TSTP Solution File: SET063+1 by SnakeForV---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : n022.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 18:18:51 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   28 (   8 unt;   0 def)
%            Number of atoms       :   81 (  16 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   90 (  37   ~;  25   |;  19   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (  37   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f83,plain,
    $false,
    inference(subsumption_resolution,[],[f81,f57]) ).

fof(f57,plain,
    ! [X0] : ~ member(X0,null_class),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] : ~ member(X0,null_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).

fof(f81,plain,
    member(sK0(sK1,null_class),null_class),
    inference(resolution,[],[f78,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subclass(X1,X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ( member(sK0(X0,X1),X1)
          & ~ member(sK0(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f52,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK0(X0,X1),X1)
        & ~ member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subclass(X0,X1) )
      & ( subclass(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subclass(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f78,plain,
    ~ subclass(null_class,sK1),
    inference(subsumption_resolution,[],[f77,f65]) ).

fof(f65,plain,
    subclass(sK1,null_class),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( subclass(sK1,null_class)
    & null_class != sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f47,f55]) ).

fof(f55,plain,
    ( ? [X0] :
        ( subclass(X0,null_class)
        & null_class != X0 )
   => ( subclass(sK1,null_class)
      & null_class != sK1 ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ? [X0] :
      ( subclass(X0,null_class)
      & null_class != X0 ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
        ( subclass(X0,null_class)
       => null_class = X0 ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0] :
      ( subclass(X0,null_class)
     => null_class = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).

fof(f77,plain,
    ( ~ subclass(null_class,sK1)
    | ~ subclass(sK1,null_class) ),
    inference(resolution,[],[f71,f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | sQ2_eqProxy(X0,X1) ),
    inference(equality_proxy_replacement,[],[f60,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( sQ2_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ2_eqProxy])]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subclass(X1,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subclass(X1,X0)
        | ~ subclass(X0,X1) )
      & ( ( subclass(X1,X0)
          & subclass(X0,X1) )
        | X0 != X1 ) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subclass(X0,X1)
        | ~ subclass(X1,X0) )
      & ( ( subclass(X0,X1)
          & subclass(X1,X0) )
        | X0 != X1 ) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ~ subclass(X0,X1)
        | ~ subclass(X1,X0) )
      & ( ( subclass(X0,X1)
          & subclass(X1,X0) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

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

fof(f71,plain,
    ~ sQ2_eqProxy(null_class,sK1),
    inference(equality_proxy_replacement,[],[f64,f69]) ).

fof(f64,plain,
    null_class != sK1,
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 13:06:41 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (15210)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)
% 0.19/0.49  % (15210)First to succeed.
% 0.19/0.49  % (15226)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.49  % (15210)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (15210)------------------------------
% 0.19/0.49  % (15210)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (15210)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (15210)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (15210)Memory used [KB]: 5884
% 0.19/0.49  % (15210)Time elapsed: 0.085 s
% 0.19/0.49  % (15210)Instructions burned: 2 (million)
% 0.19/0.49  % (15210)------------------------------
% 0.19/0.49  % (15210)------------------------------
% 0.19/0.49  % (15199)Success in time 0.149 s
%------------------------------------------------------------------------------