TSTP Solution File: SET076+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET076+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : n020.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 18:18:57 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   59 (  17 unt;   0 def)
%            Number of atoms       :  167 (  30 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  171 (  63   ~;  52   |;  42   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  115 ( 100   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f302,plain,
    $false,
    inference(avatar_sat_refutation,[],[f248,f275,f300]) ).

fof(f300,plain,
    ~ spl4_1,
    inference(avatar_contradiction_clause,[],[f299]) ).

fof(f299,plain,
    ( $false
    | ~ spl4_1 ),
    inference(subsumption_resolution,[],[f217,f286]) ).

fof(f286,plain,
    ( ! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK1,sK1))),cross_product(X4,sK2))
    | ~ spl4_1 ),
    inference(forward_demodulation,[],[f169,f243]) ).

fof(f243,plain,
    ( sK0(sK2,unordered_pair(sK1,sK3)) = sK1
    | ~ spl4_1 ),
    inference(avatar_component_clause,[],[f241]) ).

fof(f241,plain,
    ( spl4_1
  <=> sK0(sK2,unordered_pair(sK1,sK3)) = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f169,plain,
    ! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))))),cross_product(X4,sK2)),
    inference(resolution,[],[f122,f93]) ).

fof(f93,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(X1,X3))
      | member(X0,X3) ),
    inference(definition_unfolding,[],[f86,f91]) ).

fof(f91,plain,
    ! [X0,X1] : unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))) = ordered_pair(X1,X0),
    inference(definition_unfolding,[],[f71,f72,f72]) ).

fof(f72,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f71,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).

fof(f86,plain,
    ! [X2,X3,X0,X1] :
      ( member(X0,X3)
      | ~ member(ordered_pair(X2,X0),cross_product(X1,X3)) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( member(X2,X1)
          & member(X0,X3) )
        | ~ member(ordered_pair(X2,X0),cross_product(X1,X3)) )
      & ( member(ordered_pair(X2,X0),cross_product(X1,X3))
        | ~ member(X2,X1)
        | ~ member(X0,X3) ) ),
    inference(rectify,[],[f67]) ).

fof(f67,plain,
    ! [X2,X0,X1,X3] :
      ( ( ( member(X1,X0)
          & member(X2,X3) )
        | ~ member(ordered_pair(X1,X2),cross_product(X0,X3)) )
      & ( member(ordered_pair(X1,X2),cross_product(X0,X3))
        | ~ member(X1,X0)
        | ~ member(X2,X3) ) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X2,X0,X1,X3] :
      ( ( ( member(X1,X0)
          & member(X2,X3) )
        | ~ member(ordered_pair(X1,X2),cross_product(X0,X3)) )
      & ( member(ordered_pair(X1,X2),cross_product(X0,X3))
        | ~ member(X1,X0)
        | ~ member(X2,X3) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X1,X3] :
      ( ( member(X1,X0)
        & member(X2,X3) )
    <=> member(ordered_pair(X1,X2),cross_product(X0,X3)) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X2,X3,X1] :
      ( ( member(X2,X0)
        & member(X3,X1) )
    <=> member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).

fof(f122,plain,
    ~ member(sK0(sK2,unordered_pair(sK1,sK3)),sK2),
    inference(unit_resulting_resolution,[],[f82,f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X0)
      | subclass(X1,X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ( member(sK0(X0,X1),X1)
          & ~ member(sK0(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f60,f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK0(X0,X1),X1)
        & ~ member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subclass(X1,X0) )
      & ( subclass(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f59]) ).

fof(f59,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subclass(X0,X1) )
      & ( subclass(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subclass(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f82,plain,
    ~ subclass(unordered_pair(sK1,sK3),sK2),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ( member(sK3,sK2)
    & member(sK1,sK2)
    & ~ subclass(unordered_pair(sK1,sK3),sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f63,f64]) ).

fof(f64,plain,
    ( ? [X0,X1,X2] :
        ( member(X2,X1)
        & member(X0,X1)
        & ~ subclass(unordered_pair(X0,X2),X1) )
   => ( member(sK3,sK2)
      & member(sK1,sK2)
      & ~ subclass(unordered_pair(sK1,sK3),sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ? [X0,X1,X2] :
      ( member(X2,X1)
      & member(X0,X1)
      & ~ subclass(unordered_pair(X0,X2),X1) ),
    inference(rectify,[],[f53]) ).

fof(f53,plain,
    ? [X2,X0,X1] :
      ( member(X1,X0)
      & member(X2,X0)
      & ~ subclass(unordered_pair(X2,X1),X0) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X0,X2,X1] :
      ( ~ subclass(unordered_pair(X2,X1),X0)
      & member(X1,X0)
      & member(X2,X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ~ ! [X0,X2,X1] :
        ( ( member(X1,X0)
          & member(X2,X0) )
       => subclass(unordered_pair(X2,X1),X0) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X4,X1,X0] :
        ( ( member(X0,X4)
          & member(X1,X4) )
       => subclass(unordered_pair(X0,X1),X4) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X4,X1,X0] :
      ( ( member(X0,X4)
        & member(X1,X4) )
     => subclass(unordered_pair(X0,X1),X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).

fof(f217,plain,
    member(unordered_pair(unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))),unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK1,sK1))),cross_product(unordered_pair(sK1,sK3),sK2)),
    inference(unit_resulting_resolution,[],[f83,f121,f94]) ).

fof(f94,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X0,X3)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(X1,X3))
      | ~ member(X2,X1) ),
    inference(definition_unfolding,[],[f85,f91]) ).

fof(f85,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X2,X0),cross_product(X1,X3))
      | ~ member(X2,X1)
      | ~ member(X0,X3) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f121,plain,
    member(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK1,sK3)),
    inference(unit_resulting_resolution,[],[f82,f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( subclass(X1,X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f83,plain,
    member(sK1,sK2),
    inference(cnf_transformation,[],[f65]) ).

fof(f275,plain,
    ~ spl4_2,
    inference(avatar_contradiction_clause,[],[f274]) ).

fof(f274,plain,
    ( $false
    | ~ spl4_2 ),
    inference(subsumption_resolution,[],[f261,f253]) ).

fof(f253,plain,
    ( ! [X3,X4] : ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(sK3,sK3))),cross_product(X4,sK2))
    | ~ spl4_2 ),
    inference(backward_demodulation,[],[f169,f247]) ).

fof(f247,plain,
    ( sK3 = sK0(sK2,unordered_pair(sK1,sK3))
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f245,plain,
    ( spl4_2
  <=> sK3 = sK0(sK2,unordered_pair(sK1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f261,plain,
    ( member(unordered_pair(unordered_pair(sK3,sK3),unordered_pair(sK3,unordered_pair(sK3,sK3))),cross_product(unordered_pair(sK1,sK3),sK2))
    | ~ spl4_2 ),
    inference(backward_demodulation,[],[f221,f247]) ).

fof(f221,plain,
    member(unordered_pair(unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),sK0(sK2,unordered_pair(sK1,sK3))),unordered_pair(sK0(sK2,unordered_pair(sK1,sK3)),unordered_pair(sK3,sK3))),cross_product(unordered_pair(sK1,sK3),sK2)),
    inference(unit_resulting_resolution,[],[f84,f121,f94]) ).

fof(f84,plain,
    member(sK3,sK2),
    inference(cnf_transformation,[],[f65]) ).

fof(f248,plain,
    ( spl4_1
    | spl4_2 ),
    inference(avatar_split_clause,[],[f236,f245,f241]) ).

fof(f236,plain,
    ( sK3 = sK0(sK2,unordered_pair(sK1,sK3))
    | sK0(sK2,unordered_pair(sK1,sK3)) = sK1 ),
    inference(resolution,[],[f121,f73]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X2,X1))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X2,X1))
        | ~ member(X0,universal_class)
        | ( X0 != X2
          & X0 != X1 ) )
      & ( ( member(X0,universal_class)
          & ( X0 = X2
            | X0 = X1 ) )
        | ~ member(X0,unordered_pair(X2,X1)) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X0,X2,X1] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | ( X0 != X1
          & X0 != X2 ) )
      & ( ( member(X0,universal_class)
          & ( X0 = X1
            | X0 = X2 ) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X2,X1] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | ( X0 != X1
          & X0 != X2 ) )
      & ( ( member(X0,universal_class)
          & ( X0 = X1
            | X0 = X2 ) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X2,X1] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( member(X0,universal_class)
        & ( X0 = X1
          | X0 = X2 ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( ( ( X0 = X2
          | X1 = X2 )
        & member(X2,universal_class) )
    <=> member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET076+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n020.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 13:11:15 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.47  % (31810)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)
% 0.19/0.48  % (31818)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)
% 0.19/0.48  % (31801)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)
% 0.19/0.48  % (31810)Instruction limit reached!
% 0.19/0.48  % (31810)------------------------------
% 0.19/0.48  % (31810)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (31810)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (31810)Termination reason: Unknown
% 0.19/0.48  % (31810)Termination phase: Saturation
% 0.19/0.48  
% 0.19/0.48  % (31810)Memory used [KB]: 6140
% 0.19/0.48  % (31810)Time elapsed: 0.009 s
% 0.19/0.48  % (31810)Instructions burned: 8 (million)
% 0.19/0.48  % (31810)------------------------------
% 0.19/0.48  % (31810)------------------------------
% 0.19/0.50  % (31817)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (31814)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.50  % (31796)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)
% 0.19/0.50  % (31796)Instruction limit reached!
% 0.19/0.50  % (31796)------------------------------
% 0.19/0.50  % (31796)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (31796)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (31796)Termination reason: Unknown
% 0.19/0.50  % (31796)Termination phase: Function definition elimination
% 0.19/0.50  
% 0.19/0.50  % (31796)Memory used [KB]: 1535
% 0.19/0.50  % (31796)Time elapsed: 0.005 s
% 0.19/0.50  % (31796)Instructions burned: 4 (million)
% 0.19/0.50  % (31796)------------------------------
% 0.19/0.50  % (31796)------------------------------
% 0.19/0.50  % (31798)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (31806)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)
% 0.19/0.51  % (31801)First to succeed.
% 0.19/0.51  % (31799)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)
% 0.19/0.51  % (31801)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (31801)------------------------------
% 0.19/0.51  % (31801)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (31801)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (31801)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (31801)Memory used [KB]: 6140
% 0.19/0.51  % (31801)Time elapsed: 0.080 s
% 0.19/0.51  % (31801)Instructions burned: 10 (million)
% 0.19/0.51  % (31801)------------------------------
% 0.19/0.51  % (31801)------------------------------
% 0.19/0.51  % (31792)Success in time 0.163 s
%------------------------------------------------------------------------------