TSTP Solution File: SET194+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n004.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 18:19:43 EDT 2022

% Result   : Theorem 1.36s 0.53s
% Output   : Refutation 1.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   26 (  10 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   79 (  32   ~;  24   |;  14   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   55 (  46   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f45,plain,
    $false,
    inference(subsumption_resolution,[],[f44,f42]) ).

fof(f42,plain,
    member(sK2(sK1,union(sK1,sK0)),sK1),
    inference(resolution,[],[f26,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) )
      & ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f26,plain,
    ~ subset(sK1,union(sK1,sK0)),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ subset(sK1,union(sK1,sK0)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).

fof(f13,plain,
    ( ? [X0,X1] : ~ subset(X1,union(X1,X0))
   => ~ subset(sK1,union(sK1,sK0)) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0,X1] : ~ subset(X1,union(X1,X0)),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ? [X1,X0] : ~ subset(X0,union(X0,X1)),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_union) ).

fof(f44,plain,
    ~ member(sK2(sK1,union(sK1,sK0)),sK1),
    inference(resolution,[],[f41,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X2,X0))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X2,X0)) )
      & ( member(X1,union(X2,X0))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X2,X1,X0] :
      ( ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X0,X2)) )
      & ( member(X1,union(X0,X2))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) ) ),
    inference(flattening,[],[f15]) ).

fof(f15,plain,
    ! [X2,X1,X0] :
      ( ( member(X1,X2)
        | member(X1,X0)
        | ~ member(X1,union(X0,X2)) )
      & ( member(X1,union(X0,X2))
        | ( ~ member(X1,X2)
          & ~ member(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X2,X1,X0] :
      ( ( member(X1,X2)
        | member(X1,X0) )
    <=> member(X1,union(X0,X2)) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X2,X1] :
      ( ( member(X2,X1)
        | member(X2,X0) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f41,plain,
    ~ member(sK2(sK1,union(sK1,sK0)),union(sK1,sK0)),
    inference(resolution,[],[f26,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.13/0.35  % Computer : n004.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 13:22:34 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (7872)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)
% 0.20/0.52  % (7880)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (7879)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.53  % (7872)First to succeed.
% 1.36/0.53  % (7872)Refutation found. Thanks to Tanya!
% 1.36/0.53  % SZS status Theorem for theBenchmark
% 1.36/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.36/0.53  % (7872)------------------------------
% 1.36/0.53  % (7872)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53  % (7872)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53  % (7872)Termination reason: Refutation
% 1.36/0.53  
% 1.36/0.53  % (7872)Memory used [KB]: 1407
% 1.36/0.53  % (7872)Time elapsed: 0.109 s
% 1.36/0.53  % (7872)Instructions burned: 2 (million)
% 1.36/0.53  % (7872)------------------------------
% 1.36/0.53  % (7872)------------------------------
% 1.36/0.53  % (7866)Success in time 0.171 s
%------------------------------------------------------------------------------