%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n014.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 : Tue Apr 30 15:14:00 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   49 (  14 unt;   0 def)
%            Number of atoms       :   98 (  24 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   96 (  47   ~;  34   |;   5   &)
%                                         (   5 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   28 (  18   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f51,plain,
    $false,
    inference(avatar_sat_refutation,[],[f34,f38,f40,f43,f45,f48,f50]) ).

fof(f50,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f49]) ).

fof(f49,plain,
    ( $false
    | spl4_2 ),
    inference(global_subsumption,[],[f19,f20,f24,f25,f21,f18,f22,f23,f46,f32]) ).

fof(f32,plain,
    ( ~ in(sK0,sK1)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f31,plain,
    ( spl4_2
  <=> in(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f46,plain,
    empty_set != set_difference(singleton(sK0),sK1),
    inference(subsumption_resolution,[],[f19,f22]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | empty_set = set_difference(singleton(X0),X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | empty_set != set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).

fof(f22,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(singleton(X0),X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f18,plain,
    ( in(sK0,sK1)
    | empty_set = set_difference(singleton(sK0),sK1) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( ( ~ in(sK0,sK1)
      | empty_set != set_difference(singleton(sK0),sK1) )
    & ( in(sK0,sK1)
      | empty_set = set_difference(singleton(sK0),sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f11]) ).

fof(f11,plain,
    ( ? [X0,X1] :
        ( ( ~ in(X0,X1)
          | empty_set != set_difference(singleton(X0),X1) )
        & ( in(X0,X1)
          | empty_set = set_difference(singleton(X0),X1) ) )
   => ( ( ~ in(sK0,sK1)
        | empty_set != set_difference(singleton(sK0),sK1) )
      & ( in(sK0,sK1)
        | empty_set = set_difference(singleton(sK0),sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( ( ~ in(X0,X1)
        | empty_set != set_difference(singleton(X0),X1) )
      & ( in(X0,X1)
        | empty_set = set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ? [X0,X1] :
      ( empty_set = set_difference(singleton(X0),X1)
    <~> in(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X0,X1] :
        ( empty_set = set_difference(singleton(X0),X1)
      <=> in(X0,X1) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X0,X1] :
      ( empty_set = set_difference(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f25,plain,
    empty(sK3),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    empty(sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f3,f16]) ).

fof(f16,plain,
    ( ? [X0] : empty(X0)
   => empty(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f3,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f24,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ empty(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f4,f14]) ).

fof(f14,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f4,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f20,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f19,plain,
    ( ~ in(sK0,sK1)
    | empty_set != set_difference(singleton(sK0),sK1) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f48,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f47]) ).

fof(f47,plain,
    ( $false
    | ~ spl4_1 ),
    inference(global_subsumption,[],[f19,f20,f24,f25,f21,f18,f22,f23,f29,f46]) ).

fof(f29,plain,
    ( empty_set = set_difference(singleton(sK0),sK1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f27,plain,
    ( spl4_1
  <=> empty_set = set_difference(singleton(sK0),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f45,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f44]) ).

fof(f44,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f29,f19,f20,f24,f25,f21,f18,f33,f35,f22,f23,f36,f41]) ).

fof(f41,plain,
    ( empty_set != set_difference(singleton(sK0),sK1)
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f19,f33]) ).

fof(f36,plain,
    ( empty_set = set_difference(singleton(sK0),sK1)
    | ~ spl4_2 ),
    inference(resolution,[],[f23,f33]) ).

fof(f35,plain,
    ( ~ in(sK1,sK0)
    | ~ spl4_2 ),
    inference(resolution,[],[f33,f21]) ).

fof(f33,plain,
    ( in(sK0,sK1)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f43,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f42]) ).

fof(f42,plain,
    ( $false
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f19,f20,f24,f25,f21,f18,f33,f35,f22,f23,f36,f41]) ).

fof(f40,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f39]) ).

fof(f39,plain,
    ( $false
    | ~ spl4_2 ),
    inference(global_subsumption,[],[f19,f20,f24,f25,f21,f18,f33,f35,f22,f23,f36]) ).

fof(f38,plain,
    ( spl4_1
    | ~ spl4_2 ),
    inference(avatar_contradiction_clause,[],[f37]) ).

fof(f37,plain,
    ( $false
    | spl4_1
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f36,f28]) ).

fof(f28,plain,
    ( empty_set != set_difference(singleton(sK0),sK1)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f34,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f18,f31,f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 01:29:49 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (3962)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (3965)WARNING: value z3 for option sas not known
% 0.15/0.38  % (3965)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (3965)First to succeed.
% 0.15/0.38  % (3965)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (3965)------------------------------
% 0.15/0.38  % (3965)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (3965)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (3965)Memory used [KB]: 768
% 0.15/0.38  % (3965)Time elapsed: 0.003 s
% 0.15/0.38  % (3965)Instructions burned: 4 (million)
% 0.15/0.38  % (3965)------------------------------
% 0.15/0.38  % (3965)------------------------------
% 0.15/0.38  % (3962)Success in time 0.01 s
%------------------------------------------------------------------------------