TSTP Solution File: SET920+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET920+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 : n003.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 18:22:45 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   31 (   5 unt;   0 def)
%            Number of atoms       :  185 (  77 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  237 (  83   ~;  85   |;  55   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   97 (  80   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f72,plain,
    $false,
    inference(subsumption_resolution,[],[f70,f33]) ).

fof(f33,plain,
    ~ in(sK1,sK0),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ( ~ in(sK1,sK0)
    & unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f20]) ).

fof(f20,plain,
    ( ? [X0,X1,X2] :
        ( ~ in(X1,X0)
        & set_intersection2(unordered_pair(X1,X2),X0) = unordered_pair(X1,X2) )
   => ( ~ in(sK1,sK0)
      & unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0,X1,X2] :
      ( ~ in(X1,X0)
      & set_intersection2(unordered_pair(X1,X2),X0) = unordered_pair(X1,X2) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X2,X0] :
      ( ~ in(X2,X1)
      & set_intersection2(unordered_pair(X2,X0),X1) = unordered_pair(X2,X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X1,X2,X0] :
        ( set_intersection2(unordered_pair(X2,X0),X1) = unordered_pair(X2,X0)
       => in(X2,X1) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
       => in(X0,X2) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X2,X0] :
      ( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
     => in(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).

fof(f70,plain,
    in(sK1,sK0),
    inference(resolution,[],[f60,f54]) ).

fof(f54,plain,
    ! [X2,X4] : in(X4,unordered_pair(X4,X2)),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X1,X4] :
      ( in(X4,X1)
      | unordered_pair(X4,X2) != X1 ),
    inference(equality_resolution,[],[f43]) ).

fof(f43,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | X0 != X4
      | unordered_pair(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X2) = X1
        | ( ( ( sK4(X0,X1,X2) != X0
              & sK4(X0,X1,X2) != X2 )
            | ~ in(sK4(X0,X1,X2),X1) )
          & ( sK4(X0,X1,X2) = X0
            | sK4(X0,X1,X2) = X2
            | in(sK4(X0,X1,X2),X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( X0 != X4
                & X2 != X4 ) )
            & ( X0 = X4
              | X2 = X4
              | ~ in(X4,X1) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X0 != X3
              & X2 != X3 )
            | ~ in(X3,X1) )
          & ( X0 = X3
            | X2 = X3
            | in(X3,X1) ) )
     => ( ( ( sK4(X0,X1,X2) != X0
            & sK4(X0,X1,X2) != X2 )
          | ~ in(sK4(X0,X1,X2),X1) )
        & ( sK4(X0,X1,X2) = X0
          | sK4(X0,X1,X2) = X2
          | in(sK4(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X0 != X3
                & X2 != X3 )
              | ~ in(X3,X1) )
            & ( X0 = X3
              | X2 = X3
              | in(X3,X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( X0 != X4
                & X2 != X4 ) )
            & ( X0 = X4
              | X2 = X4
              | ~ in(X4,X1) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(rectify,[],[f28]) ).

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

fof(f27,plain,
    ! [X1,X2,X0] :
      ( ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X1,X0) != X2 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X2,X0] :
      ( unordered_pair(X1,X0) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( ( X1 = X3
            | X0 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f60,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK1,sK2))
      | in(X0,sK0) ),
    inference(superposition,[],[f50,f32]) ).

fof(f32,plain,
    unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0),
    inference(cnf_transformation,[],[f21]) ).

fof(f50,plain,
    ! [X2,X3,X1] :
      ( ~ in(X3,set_intersection2(X1,X2))
      | in(X3,X2) ),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | ~ in(X3,X0)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ( ( ~ in(sK3(X0,X1,X2),X0)
            | ~ in(sK3(X0,X1,X2),X2)
            | ~ in(sK3(X0,X1,X2),X1) )
          & ( in(sK3(X0,X1,X2),X0)
            | ( in(sK3(X0,X1,X2),X2)
              & in(sK3(X0,X1,X2),X1) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ~ in(X4,X2)
            | ~ in(X4,X1) )
          & ( in(X4,X0)
            | ( in(X4,X2)
              & in(X4,X1) ) ) )
     => ( ( ~ in(sK3(X0,X1,X2),X0)
          | ~ in(sK3(X0,X1,X2),X2)
          | ~ in(sK3(X0,X1,X2),X1) )
        & ( in(sK3(X0,X1,X2),X0)
          | ( in(sK3(X0,X1,X2),X2)
            & in(sK3(X0,X1,X2),X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X2)
                & in(X3,X1) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ~ in(X4,X2)
              | ~ in(X4,X1) )
            & ( in(X4,X0)
              | ( in(X4,X2)
                & in(X4,X1) ) ) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X2) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X1) != X0 )
      & ( set_intersection2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( in(X3,X0)
              | ( in(X3,X1)
                & in(X3,X2) ) ) ) ) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X2) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X1) != X0 )
      & ( set_intersection2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( in(X3,X0)
              | ( in(X3,X1)
                & in(X3,X2) ) ) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( in(X3,X1)
            & in(X3,X2) )
        <=> in(X3,X0) )
    <=> set_intersection2(X2,X1) = X0 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X1,X0] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( ( in(X3,X0)
            & in(X3,X1) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % 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 : n003.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 14:30:52 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (30187)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.50  % (30196)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)
% 0.20/0.50  % (30213)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.50  % (30188)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.50  % (30204)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50  % (30188)First to succeed.
% 0.20/0.50  % (30189)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)
% 0.20/0.51  % (30197)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  % (30188)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  % (30188)------------------------------
% 0.20/0.51  % (30188)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (30188)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (30188)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (30188)Memory used [KB]: 6012
% 0.20/0.51  % (30188)Time elapsed: 0.095 s
% 0.20/0.51  % (30188)Instructions burned: 2 (million)
% 0.20/0.51  % (30188)------------------------------
% 0.20/0.51  % (30188)------------------------------
% 0.20/0.51  % (30184)Success in time 0.151 s
%------------------------------------------------------------------------------