TSTP Solution File: SET578+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET578+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_sat --cores 0 -t %d %s

% Computer : n014.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 18:24:58 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   61 (  11 unt;   0 def)
%            Number of atoms       :  198 (  21 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  232 (  95   ~;  76   |;  44   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  104 (  86   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f102,plain,
    $false,
    inference(subsumption_resolution,[],[f101,f93]) ).

fof(f93,plain,
    ~ member(sK3(sK2,intersection(sK0,sK1)),sK2),
    inference(subsumption_resolution,[],[f92,f79]) ).

fof(f79,plain,
    ( member(sK3(intersection(sK0,sK1),sK2),sK2)
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(resolution,[],[f76,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( ~ member(sK3(X0,X1),X0)
          & member(sK3(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X0)
          & member(X3,X1) )
     => ( ~ member(sK3(X0,X1),X0)
        & member(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( ~ member(X3,X0)
            & member(X3,X1) ) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f76,plain,
    ( ~ subset(sK2,intersection(sK0,sK1))
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(resolution,[],[f73,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f73,plain,
    ( ~ subset(intersection(sK0,sK1),sK2)
    | ~ subset(sK2,intersection(sK0,sK1)) ),
    inference(forward_demodulation,[],[f72,f53]) ).

fof(f53,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f72,plain,
    ( ~ subset(intersection(sK0,sK1),sK2)
    | ~ subset(sK2,intersection(sK1,sK0)) ),
    inference(forward_demodulation,[],[f66,f53]) ).

fof(f66,plain,
    ( ~ subset(intersection(sK1,sK0),sK2)
    | ~ subset(sK2,intersection(sK1,sK0)) ),
    inference(extensionality_resolution,[],[f35,f44]) ).

fof(f44,plain,
    sK2 != intersection(sK1,sK0),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( sK2 != intersection(sK1,sK0)
    & ! [X3] :
        ( ( ( member(X3,sK0)
            & member(X3,sK1) )
          | ~ member(X3,sK2) )
        & ( member(X3,sK2)
          | ~ member(X3,sK0)
          | ~ member(X3,sK1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f24]) ).

fof(f24,plain,
    ( ? [X0,X1,X2] :
        ( intersection(X1,X0) != X2
        & ! [X3] :
            ( ( ( member(X3,X0)
                & member(X3,X1) )
              | ~ member(X3,X2) )
            & ( member(X3,X2)
              | ~ member(X3,X0)
              | ~ member(X3,X1) ) ) )
   => ( sK2 != intersection(sK1,sK0)
      & ! [X3] :
          ( ( ( member(X3,sK0)
              & member(X3,sK1) )
            | ~ member(X3,sK2) )
          & ( member(X3,sK2)
            | ~ member(X3,sK0)
            | ~ member(X3,sK1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X0) != X2
      & ! [X3] :
          ( ( ( member(X3,X0)
              & member(X3,X1) )
            | ~ member(X3,X2) )
          & ( member(X3,X2)
            | ~ member(X3,X0)
            | ~ member(X3,X1) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ? [X2,X0,X1] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( ( member(X3,X2)
              & member(X3,X0) )
            | ~ member(X3,X1) )
          & ( member(X3,X1)
            | ~ member(X3,X2)
            | ~ member(X3,X0) ) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ? [X2,X0,X1] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( ( member(X3,X2)
              & member(X3,X0) )
            | ~ member(X3,X1) )
          & ( member(X3,X1)
            | ~ member(X3,X2)
            | ~ member(X3,X0) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ? [X2,X0,X1] :
      ( intersection(X0,X2) != X1
      & ! [X3] :
          ( ( member(X3,X2)
            & member(X3,X0) )
        <=> member(X3,X1) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X1,X0,X2] :
        ( ! [X3] :
            ( ( member(X3,X2)
              & member(X3,X0) )
          <=> member(X3,X1) )
       => intersection(X0,X2) = X1 ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( ! [X3] :
            ( member(X3,X0)
          <=> ( member(X3,X1)
              & member(X3,X2) ) )
       => intersection(X1,X2) = X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X1)
            & member(X3,X2) ) )
     => intersection(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f92,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(subsumption_resolution,[],[f91,f43]) ).

fof(f43,plain,
    ! [X3] :
      ( member(X3,sK0)
      | ~ member(X3,sK2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f91,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
    | ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(resolution,[],[f88,f42]) ).

fof(f42,plain,
    ! [X3] :
      ( member(X3,sK1)
      | ~ member(X3,sK2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f88,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK1)
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2)
    | ~ member(sK3(intersection(sK0,sK1),sK2),sK0) ),
    inference(resolution,[],[f40,f78]) ).

fof(f78,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),intersection(sK0,sK1))
    | ~ member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(resolution,[],[f76,f46]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,intersection(X1,X2))
        | ~ member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,intersection(X1,X2)) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X2,X1,X0] :
      ( ( member(X2,intersection(X1,X0))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X1,X0)) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X2,X1,X0] :
      ( ( member(X2,intersection(X1,X0))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X1,X0)) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X2,X1,X0] :
      ( member(X2,intersection(X1,X0))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(f101,plain,
    member(sK3(sK2,intersection(sK0,sK1)),sK2),
    inference(subsumption_resolution,[],[f100,f98]) ).

fof(f98,plain,
    member(sK3(sK2,intersection(sK0,sK1)),sK0),
    inference(resolution,[],[f97,f39]) ).

fof(f39,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f97,plain,
    member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)),
    inference(subsumption_resolution,[],[f96,f81]) ).

fof(f81,plain,
    ( member(sK3(intersection(sK0,sK1),sK2),sK2)
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
    inference(resolution,[],[f77,f45]) ).

fof(f77,plain,
    ( ~ subset(sK2,intersection(sK0,sK1))
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
    inference(resolution,[],[f73,f45]) ).

fof(f96,plain,
    ( member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1))
    | ~ member(sK3(intersection(sK0,sK1),sK2),sK2) ),
    inference(resolution,[],[f95,f43]) ).

fof(f95,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
    inference(subsumption_resolution,[],[f94,f81]) ).

fof(f94,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK2)
    | ~ member(sK3(intersection(sK0,sK1),sK2),sK0)
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
    inference(resolution,[],[f87,f42]) ).

fof(f87,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),sK1)
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1))
    | ~ member(sK3(intersection(sK0,sK1),sK2),sK0) ),
    inference(resolution,[],[f40,f80]) ).

fof(f80,plain,
    ( ~ member(sK3(intersection(sK0,sK1),sK2),intersection(sK0,sK1))
    | member(sK3(sK2,intersection(sK0,sK1)),intersection(sK0,sK1)) ),
    inference(resolution,[],[f77,f46]) ).

fof(f100,plain,
    ( ~ member(sK3(sK2,intersection(sK0,sK1)),sK0)
    | member(sK3(sK2,intersection(sK0,sK1)),sK2) ),
    inference(resolution,[],[f99,f41]) ).

fof(f41,plain,
    ! [X3] :
      ( ~ member(X3,sK1)
      | ~ member(X3,sK0)
      | member(X3,sK2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f99,plain,
    member(sK3(sK2,intersection(sK0,sK1)),sK1),
    inference(resolution,[],[f97,f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n014.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 14:03:03 EDT 2022
% 0.20/0.35  % CPUTime    : 
% 0.20/0.50  % (21588)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.20/0.50  % (21580)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.51  % (21588)First to succeed.
% 0.20/0.51  % (21572)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.51  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.51  % (21588)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (21588)------------------------------
% 0.20/0.51  % (21588)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (21588)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (21588)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (21588)Memory used [KB]: 895
% 0.20/0.51  % (21588)Time elapsed: 0.059 s
% 0.20/0.51  % (21588)Instructions burned: 3 (million)
% 0.20/0.51  % (21588)------------------------------
% 0.20/0.51  % (21588)------------------------------
% 0.20/0.51  % (21565)Success in time 0.154 s
%------------------------------------------------------------------------------