%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET002+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 : n011.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 18:18:16 EDT 2022

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   18 (   7 unt;   0 def)
%            Number of atoms       :   43 (  20 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   43 (  18   ~;  12   |;   8   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   25 (  23   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f47,plain,
    $false,
    inference(unit_resulting_resolution,[],[f45,f41,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | union(X1,X0) = X0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | union(X1,X0) = X0 ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
     => union(X1,X0) = X0 ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
     => union(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).

fof(f41,plain,
    sK1 != union(sK1,sK1),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    sK1 != union(sK1,sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f27]) ).

fof(f27,plain,
    ( ? [X0] : union(X0,X0) != X0
   => sK1 != union(sK1,sK1) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0] : union(X0,X0) != X0,
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : union(X0,X0) = X0,
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).

fof(f45,plain,
    ! [X1] : subset(X1,X1),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] :
      ( ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET002+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 12:47:25 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.54  % (3582)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)
% 0.20/0.54  % (3560)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54  % (3560)First to succeed.
% 0.20/0.55  % (3560)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (3560)------------------------------
% 0.20/0.55  % (3560)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (3560)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (3560)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (3560)Memory used [KB]: 5884
% 0.20/0.55  % (3560)Time elapsed: 0.130 s
% 0.20/0.55  % (3560)Instructions burned: 2 (million)
% 0.20/0.55  % (3560)------------------------------
% 0.20/0.55  % (3560)------------------------------
% 0.20/0.55  % (3555)Success in time 0.195 s
%------------------------------------------------------------------------------