%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET604+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 : n025.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 18:21:34 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (  11 unt;   0 def)
%            Number of atoms       :   29 (  18 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   24 (  13   ~;   6   |;   2   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (  14   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f64,plain,
    $false,
    inference(subsumption_resolution,[],[f63,f48]) ).

fof(f48,plain,
    empty_set != sF2,
    inference(definition_folding,[],[f42,f47]) ).

fof(f47,plain,
    sF2 = difference(empty_set,sK1),
    introduced(function_definition,[]) ).

fof(f42,plain,
    empty_set != difference(empty_set,sK1),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    empty_set != difference(empty_set,sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f26]) ).

fof(f26,plain,
    ( ? [X0] : empty_set != difference(empty_set,X0)
   => empty_set != difference(empty_set,sK1) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0] : empty_set != difference(empty_set,X0),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0] : empty_set = difference(empty_set,X0),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0] : empty_set = difference(empty_set,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).

fof(f63,plain,
    empty_set = sF2,
    inference(subsumption_resolution,[],[f60,f36]) ).

fof(f36,plain,
    ! [X0] : subset(empty_set,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).

fof(f60,plain,
    ( ~ subset(empty_set,sK1)
    | empty_set = sF2 ),
    inference(superposition,[],[f47,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( empty_set = difference(X0,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | empty_set != difference(X0,X1) )
      & ( empty_set = difference(X0,X1)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | empty_set != difference(X1,X0) )
      & ( empty_set = difference(X1,X0)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> empty_set = difference(X1,X0) ),
    inference(rectify,[],[f2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET604+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13  % 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 : n025.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 14:13:15 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (22931)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (22946)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (22931)First to succeed.
% 0.19/0.51  % (22954)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.51  % (22931)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (22931)------------------------------
% 0.19/0.51  % (22931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (22931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (22931)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (22931)Memory used [KB]: 5884
% 0.19/0.51  % (22931)Time elapsed: 0.095 s
% 0.19/0.51  % (22931)Instructions burned: 2 (million)
% 0.19/0.51  % (22931)------------------------------
% 0.19/0.51  % (22931)------------------------------
% 0.19/0.51  % (22930)Success in time 0.158 s
%------------------------------------------------------------------------------