%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET618+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 : 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 18:21:38 EDT 2022

% Result   : Theorem 0.16s 0.44s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  17 unt;   0 def)
%            Number of atoms       :   19 (  14 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (  10   ~;   0   |;   0   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   12 (  10   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f63,plain,
    $false,
    inference(subsumption_resolution,[],[f62,f56]) ).

fof(f56,plain,
    sP3(empty_set),
    inference(inequality_splitting,[],[f54,f55]) ).

fof(f55,plain,
    ~ sP3(union(difference(sK2,sK2),difference(sK2,sK2))),
    introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP3])]) ).

fof(f54,plain,
    empty_set != union(difference(sK2,sK2),difference(sK2,sK2)),
    inference(definition_unfolding,[],[f52,f50]) ).

fof(f50,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f52,plain,
    empty_set != symmetric_difference(sK2,sK2),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    empty_set != symmetric_difference(sK2,sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f33]) ).

fof(f33,plain,
    ( ? [X0] : empty_set != symmetric_difference(X0,X0)
   => empty_set != symmetric_difference(sK2,sK2) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f12,conjecture,
    ! [X0] : empty_set = symmetric_difference(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).

fof(f62,plain,
    ~ sP3(empty_set),
    inference(forward_demodulation,[],[f61,f51]) ).

fof(f51,plain,
    ! [X0] : difference(X0,X0) = empty_set,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : difference(X0,X0) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).

fof(f61,plain,
    ~ sP3(difference(sK2,sK2)),
    inference(forward_demodulation,[],[f55,f36]) ).

fof(f36,plain,
    ! [X0] : union(X0,X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 14:12:37 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.16/0.43  % (7748)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.44  % (7756)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.16/0.44  % (7748)First to succeed.
% 0.16/0.44  % (7748)Refutation found. Thanks to Tanya!
% 0.16/0.44  % SZS status Theorem for theBenchmark
% 0.16/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.44  % (7748)------------------------------
% 0.16/0.44  % (7748)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.44  % (7748)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.44  % (7748)Termination reason: Refutation
% 0.16/0.44  
% 0.16/0.44  % (7748)Memory used [KB]: 5884
% 0.16/0.44  % (7748)Time elapsed: 0.005 s
% 0.16/0.44  % (7748)Instructions burned: 2 (million)
% 0.16/0.44  % (7748)------------------------------
% 0.16/0.44  % (7748)------------------------------
% 0.16/0.44  % (7733)Success in time 0.11 s
%------------------------------------------------------------------------------