TSTP Solution File: TOP025+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : TOP025+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n011.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 : Fri Sep  1 05:59:49 EDT 2023

% Result   : Theorem 0.23s 0.45s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   54 (  10 unt;   0 def)
%            Number of atoms       :  223 (  26 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  258 (  89   ~;  89   |;  58   &)
%                                         (   7 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   49 (;  41   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f427,plain,
    $false,
    inference(avatar_sat_refutation,[],[f315,f391,f426]) ).

fof(f426,plain,
    ~ spl18_1,
    inference(avatar_contradiction_clause,[],[f425]) ).

fof(f425,plain,
    ( $false
    | ~ spl18_1 ),
    inference(subsumption_resolution,[],[f423,f402]) ).

fof(f402,plain,
    ( v1_tex_2(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_1 ),
    inference(backward_demodulation,[],[f185,f400]) ).

fof(f400,plain,
    ( u1_struct_0(sK0) = sK1
    | ~ spl18_1 ),
    inference(backward_demodulation,[],[f361,f392]) ).

fof(f392,plain,
    ( sK1 = k3_tex_4(sK0,sK1)
    | ~ spl18_1 ),
    inference(unit_resulting_resolution,[],[f179,f180,f181,f310,f182,f230]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( k3_tex_4(X0,X1) = X1
      | ~ v3_pre_topc(X1,X0)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( k3_tex_4(X0,X1) = X1
          | ~ v3_pre_topc(X1,X0)
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1] :
          ( k3_tex_4(X0,X1) = X1
          | ~ v3_pre_topc(X1,X0)
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,axiom,
    ! [X0] :
      ( ( l1_pre_topc(X0)
        & v2_pre_topc(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
         => ( v3_pre_topc(X1,X0)
           => k3_tex_4(X0,X1) = X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432',t58_tex_4) ).

fof(f182,plain,
    m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
    inference(cnf_transformation,[],[f145]) ).

fof(f145,plain,
    ( v1_tex_2(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
    & v1_tsp_2(sK1,sK0)
    & ( v4_pre_topc(sK1,sK0)
      | v3_pre_topc(sK1,sK0) )
    & m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
    & l1_pre_topc(sK0)
    & v2_pre_topc(sK0)
    & ~ v3_struct_0(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f81,f144,f143]) ).

fof(f143,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(X0)))
            & v1_tsp_2(X1,X0)
            & ( v4_pre_topc(X1,X0)
              | v3_pre_topc(X1,X0) )
            & m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
        & l1_pre_topc(X0)
        & v2_pre_topc(X0)
        & ~ v3_struct_0(X0) )
   => ( ? [X1] :
          ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(sK0)))
          & v1_tsp_2(X1,sK0)
          & ( v4_pre_topc(X1,sK0)
            | v3_pre_topc(X1,sK0) )
          & m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK0))) )
      & l1_pre_topc(sK0)
      & v2_pre_topc(sK0)
      & ~ v3_struct_0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f144,plain,
    ( ? [X1] :
        ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(sK0)))
        & v1_tsp_2(X1,sK0)
        & ( v4_pre_topc(X1,sK0)
          | v3_pre_topc(X1,sK0) )
        & m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK0))) )
   => ( v1_tex_2(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
      & v1_tsp_2(sK1,sK0)
      & ( v4_pre_topc(sK1,sK0)
        | v3_pre_topc(sK1,sK0) )
      & m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ? [X0] :
      ( ? [X1] :
          ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(X0)))
          & v1_tsp_2(X1,X0)
          & ( v4_pre_topc(X1,X0)
            | v3_pre_topc(X1,X0) )
          & m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      & l1_pre_topc(X0)
      & v2_pre_topc(X0)
      & ~ v3_struct_0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ? [X0] :
      ( ? [X1] :
          ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(X0)))
          & v1_tsp_2(X1,X0)
          & ( v4_pre_topc(X1,X0)
            | v3_pre_topc(X1,X0) )
          & m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      & l1_pre_topc(X0)
      & v2_pre_topc(X0)
      & ~ v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( l1_pre_topc(X0)
          & v2_pre_topc(X0)
          & ~ v3_struct_0(X0) )
       => ! [X1] :
            ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
           => ~ ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(X0)))
                & v1_tsp_2(X1,X0)
                & ( v4_pre_topc(X1,X0)
                  | v3_pre_topc(X1,X0) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0] :
      ( ( l1_pre_topc(X0)
        & v2_pre_topc(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
         => ~ ( v1_tex_2(X1,k1_zfmisc_1(u1_struct_0(X0)))
              & v1_tsp_2(X1,X0)
              & ( v4_pre_topc(X1,X0)
                | v3_pre_topc(X1,X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432',t3_tsp_2) ).

fof(f310,plain,
    ( v3_pre_topc(sK1,sK0)
    | ~ spl18_1 ),
    inference(avatar_component_clause,[],[f308]) ).

fof(f308,plain,
    ( spl18_1
  <=> v3_pre_topc(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

fof(f181,plain,
    l1_pre_topc(sK0),
    inference(cnf_transformation,[],[f145]) ).

fof(f180,plain,
    v2_pre_topc(sK0),
    inference(cnf_transformation,[],[f145]) ).

fof(f179,plain,
    ~ v3_struct_0(sK0),
    inference(cnf_transformation,[],[f145]) ).

fof(f361,plain,
    u1_struct_0(sK0) = k3_tex_4(sK0,sK1),
    inference(unit_resulting_resolution,[],[f179,f180,f181,f184,f182,f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( u1_struct_0(X0) = k3_tex_4(X0,X1)
      | ~ v1_tsp_2(X1,X0)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( v1_tsp_2(X1,X0)
              | u1_struct_0(X0) != k3_tex_4(X0,X1)
              | ~ v1_tsp_1(X1,X0) )
            & ( ( u1_struct_0(X0) = k3_tex_4(X0,X1)
                & v1_tsp_1(X1,X0) )
              | ~ v1_tsp_2(X1,X0) ) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f150]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( v1_tsp_2(X1,X0)
              | u1_struct_0(X0) != k3_tex_4(X0,X1)
              | ~ v1_tsp_1(X1,X0) )
            & ( ( u1_struct_0(X0) = k3_tex_4(X0,X1)
                & v1_tsp_1(X1,X0) )
              | ~ v1_tsp_2(X1,X0) ) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( v1_tsp_2(X1,X0)
          <=> ( u1_struct_0(X0) = k3_tex_4(X0,X1)
              & v1_tsp_1(X1,X0) ) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( v1_tsp_2(X1,X0)
          <=> ( u1_struct_0(X0) = k3_tex_4(X0,X1)
              & v1_tsp_1(X1,X0) ) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ( l1_pre_topc(X0)
        & v2_pre_topc(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
         => ( v1_tsp_2(X1,X0)
          <=> ( u1_struct_0(X0) = k3_tex_4(X0,X1)
              & v1_tsp_1(X1,X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432',d5_tsp_2) ).

fof(f184,plain,
    v1_tsp_2(sK1,sK0),
    inference(cnf_transformation,[],[f145]) ).

fof(f185,plain,
    v1_tex_2(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
    inference(cnf_transformation,[],[f145]) ).

fof(f423,plain,
    ( ~ v1_tex_2(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_1 ),
    inference(unit_resulting_resolution,[],[f401,f304]) ).

fof(f304,plain,
    ! [X1] :
      ( ~ v1_tex_2(X1,k1_zfmisc_1(X1))
      | ~ m1_subset_1(X1,k1_zfmisc_1(X1)) ),
    inference(equality_resolution,[],[f286]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ v1_tex_2(X1,k1_zfmisc_1(X0))
      | ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
    inference(cnf_transformation,[],[f170]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( ( ( v1_tex_2(X1,k1_zfmisc_1(X0))
          | X0 = X1 )
        & ( X0 != X1
          | ~ v1_tex_2(X1,k1_zfmisc_1(X0)) ) )
      | ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
    inference(nnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ( v1_tex_2(X1,k1_zfmisc_1(X0))
      <=> X0 != X1 )
      | ~ m1_subset_1(X1,k1_zfmisc_1(X0)) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0,X1] :
      ( m1_subset_1(X1,k1_zfmisc_1(X0))
     => ( v1_tex_2(X1,k1_zfmisc_1(X0))
      <=> X0 != X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432',t5_tex_2) ).

fof(f401,plain,
    ( m1_subset_1(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_1 ),
    inference(backward_demodulation,[],[f182,f400]) ).

fof(f391,plain,
    ~ spl18_2,
    inference(avatar_contradiction_clause,[],[f390]) ).

fof(f390,plain,
    ( $false
    | ~ spl18_2 ),
    inference(subsumption_resolution,[],[f388,f367]) ).

fof(f367,plain,
    ( v1_tex_2(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_2 ),
    inference(backward_demodulation,[],[f185,f365]) ).

fof(f365,plain,
    ( u1_struct_0(sK0) = sK1
    | ~ spl18_2 ),
    inference(backward_demodulation,[],[f361,f359]) ).

fof(f359,plain,
    ( sK1 = k3_tex_4(sK0,sK1)
    | ~ spl18_2 ),
    inference(unit_resulting_resolution,[],[f179,f180,f181,f314,f182,f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( k3_tex_4(X0,X1) = X1
      | ~ v4_pre_topc(X1,X0)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( k3_tex_4(X0,X1) = X1
          | ~ v4_pre_topc(X1,X0)
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( k3_tex_4(X0,X1) = X1
          | ~ v4_pre_topc(X1,X0)
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l1_pre_topc(X0)
      | ~ v2_pre_topc(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ( l1_pre_topc(X0)
        & v2_pre_topc(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
         => ( v4_pre_topc(X1,X0)
           => k3_tex_4(X0,X1) = X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432',t62_tex_4) ).

fof(f314,plain,
    ( v4_pre_topc(sK1,sK0)
    | ~ spl18_2 ),
    inference(avatar_component_clause,[],[f312]) ).

fof(f312,plain,
    ( spl18_2
  <=> v4_pre_topc(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).

fof(f388,plain,
    ( ~ v1_tex_2(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_2 ),
    inference(unit_resulting_resolution,[],[f366,f304]) ).

fof(f366,plain,
    ( m1_subset_1(sK1,k1_zfmisc_1(sK1))
    | ~ spl18_2 ),
    inference(backward_demodulation,[],[f182,f365]) ).

fof(f315,plain,
    ( spl18_1
    | spl18_2 ),
    inference(avatar_split_clause,[],[f183,f312,f308]) ).

fof(f183,plain,
    ( v4_pre_topc(sK1,sK0)
    | v3_pre_topc(sK1,sK0) ),
    inference(cnf_transformation,[],[f145]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : TOP025+1 : TPTP v8.1.2. Released v3.4.0.
% 0.12/0.16  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sat Aug 26 22:59:39 EDT 2023
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.38  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.mqGIyEvjU5/Vampire---4.8_29432
% 0.23/0.38  % (29807)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44  % (29816)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.44  % (29817)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.44  % (29820)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.44  % (29819)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.44  % (29818)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44  % (29815)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.44  % (29814)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.45  % (29817)First to succeed.
% 0.23/0.45  % (29817)Refutation found. Thanks to Tanya!
% 0.23/0.45  % SZS status Theorem for Vampire---4
% 0.23/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.45  % (29817)------------------------------
% 0.23/0.45  % (29817)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.45  % (29817)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.45  % (29817)Termination reason: Refutation
% 0.23/0.45  
% 0.23/0.45  % (29817)Memory used [KB]: 5756
% 0.23/0.45  % (29817)Time elapsed: 0.011 s
% 0.23/0.45  % (29817)------------------------------
% 0.23/0.45  % (29817)------------------------------
% 0.23/0.45  % (29807)Success in time 0.073 s
% 0.23/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------