TSTP Solution File: SEU321+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n005.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 : Sat Sep  2 00:14:46 EDT 2023

% Result   : Theorem 0.17s 0.44s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (   9 unt;   0 def)
%            Number of atoms       :  174 (  10 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  212 (  80   ~;  61   |;  52   &)
%                                         (   2 <=>;  15  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   55 (;  34   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f789,plain,
    $false,
    inference(resolution,[],[f602,f116]) ).

fof(f116,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( v5_membered(empty_set)
    & v4_membered(empty_set)
    & v3_membered(empty_set)
    & v2_membered(empty_set)
    & v1_membered(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',fc6_membered) ).

fof(f602,plain,
    ~ empty(empty_set),
    inference(backward_demodulation,[],[f200,f595]) ).

fof(f595,plain,
    empty_set = the_carrier(sK3),
    inference(resolution,[],[f591,f113]) ).

fof(f113,plain,
    element(sK5,the_carrier(sK3)),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ( in(sK5,sK4)
      | ~ in(sK5,subset_complement(the_carrier(sK3),sK4)) )
    & ( ~ in(sK5,sK4)
      | in(sK5,subset_complement(the_carrier(sK3),sK4)) )
    & element(sK5,the_carrier(sK3))
    & element(sK4,powerset(the_carrier(sK3)))
    & one_sorted_str(sK3)
    & ~ empty_carrier(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f89,f92,f91,f90]) ).

fof(f90,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ( in(X2,X1)
                  | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
                & ( ~ in(X2,X1)
                  | in(X2,subset_complement(the_carrier(X0),X1)) )
                & element(X2,the_carrier(X0)) )
            & element(X1,powerset(the_carrier(X0))) )
        & one_sorted_str(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(sK3),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(sK3),X1)) )
              & element(X2,the_carrier(sK3)) )
          & element(X1,powerset(the_carrier(sK3))) )
      & one_sorted_str(sK3)
      & ~ empty_carrier(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ( in(X2,X1)
              | ~ in(X2,subset_complement(the_carrier(sK3),X1)) )
            & ( ~ in(X2,X1)
              | in(X2,subset_complement(the_carrier(sK3),X1)) )
            & element(X2,the_carrier(sK3)) )
        & element(X1,powerset(the_carrier(sK3))) )
   => ( ? [X2] :
          ( ( in(X2,sK4)
            | ~ in(X2,subset_complement(the_carrier(sK3),sK4)) )
          & ( ~ in(X2,sK4)
            | in(X2,subset_complement(the_carrier(sK3),sK4)) )
          & element(X2,the_carrier(sK3)) )
      & element(sK4,powerset(the_carrier(sK3))) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ( ? [X2] :
        ( ( in(X2,sK4)
          | ~ in(X2,subset_complement(the_carrier(sK3),sK4)) )
        & ( ~ in(X2,sK4)
          | in(X2,subset_complement(the_carrier(sK3),sK4)) )
        & element(X2,the_carrier(sK3)) )
   => ( ( in(sK5,sK4)
        | ~ in(sK5,subset_complement(the_carrier(sK3),sK4)) )
      & ( ~ in(sK5,sK4)
        | in(sK5,subset_complement(the_carrier(sK3),sK4)) )
      & element(sK5,the_carrier(sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,X1)
                | ~ in(X2,subset_complement(the_carrier(X0),X1)) )
              & ( ~ in(X2,X1)
                | in(X2,subset_complement(the_carrier(X0),X1)) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <~> ~ in(X2,X1) )
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & one_sorted_str(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( one_sorted_str(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( in(X2,subset_complement(the_carrier(X0),X1))
                <=> ~ in(X2,X1) ) ) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',l40_tops_1) ).

fof(f591,plain,
    ( ~ element(sK5,the_carrier(sK3))
    | empty_set = the_carrier(sK3) ),
    inference(resolution,[],[f457,f112]) ).

fof(f112,plain,
    element(sK4,powerset(the_carrier(sK3))),
    inference(cnf_transformation,[],[f93]) ).

fof(f457,plain,
    ( ~ element(sK4,powerset(the_carrier(sK3)))
    | ~ element(sK5,the_carrier(sK3))
    | empty_set = the_carrier(sK3) ),
    inference(duplicate_literal_removal,[],[f444]) ).

fof(f444,plain,
    ( ~ element(sK5,the_carrier(sK3))
    | ~ element(sK4,powerset(the_carrier(sK3)))
    | empty_set = the_carrier(sK3)
    | ~ element(sK4,powerset(the_carrier(sK3))) ),
    inference(resolution,[],[f407,f371]) ).

fof(f371,plain,
    ( ~ in(sK5,sK4)
    | ~ element(sK4,powerset(the_carrier(sK3))) ),
    inference(duplicate_literal_removal,[],[f368]) ).

fof(f368,plain,
    ( ~ in(sK5,sK4)
    | ~ element(sK4,powerset(the_carrier(sK3)))
    | ~ in(sK5,sK4) ),
    inference(resolution,[],[f180,f114]) ).

fof(f114,plain,
    ( in(sK5,subset_complement(the_carrier(sK3),sK4))
    | ~ in(sK5,sK4) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f180,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,subset_complement(X0,X2))
      | ~ in(X1,X2)
      | ~ element(X2,powerset(X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(X0))
     => ~ ( in(X1,X2)
          & in(X1,subset_complement(X0,X2)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',t54_subset_1) ).

fof(f407,plain,
    ( in(sK5,sK4)
    | ~ element(sK5,the_carrier(sK3))
    | ~ element(sK4,powerset(the_carrier(sK3)))
    | empty_set = the_carrier(sK3) ),
    inference(duplicate_literal_removal,[],[f401]) ).

fof(f401,plain,
    ( in(sK5,sK4)
    | ~ element(sK5,the_carrier(sK3))
    | ~ element(sK4,powerset(the_carrier(sK3)))
    | empty_set = the_carrier(sK3)
    | in(sK5,sK4) ),
    inference(resolution,[],[f165,f115]) ).

fof(f115,plain,
    ( ~ in(sK5,subset_complement(the_carrier(sK3),sK4))
    | in(sK5,sK4) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( in(X2,subset_complement(X0,X1))
      | in(X2,X1)
      | ~ element(X2,X0)
      | ~ element(X1,powerset(X0))
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,subset_complement(X0,X1))
              | in(X2,X1)
              | ~ element(X2,X0) )
          | ~ element(X1,powerset(X0)) )
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( empty_set != X0
     => ! [X1] :
          ( element(X1,powerset(X0))
         => ! [X2] :
              ( element(X2,X0)
             => ( ~ in(X2,X1)
               => in(X2,subset_complement(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',t50_subset_1) ).

fof(f200,plain,
    ~ empty(the_carrier(sK3)),
    inference(resolution,[],[f198,f111]) ).

fof(f111,plain,
    one_sorted_str(sK3),
    inference(cnf_transformation,[],[f93]) ).

fof(f198,plain,
    ( ~ one_sorted_str(sK3)
    | ~ empty(the_carrier(sK3)) ),
    inference(resolution,[],[f166,f110]) ).

fof(f110,plain,
    ~ empty_carrier(sK3),
    inference(cnf_transformation,[],[f93]) ).

fof(f166,plain,
    ! [X0] :
      ( empty_carrier(X0)
      | ~ one_sorted_str(X0)
      | ~ empty(the_carrier(X0)) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ~ empty(the_carrier(X0)) ),
    file('/export/starexec/sandbox2/tmp/tmp.AA362zXckC/Vampire---4.8_15723',fc1_struct_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.34  % Computer : n005.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Wed Aug 30 14:09:37 EDT 2023
% 0.11/0.34  % CPUTime    : 
% 0.17/0.40  % (15865)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.41  % (15867)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.41  % (15869)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.41  % (15870)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.17/0.41  % (15868)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.17/0.41  % (15871)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.17/0.41  % (15872)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.17/0.41  % (15866)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.41  TRYING [1]
% 0.17/0.41  TRYING [2]
% 0.17/0.41  TRYING [3]
% 0.17/0.42  TRYING [4]
% 0.17/0.42  TRYING [1]
% 0.17/0.42  TRYING [2]
% 0.17/0.42  TRYING [1]
% 0.17/0.42  TRYING [2]
% 0.17/0.42  TRYING [3]
% 0.17/0.42  TRYING [5]
% 0.17/0.43  TRYING [4]
% 0.17/0.43  TRYING [3]
% 0.17/0.43  TRYING [5]
% 0.17/0.44  TRYING [6]
% 0.17/0.44  % (15871)First to succeed.
% 0.17/0.44  % (15870)Also succeeded, but the first one will report.
% 0.17/0.44  % (15871)Refutation found. Thanks to Tanya!
% 0.17/0.44  % SZS status Theorem for Vampire---4
% 0.17/0.44  % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.44  % (15871)------------------------------
% 0.17/0.44  % (15871)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.44  % (15871)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.44  % (15871)Termination reason: Refutation
% 0.17/0.44  
% 0.17/0.44  % (15871)Memory used [KB]: 1407
% 0.17/0.44  % (15871)Time elapsed: 0.031 s
% 0.17/0.44  % (15871)------------------------------
% 0.17/0.44  % (15871)------------------------------
% 0.17/0.44  % (15865)Success in time 0.094 s
% 0.17/0.44  % Vampire---4.8 exiting
%------------------------------------------------------------------------------