TSTP Solution File: SEU125+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n002.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 18:26:45 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (   8 unt;   0 def)
%            Number of atoms       :  174 (  11 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  200 (  71   ~;  69   |;  46   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   85 (  66   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f150,plain,
    $false,
    inference(avatar_sat_refutation,[],[f129,f140,f149]) ).

fof(f149,plain,
    ~ spl8_1,
    inference(avatar_contradiction_clause,[],[f148]) ).

fof(f148,plain,
    ( $false
    | ~ spl8_1 ),
    inference(subsumption_resolution,[],[f141,f95]) ).

fof(f95,plain,
    ~ in(sK2(sK5,set_union2(sK4,sK3)),sK5),
    inference(resolution,[],[f70,f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ in(sK2(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( in(sK2(X0,X1),X1)
          & ~ in(sK2(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f43,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & ~ in(X3,X0) )
     => ( in(sK2(X0,X1),X1)
        & ~ in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X0) ) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f70,plain,
    ~ subset(set_union2(sK4,sK3),sK5),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( subset(sK4,sK5)
    & subset(sK3,sK5)
    & ~ subset(set_union2(sK4,sK3),sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f46,f47]) ).

fof(f47,plain,
    ( ? [X0,X1,X2] :
        ( subset(X1,X2)
        & subset(X0,X2)
        & ~ subset(set_union2(X1,X0),X2) )
   => ( subset(sK4,sK5)
      & subset(sK3,sK5)
      & ~ subset(set_union2(sK4,sK3),sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ? [X0,X1,X2] :
      ( subset(X1,X2)
      & subset(X0,X2)
      & ~ subset(set_union2(X1,X0),X2) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ? [X2,X0,X1] :
      ( subset(X0,X1)
      & subset(X2,X1)
      & ~ subset(set_union2(X0,X2),X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ? [X0,X2,X1] :
      ( ~ subset(set_union2(X0,X2),X1)
      & subset(X0,X1)
      & subset(X2,X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( ( subset(X0,X1)
          & subset(X2,X1) )
       => subset(set_union2(X0,X2),X1) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f18,conjecture,
    ! [X0,X2,X1] :
      ( ( subset(X0,X1)
        & subset(X2,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(f141,plain,
    ( in(sK2(sK5,set_union2(sK4,sK3)),sK5)
    | ~ spl8_1 ),
    inference(resolution,[],[f124,f94]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ in(X0,sK4)
      | in(X0,sK5) ),
    inference(resolution,[],[f72,f68]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | in(X2,X0)
      | ~ in(X2,X1) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f72,plain,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f48]) ).

fof(f124,plain,
    ( in(sK2(sK5,set_union2(sK4,sK3)),sK4)
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f122,plain,
    ( spl8_1
  <=> in(sK2(sK5,set_union2(sK4,sK3)),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f140,plain,
    ~ spl8_2,
    inference(avatar_contradiction_clause,[],[f139]) ).

fof(f139,plain,
    ( $false
    | ~ spl8_2 ),
    inference(subsumption_resolution,[],[f132,f95]) ).

fof(f132,plain,
    ( in(sK2(sK5,set_union2(sK4,sK3)),sK5)
    | ~ spl8_2 ),
    inference(resolution,[],[f128,f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ in(X0,sK3)
      | in(X0,sK5) ),
    inference(resolution,[],[f71,f68]) ).

fof(f71,plain,
    subset(sK3,sK5),
    inference(cnf_transformation,[],[f48]) ).

fof(f128,plain,
    ( in(sK2(sK5,set_union2(sK4,sK3)),sK3)
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f126,plain,
    ( spl8_2
  <=> in(sK2(sK5,set_union2(sK4,sK3)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f129,plain,
    ( spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f114,f126,f122]) ).

fof(f114,plain,
    ( in(sK2(sK5,set_union2(sK4,sK3)),sK3)
    | in(sK2(sK5,set_union2(sK4,sK3)),sK4) ),
    inference(resolution,[],[f96,f80]) ).

fof(f80,plain,
    ! [X2,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,set_union2(X1,X2))
      | in(X4,X1) ),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ( ( ~ in(sK0(X0,X1,X2),X0)
            | ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X2) ) )
          & ( in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | in(X4,X2)
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f37,f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ( ~ in(X3,X1)
              & ~ in(X3,X2) ) )
          & ( in(X3,X0)
            | in(X3,X1)
            | in(X3,X2) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X0)
          | ( ~ in(sK0(X0,X1,X2),X1)
            & ~ in(sK0(X0,X1,X2),X2) ) )
        & ( in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X1)
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | in(X4,X2)
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( set_union2(X1,X2) = X0
    <=> ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X2) )
        <=> in(X3,X0) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X0) )
        <=> in(X3,X2) )
    <=> set_union2(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f96,plain,
    in(sK2(sK5,set_union2(sK4,sK3)),set_union2(sK4,sK3)),
    inference(resolution,[],[f70,f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( in(sK2(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU125+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14  % 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 : n002.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 14:52:29 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (10944)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50  % (10952)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)
% 0.20/0.51  % (10951)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)
% 0.20/0.51  % (10971)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)
% 0.20/0.51  % (10960)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (10952)First to succeed.
% 0.20/0.51  % (10950)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  % (10952)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (10952)------------------------------
% 0.20/0.52  % (10952)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (10952)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (10952)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (10952)Memory used [KB]: 6012
% 0.20/0.52  % (10952)Time elapsed: 0.104 s
% 0.20/0.52  % (10952)Instructions burned: 3 (million)
% 0.20/0.52  % (10952)------------------------------
% 0.20/0.52  % (10952)------------------------------
% 0.20/0.52  % (10941)Success in time 0.159 s
%------------------------------------------------------------------------------