZS status Theorem for theBenchmark
% 1.48/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.48/0.57  % (2901)------------------------------
% 1.48/0.57  % (2901)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.48/0.57  % (2901)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.48/0.57  % (2901)Termination reason: Refutation
% 1.48/0.57  
% 1.48/0.57  % (2901)Memory used [KB]: 6140
% 1.48/0.57  % (2901)Time elapsed: 0.127 s
% 1.48/0.57  % (2901)Instructions burned: 7 (million)
% 1.48/0.57  % (2901)------------------------------
% 1.48/0.57  % (2901)------------------------------
% 1.48/0.57  % (2894)Success in time 0.21 s
%------------------------------------------------------------------------------