%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET617+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 : n027.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 18:21:37 EDT 2022

% Result   : Theorem 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  13 unt;   0 def)
%            Number of atoms       :   67 (  41 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   59 (  30   ~;  24   |;   2   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   20 (  18   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f92,plain,
    $false,
    inference(avatar_sat_refutation,[],[f67,f73,f91]) ).

fof(f91,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_contradiction_clause,[],[f90]) ).

fof(f90,plain,
    ( $false
    | ~ spl3_1
    | spl3_2 ),
    inference(trivial_inequality_removal,[],[f89]) ).

fof(f89,plain,
    ( sK0 != sK0
    | ~ spl3_1
    | spl3_2 ),
    inference(superposition,[],[f75,f79]) ).

fof(f79,plain,
    ( union(empty_set,sK0) = sK0
    | ~ spl3_1 ),
    inference(superposition,[],[f36,f77]) ).

fof(f77,plain,
    ( union(sK0,empty_set) = sK0
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f76,f52]) ).

fof(f52,plain,
    ! [X0] : difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : difference(X0,empty_set) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).

fof(f76,plain,
    ( sK0 = union(difference(sK0,empty_set),empty_set)
    | ~ spl3_1 ),
    inference(forward_demodulation,[],[f61,f37]) ).

fof(f37,plain,
    ! [X0] : empty_set = difference(empty_set,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : empty_set = difference(empty_set,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).

fof(f61,plain,
    ( sK0 = union(difference(sK0,empty_set),difference(empty_set,sK0))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl3_1
  <=> sK0 = union(difference(sK0,empty_set),difference(empty_set,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f36,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f75,plain,
    ( union(empty_set,sK0) != sK0
    | spl3_2 ),
    inference(forward_demodulation,[],[f74,f37]) ).

fof(f74,plain,
    ( sK0 != union(difference(empty_set,sK0),sK0)
    | spl3_2 ),
    inference(forward_demodulation,[],[f66,f52]) ).

fof(f66,plain,
    ( union(difference(empty_set,sK0),difference(sK0,empty_set)) != sK0
    | spl3_2 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl3_2
  <=> union(difference(empty_set,sK0),difference(sK0,empty_set)) = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f73,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f72]) ).

fof(f72,plain,
    ( $false
    | spl3_1 ),
    inference(trivial_inequality_removal,[],[f71]) ).

fof(f71,plain,
    ( sK0 != sK0
    | spl3_1 ),
    inference(superposition,[],[f70,f38]) ).

fof(f38,plain,
    ! [X0] : union(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : union(X0,empty_set) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).

fof(f70,plain,
    ( union(sK0,empty_set) != sK0
    | spl3_1 ),
    inference(backward_demodulation,[],[f68,f52]) ).

fof(f68,plain,
    ( sK0 != union(difference(sK0,empty_set),empty_set)
    | spl3_1 ),
    inference(backward_demodulation,[],[f62,f37]) ).

fof(f62,plain,
    ( sK0 != union(difference(sK0,empty_set),difference(empty_set,sK0))
    | spl3_1 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f67,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f53,f64,f60]) ).

fof(f53,plain,
    ( union(difference(empty_set,sK0),difference(sK0,empty_set)) != sK0
    | sK0 != union(difference(sK0,empty_set),difference(empty_set,sK0)) ),
    inference(definition_unfolding,[],[f34,f40,f40]) ).

fof(f40,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/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(f34,plain,
    ( symmetric_difference(empty_set,sK0) != sK0
    | symmetric_difference(sK0,empty_set) != sK0 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( symmetric_difference(empty_set,sK0) != sK0
    | symmetric_difference(sK0,empty_set) != sK0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f21]) ).

fof(f21,plain,
    ( ? [X0] :
        ( symmetric_difference(empty_set,X0) != X0
        | symmetric_difference(X0,empty_set) != X0 )
   => ( symmetric_difference(empty_set,sK0) != sK0
      | symmetric_difference(sK0,empty_set) != sK0 ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ? [X0] :
      ( symmetric_difference(empty_set,X0) != X0
      | symmetric_difference(X0,empty_set) != X0 ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0] :
        ( symmetric_difference(X0,empty_set) = X0
        & symmetric_difference(empty_set,X0) = X0 ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0] :
      ( symmetric_difference(X0,empty_set) = X0
      & symmetric_difference(empty_set,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% 0.14/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:26:31 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.50  % (13793)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.50  % (13808)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)
% 0.20/0.50  % (13800)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)
% 0.20/0.51  % (13808)First to succeed.
% 0.20/0.51  % (13791)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.51  % (13794)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.51  % (13791)Refutation not found, incomplete strategy% (13791)------------------------------
% 0.20/0.51  % (13791)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (13791)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (13791)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (13791)Memory used [KB]: 1407
% 0.20/0.51  % (13791)Time elapsed: 0.107 s
% 0.20/0.51  % (13791)Instructions burned: 2 (million)
% 0.20/0.51  % (13791)------------------------------
% 0.20/0.51  % (13791)------------------------------
% 0.20/0.51  % (13795)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.51  % (13800)Also succeeded, but the first one will report.
% 0.20/0.51  % (13808)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (13808)------------------------------
% 0.20/0.51  % (13808)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (13808)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (13808)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (13808)Memory used [KB]: 5884
% 0.20/0.51  % (13808)Time elapsed: 0.064 s
% 0.20/0.51  % (13808)Instructions burned: 2 (million)
% 0.20/0.51  % (13808)------------------------------
% 0.20/0.51  % (13808)------------------------------
% 0.20/0.51  % (13785)Success in time 0.162 s
%------------------------------------------------------------------------------