TSTP Solution File: SET636+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET636+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 : n025.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 18:21:42 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   67 (   5 unt;   0 def)
%            Number of atoms       :  216 (  30 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  243 (  94   ~; 100   |;  35   &)
%                                         (  10 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   98 (  83   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f235,plain,
    $false,
    inference(avatar_sat_refutation,[],[f76,f79,f182,f234]) ).

fof(f234,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f233]) ).

fof(f233,plain,
    ( $false
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f219,f207]) ).

fof(f207,plain,
    ( member(sK2(sK1,sK0),sK0)
    | spl5_1 ),
    inference(resolution,[],[f184,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | member(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ( member(sK2(X0,X1),X1)
          & member(sK2(X0,X1),X0) )
        | ~ intersect(X0,X1) )
      & ( intersect(X0,X1)
        | ! [X3] :
            ( ~ member(X3,X1)
            | ~ member(X3,X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
     => ( member(sK2(X0,X1),X1)
        & member(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
        | ~ intersect(X0,X1) )
      & ( intersect(X0,X1)
        | ! [X3] :
            ( ~ member(X3,X1)
            | ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
        | ~ intersect(X0,X1) )
      & ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) )
    <=> intersect(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).

fof(f184,plain,
    ( intersect(sK1,sK0)
    | spl5_1 ),
    inference(resolution,[],[f71,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | intersect(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( disjoint(X1,X0)
        | intersect(X1,X0) )
      & ( ~ intersect(X1,X0)
        | ~ disjoint(X1,X0) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0] :
      ( ( disjoint(X0,X1)
        | intersect(X0,X1) )
      & ( ~ intersect(X0,X1)
        | ~ disjoint(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
    <=> ~ intersect(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).

fof(f71,plain,
    ( ~ disjoint(sK1,sK0)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f69,plain,
    ( spl5_1
  <=> disjoint(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f219,plain,
    ( ~ member(sK2(sK1,sK0),sK0)
    | spl5_1
    | ~ spl5_2 ),
    inference(unit_resulting_resolution,[],[f205,f196]) ).

fof(f196,plain,
    ( ! [X2] :
        ( ~ member(X2,sK1)
        | ~ member(X2,sK0) )
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f193,f43]) ).

fof(f43,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f193,plain,
    ( ! [X2] :
        ( ~ member(X2,sK0)
        | ~ member(X2,sK1)
        | member(X2,empty_set) )
    | ~ spl5_2 ),
    inference(superposition,[],[f46,f74]) ).

fof(f74,plain,
    ( empty_set = intersection(sK0,sK1)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f73,plain,
    ( spl5_2
  <=> empty_set = intersection(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X0,intersection(X2,X1))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

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

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

fof(f19,plain,
    ! [X2,X0,X1] :
      ( ( member(X2,intersection(X1,X0))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X1,X0)) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X1,X0))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

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

fof(f205,plain,
    ( member(sK2(sK1,sK0),sK1)
    | spl5_1 ),
    inference(resolution,[],[f184,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f182,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f181]) ).

fof(f181,plain,
    ( $false
    | ~ spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f171,f107]) ).

fof(f107,plain,
    ( member(sK3(empty_set,intersection(sK0,sK1)),sK0)
    | spl5_2 ),
    inference(resolution,[],[f82,f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f82,plain,
    ( member(sK3(empty_set,intersection(sK0,sK1)),intersection(sK0,sK1))
    | spl5_2 ),
    inference(unit_resulting_resolution,[],[f43,f75,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X0)
      | member(sK3(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ( ( ~ member(sK3(X0,X1),X0)
            | ~ member(sK3(X0,X1),X1) )
          & ( member(sK3(X0,X1),X0)
            | member(sK3(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ member(X3,X0)
            | ~ member(X3,X1) )
          & ( member(X3,X0)
            | member(X3,X1) ) )
     => ( ( ~ member(sK3(X0,X1),X0)
          | ~ member(sK3(X0,X1),X1) )
        & ( member(sK3(X0,X1),X0)
          | member(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ? [X3] :
            ( ( ~ member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X0)
              | member(X3,X1) ) ) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
        <=> member(X2,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f75,plain,
    ( empty_set != intersection(sK0,sK1)
    | spl5_2 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f171,plain,
    ( ~ member(sK3(empty_set,intersection(sK0,sK1)),sK0)
    | ~ spl5_1
    | spl5_2 ),
    inference(resolution,[],[f106,f86]) ).

fof(f86,plain,
    ( ! [X0] :
        ( ~ member(X0,sK1)
        | ~ member(X0,sK0) )
    | ~ spl5_1 ),
    inference(resolution,[],[f81,f50]) ).

fof(f50,plain,
    ! [X3,X0,X1] :
      ( intersect(X0,X1)
      | ~ member(X3,X0)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f81,plain,
    ( ~ intersect(sK1,sK0)
    | ~ spl5_1 ),
    inference(resolution,[],[f70,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ disjoint(X1,X0)
      | ~ intersect(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f70,plain,
    ( disjoint(sK1,sK0)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f106,plain,
    ( member(sK3(empty_set,intersection(sK0,sK1)),sK1)
    | spl5_2 ),
    inference(resolution,[],[f82,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,intersection(X2,X1))
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f79,plain,
    ( spl5_2
    | spl5_1 ),
    inference(avatar_split_clause,[],[f67,f69,f73]) ).

fof(f67,plain,
    ( disjoint(sK1,sK0)
    | empty_set = intersection(sK0,sK1) ),
    inference(forward_demodulation,[],[f47,f42]) ).

fof(f42,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f47,plain,
    ( empty_set = intersection(sK1,sK0)
    | disjoint(sK1,sK0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ( ~ disjoint(sK1,sK0)
      | empty_set != intersection(sK1,sK0) )
    & ( disjoint(sK1,sK0)
      | empty_set = intersection(sK1,sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f24]) ).

fof(f24,plain,
    ( ? [X0,X1] :
        ( ( ~ disjoint(X1,X0)
          | empty_set != intersection(X1,X0) )
        & ( disjoint(X1,X0)
          | empty_set = intersection(X1,X0) ) )
   => ( ( ~ disjoint(sK1,sK0)
        | empty_set != intersection(sK1,sK0) )
      & ( disjoint(sK1,sK0)
        | empty_set = intersection(sK1,sK0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0,X1] :
      ( ( ~ disjoint(X1,X0)
        | empty_set != intersection(X1,X0) )
      & ( disjoint(X1,X0)
        | empty_set = intersection(X1,X0) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ? [X1,X0] :
      ( ( ~ disjoint(X0,X1)
        | intersection(X0,X1) != empty_set )
      & ( disjoint(X0,X1)
        | intersection(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ? [X1,X0] :
      ( intersection(X0,X1) = empty_set
    <~> disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1] :
        ( intersection(X0,X1) = empty_set
      <=> disjoint(X0,X1) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X1] :
      ( intersection(X0,X1) = empty_set
    <=> disjoint(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).

fof(f76,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f66,f73,f69]) ).

fof(f66,plain,
    ( empty_set != intersection(sK0,sK1)
    | ~ disjoint(sK1,sK0) ),
    inference(forward_demodulation,[],[f48,f42]) ).

fof(f48,plain,
    ( ~ disjoint(sK1,sK0)
    | empty_set != intersection(sK1,sK0) ),
    inference(cnf_transformation,[],[f25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % 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 : n025.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 14:18:00 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (7755)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)
% 0.21/0.50  % (7763)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (7756)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.51  % (7755)Refutation not found, incomplete strategy% (7755)------------------------------
% 0.21/0.51  % (7755)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (7755)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (7755)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51  
% 0.21/0.51  % (7755)Memory used [KB]: 1407
% 0.21/0.51  % (7755)Time elapsed: 0.106 s
% 0.21/0.51  % (7755)Instructions burned: 2 (million)
% 0.21/0.51  % (7755)------------------------------
% 0.21/0.51  % (7755)------------------------------
% 0.21/0.51  % (7771)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)
% 0.21/0.51  % (7767)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.51  % (7750)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)
% 0.21/0.52  % (7771)First to succeed.
% 0.21/0.52  % (7768)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.52  % (7750)Refutation not found, incomplete strategy% (7750)------------------------------
% 0.21/0.52  % (7750)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (7750)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (7750)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52  
% 0.21/0.52  % (7750)Memory used [KB]: 5884
% 0.21/0.52  % (7750)Time elapsed: 0.112 s
% 0.21/0.52  % (7750)Instructions burned: 2 (million)
% 0.21/0.52  % (7750)------------------------------
% 0.21/0.52  % (7750)------------------------------
% 0.21/0.52  % (7773)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)
% 0.21/0.52  % (7759)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)
% 0.21/0.52  % (7771)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (7771)------------------------------
% 0.21/0.52  % (7771)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (7771)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (7771)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (7771)Memory used [KB]: 6012
% 0.21/0.52  % (7771)Time elapsed: 0.113 s
% 0.21/0.52  % (7771)Instructions burned: 6 (million)
% 0.21/0.52  % (7771)------------------------------
% 0.21/0.52  % (7771)------------------------------
% 0.21/0.52  % (7746)Success in time 0.165 s
%------------------------------------------------------------------------------