%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET605+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_sat --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 18:25:04 EDT 2022

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   16 (  11 unt;   0 def)
%            Number of atoms       :   25 (  15 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   21 (  12   ~;   5   |;   2   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (  20   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f110,plain,
    $false,
    inference(trivial_inequality_removal,[],[f105]) ).

fof(f105,plain,
    empty_set != empty_set,
    inference(superposition,[],[f53,f72]) ).

fof(f72,plain,
    ! [X2,X1] : empty_set = difference(X1,union(X1,X2)),
    inference(resolution,[],[f54,f48]) ).

fof(f48,plain,
    ! [X0,X1] : subset(X1,union(X1,X0)),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] : subset(X1,union(X1,X0)),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] : subset(X0,union(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | empty_set = difference(X1,X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | empty_set != difference(X1,X0) )
      & ( empty_set = difference(X1,X0)
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | difference(X0,X1) != empty_set )
      & ( difference(X0,X1) = empty_set
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

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

fof(f53,plain,
    empty_set != difference(sK1,union(sK1,sK2)),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    empty_set != difference(sK1,union(sK1,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f19,f29]) ).

fof(f29,plain,
    ( ? [X0,X1] : empty_set != difference(X0,union(X0,X1))
   => empty_set != difference(sK1,union(sK1,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0,X1] : empty_set != difference(X0,union(X0,X1)),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0] : empty_set = difference(X0,union(X0,X1)),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0] : empty_set = difference(X0,union(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th76) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:04:52 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.51  % (9645)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.51  % (9642)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.52  % (9635)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52  % (9642)First to succeed.
% 0.21/0.53  % (9642)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (9642)------------------------------
% 0.21/0.53  % (9642)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (9642)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (9642)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (9642)Memory used [KB]: 5373
% 0.21/0.53  % (9642)Time elapsed: 0.127 s
% 0.21/0.53  % (9642)Instructions burned: 4 (million)
% 0.21/0.53  % (9642)------------------------------
% 0.21/0.53  % (9642)------------------------------
% 0.21/0.53  % (9631)Success in time 0.172 s
%------------------------------------------------------------------------------