TSTP Solution File: SET014+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET014+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 : n008.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 18:18:21 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   48 (  11 unt;   0 def)
%            Number of atoms       :  128 (   3 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  127 (  47   ~;  39   |;  29   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   74 (  59   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f99,plain,
    $false,
    inference(avatar_sat_refutation,[],[f70,f81,f98]) ).

fof(f98,plain,
    ~ spl5_1,
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f95,f45]) ).

fof(f45,plain,
    ~ subset(union(sK2,sK3),sK1),
    inference(backward_demodulation,[],[f38,f28]) ).

fof(f28,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(f38,plain,
    ~ subset(union(sK3,sK2),sK1),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ( subset(sK2,sK1)
    & ~ subset(union(sK3,sK2),sK1)
    & subset(sK3,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f21,f22]) ).

fof(f22,plain,
    ( ? [X0,X1,X2] :
        ( subset(X1,X0)
        & ~ subset(union(X2,X1),X0)
        & subset(X2,X0) )
   => ( subset(sK2,sK1)
      & ~ subset(union(sK3,sK2),sK1)
      & subset(sK3,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ? [X0,X1,X2] :
      ( subset(X1,X0)
      & ~ subset(union(X2,X1),X0)
      & subset(X2,X0) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ? [X0,X2,X1] :
      ( subset(X2,X0)
      & ~ subset(union(X1,X2),X0)
      & subset(X1,X0) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ? [X2,X1,X0] :
      ( ~ subset(union(X1,X2),X0)
      & subset(X2,X0)
      & subset(X1,X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X2,X1,X0] :
        ( ( subset(X2,X0)
          & subset(X1,X0) )
       => subset(union(X1,X2),X0) ),
    inference(rectify,[],[f7]) ).

fof(f7,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( ( subset(X0,X1)
          & subset(X2,X1) )
       => subset(union(X0,X2),X1) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f6,conjecture,
    ! [X1,X0,X2] :
      ( ( subset(X0,X1)
        & subset(X2,X1) )
     => subset(union(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_subset) ).

fof(f95,plain,
    ( subset(union(sK2,sK3),sK1)
    | ~ spl5_1 ),
    inference(resolution,[],[f82,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( member(sK4(X0,X1),X1)
          & ~ member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & ~ member(X2,X0) )
     => ( member(sK4(X0,X1),X1)
        & ~ member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X0) )
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) )
      & ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f82,plain,
    ( member(sK4(sK1,union(sK2,sK3)),sK1)
    | ~ spl5_1 ),
    inference(resolution,[],[f65,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(X0,sK1) ),
    inference(resolution,[],[f40,f37]) ).

fof(f37,plain,
    subset(sK3,sK1),
    inference(cnf_transformation,[],[f23]) ).

fof(f40,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X1,X0)
      | ~ member(X3,X1)
      | member(X3,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f65,plain,
    ( member(sK4(sK1,union(sK2,sK3)),sK3)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f63,plain,
    ( spl5_1
  <=> member(sK4(sK1,union(sK2,sK3)),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f81,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f79,f45]) ).

fof(f79,plain,
    ( subset(union(sK2,sK3),sK1)
    | ~ spl5_2 ),
    inference(resolution,[],[f71,f41]) ).

fof(f71,plain,
    ( member(sK4(sK1,union(sK2,sK3)),sK1)
    | ~ spl5_2 ),
    inference(resolution,[],[f69,f54]) ).

fof(f54,plain,
    ! [X1] :
      ( ~ member(X1,sK2)
      | member(X1,sK1) ),
    inference(resolution,[],[f40,f39]) ).

fof(f39,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f23]) ).

fof(f69,plain,
    ( member(sK4(sK1,union(sK2,sK3)),sK2)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl5_2
  <=> member(sK4(sK1,union(sK2,sK3)),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f70,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f61,f67,f63]) ).

fof(f61,plain,
    ( member(sK4(sK1,union(sK2,sK3)),sK2)
    | member(sK4(sK1,union(sK2,sK3)),sK3) ),
    inference(resolution,[],[f52,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X2,X1))
      | member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X2,X0,X1] :
      ( ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X1,X0)) )
      & ( member(X2,union(X1,X0))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X2,X0,X1] :
      ( ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X1,X0)) )
      & ( member(X2,union(X1,X0))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X2,X0,X1] :
      ( ( member(X2,X1)
        | member(X2,X0) )
    <=> member(X2,union(X1,X0)) ),
    inference(rectify,[],[f1]) ).

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

fof(f52,plain,
    member(sK4(sK1,union(sK2,sK3)),union(sK2,sK3)),
    inference(resolution,[],[f42,f45]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET014+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
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 12:56:10 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.48  % (30092)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.48  % (30065)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.49  % (30078)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)
% 0.19/0.49  % (30087)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.49  % (30084)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.49  % (30065)Refutation not found, incomplete strategy% (30065)------------------------------
% 0.19/0.49  % (30065)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (30065)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (30065)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.49  
% 0.19/0.49  % (30065)Memory used [KB]: 5884
% 0.19/0.49  % (30065)Time elapsed: 0.094 s
% 0.19/0.49  % (30065)Instructions burned: 1 (million)
% 0.19/0.49  % (30065)------------------------------
% 0.19/0.49  % (30065)------------------------------
% 0.19/0.49  % (30063)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.49  % (30078)First to succeed.
% 0.19/0.49  % (30064)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.49  % (30070)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)
% 0.19/0.50  % (30086)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)
% 0.19/0.50  % (30074)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (30078)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (30078)------------------------------
% 0.19/0.50  % (30078)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (30078)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (30078)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (30078)Memory used [KB]: 6012
% 0.19/0.50  % (30078)Time elapsed: 0.061 s
% 0.19/0.50  % (30078)Instructions burned: 4 (million)
% 0.19/0.50  % (30078)------------------------------
% 0.19/0.50  % (30078)------------------------------
% 0.19/0.50  % (30060)Success in time 0.158 s
%------------------------------------------------------------------------------