TSTP Solution File: SET600+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET600+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 : n002.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 18:21:33 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   58 (   3 unt;   0 def)
%            Number of atoms       :  204 (  66 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  240 (  94   ~; 104   |;  30   &)
%                                         (   9 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   63 (  52   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f228,plain,
    $false,
    inference(avatar_sat_refutation,[],[f66,f71,f72,f96,f210,f226]) ).

fof(f226,plain,
    ( ~ spl4_1
    | ~ spl4_2
    | spl4_3 ),
    inference(avatar_contradiction_clause,[],[f225]) ).

fof(f225,plain,
    ( $false
    | ~ spl4_1
    | ~ spl4_2
    | spl4_3 ),
    inference(subsumption_resolution,[],[f216,f177]) ).

fof(f177,plain,
    ( ! [X1] : ~ member(X1,sK0)
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f174,f38]) ).

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

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f174,plain,
    ( ! [X1] :
        ( member(X1,empty_set)
        | ~ member(X1,sK0) )
    | ~ spl4_1 ),
    inference(superposition,[],[f46,f61]) ).

fof(f61,plain,
    ( empty_set = union(sK0,sK1)
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f59,plain,
    ( spl4_1
  <=> empty_set = union(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X0)
          & ~ member(X2,X1) ) )
      & ( member(X2,X0)
        | member(X2,X1)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X2,X1,X0] :
      ( ( member(X0,union(X2,X1))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X2,X1)) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X2,X1,X0] :
      ( ( member(X0,union(X2,X1))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X2,X1)) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X2,X1,X0] :
      ( member(X0,union(X2,X1))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X2,X1,X0] :
      ( ( member(X2,X0)
        | member(X2,X1) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f216,plain,
    ( member(sK2(sK1,sK0),sK0)
    | ~ spl4_2
    | spl4_3 ),
    inference(backward_demodulation,[],[f165,f65]) ).

fof(f65,plain,
    ( empty_set = sK1
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f63,plain,
    ( spl4_2
  <=> empty_set = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f165,plain,
    ( member(sK2(empty_set,sK0),sK0)
    | spl4_3 ),
    inference(unit_resulting_resolution,[],[f70,f38,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X0)
      | X0 = X1
      | member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK2(X0,X1),X0)
            | ~ member(sK2(X0,X1),X1) )
          & ( member(sK2(X0,X1),X0)
            | member(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK2(X0,X1),X0)
          | ~ member(sK2(X0,X1),X1) )
        & ( member(sK2(X0,X1),X0)
          | member(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X1)
        <=> member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f70,plain,
    ( empty_set != sK0
    | spl4_3 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f68,plain,
    ( spl4_3
  <=> empty_set = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f210,plain,
    ( ~ spl4_1
    | spl4_2 ),
    inference(avatar_contradiction_clause,[],[f209]) ).

fof(f209,plain,
    ( $false
    | ~ spl4_1
    | spl4_2 ),
    inference(subsumption_resolution,[],[f190,f38]) ).

fof(f190,plain,
    ( member(sK2(sK1,empty_set),empty_set)
    | ~ spl4_1
    | spl4_2 ),
    inference(unit_resulting_resolution,[],[f64,f176,f41]) ).

fof(f176,plain,
    ( ! [X0] : ~ member(X0,sK1)
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f173,f38]) ).

fof(f173,plain,
    ( ! [X0] :
        ( member(X0,empty_set)
        | ~ member(X0,sK1) )
    | ~ spl4_1 ),
    inference(superposition,[],[f45,f61]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f64,plain,
    ( empty_set != sK1
    | spl4_2 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f96,plain,
    ( spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(avatar_contradiction_clause,[],[f95]) ).

fof(f95,plain,
    ( $false
    | spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(subsumption_resolution,[],[f91,f81]) ).

fof(f81,plain,
    ( ! [X0] : ~ member(X0,union(sK0,sK0))
    | ~ spl4_3 ),
    inference(unit_resulting_resolution,[],[f73,f73,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f73,plain,
    ( ! [X0] : ~ member(X0,sK0)
    | ~ spl4_3 ),
    inference(backward_demodulation,[],[f38,f69]) ).

fof(f69,plain,
    ( empty_set = sK0
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f91,plain,
    ( member(sK2(sK0,union(sK0,sK0)),union(sK0,sK0))
    | spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(unit_resulting_resolution,[],[f73,f76,f41]) ).

fof(f76,plain,
    ( sK0 != union(sK0,sK0)
    | spl4_1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(backward_demodulation,[],[f74,f75]) ).

fof(f75,plain,
    ( sK0 = sK1
    | ~ spl4_2
    | ~ spl4_3 ),
    inference(forward_demodulation,[],[f65,f69]) ).

fof(f74,plain,
    ( sK0 != union(sK0,sK1)
    | spl4_1
    | ~ spl4_3 ),
    inference(forward_demodulation,[],[f60,f69]) ).

fof(f60,plain,
    ( empty_set != union(sK0,sK1)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f72,plain,
    ( spl4_3
    | spl4_1 ),
    inference(avatar_split_clause,[],[f35,f59,f68]) ).

fof(f35,plain,
    ( empty_set = union(sK0,sK1)
    | empty_set = sK0 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( ( empty_set != union(sK0,sK1)
      | empty_set != sK1
      | empty_set != sK0 )
    & ( empty_set = union(sK0,sK1)
      | ( empty_set = sK1
        & empty_set = sK0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).

fof(f18,plain,
    ( ? [X0,X1] :
        ( ( union(X0,X1) != empty_set
          | empty_set != X1
          | empty_set != X0 )
        & ( union(X0,X1) = empty_set
          | ( empty_set = X1
            & empty_set = X0 ) ) )
   => ( ( empty_set != union(sK0,sK1)
        | empty_set != sK1
        | empty_set != sK0 )
      & ( empty_set = union(sK0,sK1)
        | ( empty_set = sK1
          & empty_set = sK0 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ? [X0,X1] :
      ( ( union(X0,X1) != empty_set
        | empty_set != X1
        | empty_set != X0 )
      & ( union(X0,X1) = empty_set
        | ( empty_set = X1
          & empty_set = X0 ) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( ( union(X0,X1) != empty_set
        | empty_set != X1
        | empty_set != X0 )
      & ( union(X0,X1) = empty_set
        | ( empty_set = X1
          & empty_set = X0 ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ? [X0,X1] :
      ( ( empty_set = X1
        & empty_set = X0 )
    <~> union(X0,X1) = empty_set ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X0] :
        ( union(X0,X1) = empty_set
      <=> ( empty_set = X1
          & empty_set = X0 ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X0] :
      ( union(X0,X1) = empty_set
    <=> ( empty_set = X1
        & empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).

fof(f71,plain,
    ( ~ spl4_1
    | ~ spl4_3
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f37,f63,f68,f59]) ).

fof(f37,plain,
    ( empty_set != sK1
    | empty_set != sK0
    | empty_set != union(sK0,sK1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f66,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f36,f63,f59]) ).

fof(f36,plain,
    ( empty_set = sK1
    | empty_set = union(sK0,sK1) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n002.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 14:16:14 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.44  % (14051)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.45  % (14043)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.47  % (14051)Refutation not found, incomplete strategy% (14051)------------------------------
% 0.20/0.47  % (14051)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47  % (14051)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47  % (14051)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.47  
% 0.20/0.47  % (14051)Memory used [KB]: 1535
% 0.20/0.47  % (14051)Time elapsed: 0.065 s
% 0.20/0.47  % (14051)Instructions burned: 7 (million)
% 0.20/0.47  % (14051)------------------------------
% 0.20/0.47  % (14051)------------------------------
% 0.20/0.47  % (14043)Instruction limit reached!
% 0.20/0.47  % (14043)------------------------------
% 0.20/0.47  % (14043)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (14035)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)
% 0.20/0.48  % (14043)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (14043)Termination reason: Unknown
% 0.20/0.48  % (14043)Termination phase: Saturation
% 0.20/0.48  
% 0.20/0.48  % (14043)Memory used [KB]: 6012
% 0.20/0.48  % (14043)Time elapsed: 0.058 s
% 0.20/0.48  % (14043)Instructions burned: 7 (million)
% 0.20/0.48  % (14043)------------------------------
% 0.20/0.48  % (14043)------------------------------
% 0.20/0.48  % (14035)First to succeed.
% 0.20/0.49  % (14035)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (14035)------------------------------
% 0.20/0.49  % (14035)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (14035)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (14035)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (14035)Memory used [KB]: 6012
% 0.20/0.49  % (14035)Time elapsed: 0.070 s
% 0.20/0.49  % (14035)Instructions burned: 5 (million)
% 0.20/0.49  % (14035)------------------------------
% 0.20/0.49  % (14035)------------------------------
% 0.20/0.49  % (14025)Success in time 0.145 s
%------------------------------------------------------------------------------