TSTP Solution File: SEU189+1 by SnakeForV-SAT---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n028.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 18:32:25 EDT 2022

% Result   : Theorem 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   59 (  10 unt;   0 def)
%            Number of atoms       :  146 (  55 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  151 (  64   ~;  61   |;  14   &)
%                                         (   4 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   20 (  14   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f168,plain,
    $false,
    inference(avatar_sat_refutation,[],[f104,f105,f152,f166]) ).

fof(f166,plain,
    ( ~ spl6_1
    | spl6_2 ),
    inference(avatar_contradiction_clause,[],[f165]) ).

fof(f165,plain,
    ( $false
    | ~ spl6_1
    | spl6_2 ),
    inference(subsumption_resolution,[],[f163,f116]) ).

fof(f116,plain,
    sK1 = relation_rng(sK1),
    inference(backward_demodulation,[],[f90,f111]) ).

fof(f111,plain,
    empty_set = sK1,
    inference(resolution,[],[f78,f72]) ).

fof(f72,plain,
    empty(sK1),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    empty(sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f53]) ).

fof(f53,plain,
    ( ? [X0] : empty(X0)
   => empty(sK1) ),
    introduced(choice_axiom,[]) ).

fof(f13,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f78,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f90,plain,
    empty_set = relation_rng(empty_set),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,axiom,
    ( empty_set = relation_rng(empty_set)
    & empty_set = relation_dom(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

fof(f163,plain,
    ( sK1 != relation_rng(sK1)
    | ~ spl6_1
    | spl6_2 ),
    inference(backward_demodulation,[],[f153,f159]) ).

fof(f159,plain,
    ( sK1 = sK0
    | ~ spl6_1 ),
    inference(resolution,[],[f158,f114]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ empty(X0)
      | sK1 = X0 ),
    inference(backward_demodulation,[],[f78,f111]) ).

fof(f158,plain,
    ( empty(sK0)
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f157,f72]) ).

fof(f157,plain,
    ( ~ empty(sK1)
    | empty(sK0)
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f156,f68]) ).

fof(f68,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( relation(sK0)
    & ( empty_set != relation_rng(sK0)
      | empty_set != relation_dom(sK0) )
    & ( empty_set = relation_rng(sK0)
      | empty_set = relation_dom(sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f50,f51]) ).

fof(f51,plain,
    ( ? [X0] :
        ( relation(X0)
        & ( relation_rng(X0) != empty_set
          | relation_dom(X0) != empty_set )
        & ( relation_rng(X0) = empty_set
          | relation_dom(X0) = empty_set ) )
   => ( relation(sK0)
      & ( empty_set != relation_rng(sK0)
        | empty_set != relation_dom(sK0) )
      & ( empty_set = relation_rng(sK0)
        | empty_set = relation_dom(sK0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0] :
      ( relation(X0)
      & ( relation_rng(X0) != empty_set
        | relation_dom(X0) != empty_set )
      & ( relation_rng(X0) = empty_set
        | relation_dom(X0) = empty_set ) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ? [X0] :
      ( relation(X0)
      & ( relation_rng(X0) != empty_set
        | relation_dom(X0) != empty_set )
      & ( relation_rng(X0) = empty_set
        | relation_dom(X0) = empty_set ) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ? [X0] :
      ( relation(X0)
      & ( relation_dom(X0) = empty_set
      <~> relation_rng(X0) = empty_set ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ( relation_rng(X0) = empty_set
        <=> relation_dom(X0) = empty_set ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ! [X0] :
      ( relation(X0)
     => ( relation_rng(X0) = empty_set
      <=> relation_dom(X0) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).

fof(f156,plain,
    ( ~ relation(sK0)
    | empty(sK0)
    | ~ empty(sK1)
    | ~ spl6_1 ),
    inference(superposition,[],[f91,f154]) ).

fof(f154,plain,
    ( sK1 = relation_dom(sK0)
    | ~ spl6_1 ),
    inference(forward_demodulation,[],[f99,f111]) ).

fof(f99,plain,
    ( empty_set = relation_dom(sK0)
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f97,plain,
    ( spl6_1
  <=> empty_set = relation_dom(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ empty(relation_dom(X0))
      | empty(X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ( ~ empty(X0)
        & relation(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f153,plain,
    ( sK1 != relation_rng(sK0)
    | spl6_2 ),
    inference(forward_demodulation,[],[f102,f111]) ).

fof(f102,plain,
    ( empty_set != relation_rng(sK0)
    | spl6_2 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f101,plain,
    ( spl6_2
  <=> empty_set = relation_rng(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f152,plain,
    ( spl6_1
    | ~ spl6_2 ),
    inference(avatar_contradiction_clause,[],[f151]) ).

fof(f151,plain,
    ( $false
    | spl6_1
    | ~ spl6_2 ),
    inference(subsumption_resolution,[],[f148,f115]) ).

fof(f115,plain,
    relation_dom(sK1) = sK1,
    inference(backward_demodulation,[],[f89,f111]) ).

fof(f89,plain,
    empty_set = relation_dom(empty_set),
    inference(cnf_transformation,[],[f25]) ).

fof(f148,plain,
    ( relation_dom(sK1) != sK1
    | spl6_1
    | ~ spl6_2 ),
    inference(backward_demodulation,[],[f119,f145]) ).

fof(f145,plain,
    ( sK1 = sK0
    | ~ spl6_2 ),
    inference(resolution,[],[f144,f114]) ).

fof(f144,plain,
    ( empty(sK0)
    | ~ spl6_2 ),
    inference(subsumption_resolution,[],[f143,f68]) ).

fof(f143,plain,
    ( empty(sK0)
    | ~ relation(sK0)
    | ~ spl6_2 ),
    inference(subsumption_resolution,[],[f141,f72]) ).

fof(f141,plain,
    ( empty(sK0)
    | ~ empty(sK1)
    | ~ relation(sK0)
    | ~ spl6_2 ),
    inference(superposition,[],[f83,f120]) ).

fof(f120,plain,
    ( sK1 = relation_rng(sK0)
    | ~ spl6_2 ),
    inference(backward_demodulation,[],[f103,f111]) ).

fof(f103,plain,
    ( empty_set = relation_rng(sK0)
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f119,plain,
    ( sK1 != relation_dom(sK0)
    | spl6_1 ),
    inference(backward_demodulation,[],[f98,f111]) ).

fof(f98,plain,
    ( empty_set != relation_dom(sK0)
    | spl6_1 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f105,plain,
    ( ~ spl6_2
    | ~ spl6_1 ),
    inference(avatar_split_clause,[],[f67,f97,f101]) ).

fof(f67,plain,
    ( empty_set != relation_dom(sK0)
    | empty_set != relation_rng(sK0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f104,plain,
    ( spl6_1
    | spl6_2 ),
    inference(avatar_split_clause,[],[f66,f101,f97]) ).

fof(f66,plain,
    ( empty_set = relation_rng(sK0)
    | empty_set = relation_dom(sK0) ),
    inference(cnf_transformation,[],[f52]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:57:03 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.46  % (4296)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.46  % (4287)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.47  % (4296)First to succeed.
% 0.19/0.47  % (4296)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Theorem for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (4296)------------------------------
% 0.19/0.47  % (4296)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (4296)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (4296)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (4296)Memory used [KB]: 5500
% 0.19/0.47  % (4296)Time elapsed: 0.076 s
% 0.19/0.47  % (4296)Instructions burned: 4 (million)
% 0.19/0.47  % (4296)------------------------------
% 0.19/0.47  % (4296)------------------------------
% 0.19/0.47  % (4275)Success in time 0.126 s
%------------------------------------------------------------------------------