TSTP Solution File: SEU328+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU328+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_uns --cores 0 -t %d %s

% Computer : n009.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 18:28:48 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   50 (  20 unt;   0 def)
%            Number of atoms       :   99 (  54 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   84 (  35   ~;  20   |;  12   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :   65 (  59   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f442,plain,
    $false,
    inference(subsumption_resolution,[],[f440,f311]) ).

fof(f311,plain,
    subset_complement(sK2,set_meet(sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(backward_demodulation,[],[f184,f257]) ).

fof(f257,plain,
    meet_of_subsets(sK2,sK1) = set_meet(sK1),
    inference(unit_resulting_resolution,[],[f186,f240]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(powerset(X0)))
      | meet_of_subsets(X0,X1) = set_meet(X1) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( meet_of_subsets(X0,X1) = set_meet(X1)
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X1,X0] :
      ( set_meet(X0) = meet_of_subsets(X1,X0)
      | ~ element(X0,powerset(powerset(X1))) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X1,X0] :
      ( element(X0,powerset(powerset(X1)))
     => set_meet(X0) = meet_of_subsets(X1,X0) ),
    inference(rectify,[],[f45]) ).

fof(f45,axiom,
    ! [X1,X0] :
      ( element(X1,powerset(powerset(X0)))
     => meet_of_subsets(X0,X1) = set_meet(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).

fof(f186,plain,
    element(sK1,powerset(powerset(sK2))),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ( element(sK1,powerset(powerset(sK2)))
    & empty_set != sK1
    & subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f100,f148]) ).

fof(f148,plain,
    ( ? [X0,X1] :
        ( element(X0,powerset(powerset(X1)))
        & empty_set != X0
        & subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0)) )
   => ( element(sK1,powerset(powerset(sK2)))
      & empty_set != sK1
      & subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0,X1] :
      ( element(X0,powerset(powerset(X1)))
      & empty_set != X0
      & subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0)) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X1,X0] :
      ( subset_complement(X1,meet_of_subsets(X1,X0)) != union_of_subsets(X1,complements_of_subsets(X1,X0))
      & empty_set != X0
      & element(X0,powerset(powerset(X1))) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ~ ! [X1,X0] :
        ( element(X0,powerset(powerset(X1)))
       => ( empty_set != X0
         => subset_complement(X1,meet_of_subsets(X1,X0)) = union_of_subsets(X1,complements_of_subsets(X1,X0)) ) ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X1,X0] :
        ( element(X1,powerset(powerset(X0)))
       => ( empty_set != X1
         => union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X1,X0] :
      ( element(X1,powerset(powerset(X0)))
     => ( empty_set != X1
       => union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_complement(X0,meet_of_subsets(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_tops_2) ).

fof(f184,plain,
    subset_complement(sK2,meet_of_subsets(sK2,sK1)) != union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(cnf_transformation,[],[f149]) ).

fof(f440,plain,
    subset_complement(sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(backward_demodulation,[],[f428,f383]) ).

fof(f383,plain,
    set_difference(sK2,set_meet(sK1)) = subset_complement(sK2,set_meet(sK1)),
    inference(unit_resulting_resolution,[],[f324,f177]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X1,X0] :
      ( element(X0,powerset(X1))
     => subset_complement(X1,X0) = set_difference(X1,X0) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X1,X0] :
      ( element(X1,powerset(X0))
     => subset_complement(X0,X1) = set_difference(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f324,plain,
    element(set_meet(sK1),powerset(sK2)),
    inference(forward_demodulation,[],[f254,f257]) ).

fof(f254,plain,
    element(meet_of_subsets(sK2,sK1),powerset(sK2)),
    inference(unit_resulting_resolution,[],[f186,f178]) ).

fof(f178,plain,
    ! [X0,X1] :
      ( element(meet_of_subsets(X1,X0),powerset(X1))
      | ~ element(X0,powerset(powerset(X1))) ),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( element(meet_of_subsets(X1,X0),powerset(X1))
      | ~ element(X0,powerset(powerset(X1))) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X1,X0] :
      ( element(X0,powerset(powerset(X1)))
     => element(meet_of_subsets(X1,X0),powerset(X1)) ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X1,X0] :
      ( element(X1,powerset(powerset(X0)))
     => element(meet_of_subsets(X0,X1),powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).

fof(f428,plain,
    set_difference(sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(backward_demodulation,[],[f310,f427]) ).

fof(f427,plain,
    set_difference(sK2,set_meet(sK1)) = subset_difference(sK2,sK2,set_meet(sK1)),
    inference(forward_demodulation,[],[f384,f220]) ).

fof(f220,plain,
    ! [X0] : cast_to_subset(X0) = X0,
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] : cast_to_subset(X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).

fof(f384,plain,
    subset_difference(sK2,cast_to_subset(sK2),set_meet(sK1)) = set_difference(cast_to_subset(sK2),set_meet(sK1)),
    inference(unit_resulting_resolution,[],[f168,f324,f187]) ).

fof(f187,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X0))
      | ~ element(X2,powerset(X0))
      | set_difference(X2,X1) = subset_difference(X0,X2,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( ~ element(X1,powerset(X0))
      | set_difference(X2,X1) = subset_difference(X0,X2,X1)
      | ~ element(X2,powerset(X0)) ),
    inference(flattening,[],[f114]) ).

fof(f114,plain,
    ! [X2,X0,X1] :
      ( set_difference(X2,X1) = subset_difference(X0,X2,X1)
      | ~ element(X2,powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( ( element(X2,powerset(X0))
        & element(X1,powerset(X0)) )
     => set_difference(X2,X1) = subset_difference(X0,X2,X1) ),
    inference(rectify,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X2,X1] :
      ( ( element(X1,powerset(X0))
        & element(X2,powerset(X0)) )
     => subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

fof(f168,plain,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).

fof(f310,plain,
    subset_difference(sK2,sK2,set_meet(sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(backward_demodulation,[],[f305,f257]) ).

fof(f305,plain,
    subset_difference(sK2,sK2,meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(forward_demodulation,[],[f304,f220]) ).

fof(f304,plain,
    subset_difference(sK2,cast_to_subset(sK2),meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)),
    inference(subsumption_resolution,[],[f282,f185]) ).

fof(f185,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f149]) ).

fof(f282,plain,
    ( empty_set = sK1
    | subset_difference(sK2,cast_to_subset(sK2),meet_of_subsets(sK2,sK1)) = union_of_subsets(sK2,complements_of_subsets(sK2,sK1)) ),
    inference(resolution,[],[f186,f230]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(powerset(X0)))
      | union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
      | empty_set = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f128]) ).

fof(f128,plain,
    ! [X1,X0] :
      ( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
      | empty_set = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,axiom,
    ! [X1,X0] :
      ( element(X1,powerset(powerset(X0)))
     => ( empty_set != X1
       => union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_setfam_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SEU328+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.33  % Computer : n009.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Tue Aug 30 15:10:05 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.19/0.45  % (26605)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)
% 0.19/0.47  % (26613)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)
% 0.19/0.47  % (26613)First to succeed.
% 0.19/0.49  % (26613)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (26613)------------------------------
% 0.19/0.49  % (26613)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (26613)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (26613)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (26613)Memory used [KB]: 6140
% 0.19/0.49  % (26613)Time elapsed: 0.079 s
% 0.19/0.49  % (26613)Instructions burned: 12 (million)
% 0.19/0.49  % (26613)------------------------------
% 0.19/0.49  % (26613)------------------------------
% 0.19/0.49  % (26591)Success in time 0.152 s
%------------------------------------------------------------------------------