TSTP Solution File: SET945+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n008.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 18:22:49 EDT 2022

% Result   : Theorem 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   51 (   3 unt;   0 def)
%            Number of atoms       :  243 (  23 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  310 ( 118   ~; 110   |;  64   &)
%                                         (   8 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  159 ( 133   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f354,plain,
    $false,
    inference(subsumption_resolution,[],[f353,f43]) ).

fof(f43,plain,
    ~ disjoint(union(sK0),sK1),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ( ~ disjoint(union(sK0),sK1)
    & ! [X2] :
        ( ~ in(X2,sK0)
        | disjoint(X2,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23]) ).

fof(f23,plain,
    ( ? [X0,X1] :
        ( ~ disjoint(union(X0),X1)
        & ! [X2] :
            ( ~ in(X2,X0)
            | disjoint(X2,X1) ) )
   => ( ~ disjoint(union(sK0),sK1)
      & ! [X2] :
          ( ~ in(X2,sK0)
          | disjoint(X2,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ? [X0,X1] :
      ( ~ disjoint(union(X0),X1)
      & ! [X2] :
          ( ~ in(X2,X0)
          | disjoint(X2,X1) ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X1,X0] :
        ( ! [X2] :
            ( in(X2,X0)
           => disjoint(X2,X1) )
       => disjoint(union(X0),X1) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => disjoint(X2,X1) )
     => disjoint(union(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).

fof(f353,plain,
    disjoint(union(sK0),sK1),
    inference(duplicate_literal_removal,[],[f352]) ).

fof(f352,plain,
    ( disjoint(union(sK0),sK1)
    | disjoint(union(sK0),sK1) ),
    inference(resolution,[],[f347,f106]) ).

fof(f106,plain,
    ! [X4,X5] :
      ( in(sK6(X4,X5),X5)
      | disjoint(X4,X5) ),
    inference(resolution,[],[f60,f63]) ).

fof(f63,plain,
    ! [X2,X3,X1] :
      ( ~ in(X3,set_intersection2(X1,X2))
      | in(X3,X2) ),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X0)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ( ( ~ in(sK2(X0,X1,X2),X2)
            | ~ in(sK2(X0,X1,X2),X1)
            | ~ in(sK2(X0,X1,X2),X0) )
          & ( ( in(sK2(X0,X1,X2),X2)
              & in(sK2(X0,X1,X2),X1) )
            | in(sK2(X0,X1,X2),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X2)
            | ~ in(X4,X1)
            | ~ in(X4,X0) )
          & ( ( in(X4,X2)
              & in(X4,X1) )
            | in(X4,X0) ) )
     => ( ( ~ in(sK2(X0,X1,X2),X2)
          | ~ in(sK2(X0,X1,X2),X1)
          | ~ in(sK2(X0,X1,X2),X0) )
        & ( ( in(sK2(X0,X1,X2),X2)
            & in(sK2(X0,X1,X2),X1) )
          | in(sK2(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ? [X4] :
            ( ( ~ in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X2)
                & in(X4,X1) )
              | in(X4,X0) ) ) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | in(X3,X0) ) ) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X2)
                & in(X3,X1) )
              | in(X3,X0) ) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( in(X3,X0)
        <=> ( in(X3,X2)
            & in(X3,X1) ) )
    <=> set_intersection2(X1,X2) = X0 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            & in(X3,X1) ) )
    <=> set_intersection2(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f60,plain,
    ! [X0,X1] :
      ( in(sK6(X0,X1),set_intersection2(X0,X1))
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | in(sK6(X0,X1),set_intersection2(X0,X1)) )
      & ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
        | ~ disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f38,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X2] : in(X2,set_intersection2(X0,X1))
     => in(sK6(X0,X1),set_intersection2(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
        | ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( disjoint(X0,X1)
        | ? [X3] : in(X3,set_intersection2(X0,X1)) )
      & ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
        | ~ disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ~ ( ~ disjoint(X0,X1)
          & ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
      & ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f347,plain,
    ! [X3] :
      ( ~ in(sK6(union(sK0),X3),sK1)
      | disjoint(union(sK0),X3) ),
    inference(resolution,[],[f344,f105]) ).

fof(f105,plain,
    ! [X2,X3] :
      ( in(sK6(X2,X3),X2)
      | disjoint(X2,X3) ),
    inference(resolution,[],[f60,f64]) ).

fof(f64,plain,
    ! [X2,X3,X1] :
      ( ~ in(X3,set_intersection2(X1,X2))
      | in(X3,X1) ),
    inference(equality_resolution,[],[f48]) ).

fof(f48,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f344,plain,
    ! [X2] :
      ( ~ in(X2,union(sK0))
      | ~ in(X2,sK1) ),
    inference(duplicate_literal_removal,[],[f341]) ).

fof(f341,plain,
    ! [X2] :
      ( ~ in(X2,union(sK0))
      | ~ in(X2,sK1)
      | ~ in(X2,union(sK0)) ),
    inference(resolution,[],[f331,f66]) ).

fof(f66,plain,
    ! [X2,X1] :
      ( in(X2,sK3(X1,X2))
      | ~ in(X2,union(X1)) ),
    inference(equality_resolution,[],[f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( in(X2,sK3(X1,X2))
      | ~ in(X2,X0)
      | union(X1) != X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( ( in(sK3(X1,X2),X1)
                & in(X2,sK3(X1,X2)) )
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ in(X2,X4) ) ) )
        | union(X1) != X0 )
      & ( union(X1) = X0
        | ( ( ~ in(sK4(X0,X1),X0)
            | ! [X6] :
                ( ~ in(X6,X1)
                | ~ in(sK4(X0,X1),X6) ) )
          & ( in(sK4(X0,X1),X0)
            | ( in(sK5(X0,X1),X1)
              & in(sK4(X0,X1),sK5(X0,X1)) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f33,f36,f35,f34]) ).

fof(f34,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( in(X3,X1)
          & in(X2,X3) )
     => ( in(sK3(X1,X2),X1)
        & in(X2,sK3(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ~ in(X5,X0)
            | ! [X6] :
                ( ~ in(X6,X1)
                | ~ in(X5,X6) ) )
          & ( in(X5,X0)
            | ? [X7] :
                ( in(X7,X1)
                & in(X5,X7) ) ) )
     => ( ( ~ in(sK4(X0,X1),X0)
          | ! [X6] :
              ( ~ in(X6,X1)
              | ~ in(sK4(X0,X1),X6) ) )
        & ( in(sK4(X0,X1),X0)
          | ? [X7] :
              ( in(X7,X1)
              & in(sK4(X0,X1),X7) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X7] :
          ( in(X7,X1)
          & in(sK4(X0,X1),X7) )
     => ( in(sK5(X0,X1),X1)
        & in(sK4(X0,X1),sK5(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( ? [X3] :
                  ( in(X3,X1)
                  & in(X2,X3) )
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ in(X2,X4) ) ) )
        | union(X1) != X0 )
      & ( union(X1) = X0
        | ? [X5] :
            ( ( ~ in(X5,X0)
              | ! [X6] :
                  ( ~ in(X6,X1)
                  | ~ in(X5,X6) ) )
            & ( in(X5,X0)
              | ? [X7] :
                  ( in(X7,X1)
                  & in(X5,X7) ) ) ) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( ? [X3] :
                  ( in(X3,X1)
                  & in(X2,X3) )
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | ! [X3] :
                  ( ~ in(X3,X1)
                  | ~ in(X2,X3) ) ) )
        | union(X1) != X0 )
      & ( union(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | ! [X3] :
                  ( ~ in(X3,X1)
                  | ~ in(X2,X3) ) )
            & ( in(X2,X0)
              | ? [X3] :
                  ( in(X3,X1)
                  & in(X2,X3) ) ) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ? [X3] :
              ( in(X3,X1)
              & in(X2,X3) )
        <=> in(X2,X0) )
    <=> union(X1) = X0 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

fof(f331,plain,
    ! [X78,X79] :
      ( ~ in(X78,sK3(sK0,X79))
      | ~ in(X79,union(sK0))
      | ~ in(X78,sK1) ),
    inference(resolution,[],[f300,f80]) ).

fof(f80,plain,
    ! [X0] :
      ( disjoint(sK3(sK0,X0),sK1)
      | ~ in(X0,union(sK0)) ),
    inference(resolution,[],[f65,f42]) ).

fof(f42,plain,
    ! [X2] :
      ( ~ in(X2,sK0)
      | disjoint(X2,sK1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f65,plain,
    ! [X2,X1] :
      ( in(sK3(X1,X2),X1)
      | ~ in(X2,union(X1)) ),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( in(sK3(X1,X2),X1)
      | ~ in(X2,X0)
      | union(X1) != X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f300,plain,
    ! [X10,X11,X9] :
      ( ~ disjoint(X11,X10)
      | ~ in(X9,X10)
      | ~ in(X9,X11) ),
    inference(resolution,[],[f62,f59]) ).

fof(f59,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,set_intersection2(X0,X1))
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f62,plain,
    ! [X2,X3,X1] :
      ( in(X3,set_intersection2(X1,X2))
      | ~ in(X3,X2)
      | ~ in(X3,X1) ),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(X3,X2)
      | ~ in(X3,X1)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:35:25 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.43  % (23445)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)
% 0.18/0.45  % (23451)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)
% 0.18/0.46  % (23445)First to succeed.
% 0.18/0.46  % (23459)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)
% 0.18/0.47  % (23445)Refutation found. Thanks to Tanya!
% 0.18/0.47  % SZS status Theorem for theBenchmark
% 0.18/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47  % (23445)------------------------------
% 0.18/0.47  % (23445)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.47  % (23445)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47  % (23445)Termination reason: Refutation
% 0.18/0.47  
% 0.18/0.47  % (23445)Memory used [KB]: 6012
% 0.18/0.47  % (23445)Time elapsed: 0.093 s
% 0.18/0.47  % (23445)Instructions burned: 15 (million)
% 0.18/0.47  % (23445)------------------------------
% 0.18/0.47  % (23445)------------------------------
% 0.18/0.47  % (23438)Success in time 0.134 s
%------------------------------------------------------------------------------