TSTP Solution File: NUM414+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n014.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 : Tue Apr 30 14:22:00 EDT 2024

% Result   : Theorem 0.22s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   36 (  10 unt;   0 def)
%            Number of atoms       :  120 (  15 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  148 (  64   ~;  36   |;  35   &)
%                                         (   4 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   41 (  33   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f730,plain,
    $false,
    inference(subsumption_resolution,[],[f729,f698]) ).

fof(f698,plain,
    ~ ordinal_subset(sK1,sK2),
    inference(unit_resulting_resolution,[],[f124,f125,f586,f161]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ ordinal_subset(X0,X1)
      | subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

fof(f586,plain,
    ~ subset(sK1,sK2),
    inference(unit_resulting_resolution,[],[f126,f127,f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | X0 = X1
      | proper_subset(X0,X1) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( proper_subset(X0,X1)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( proper_subset(X0,X1)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        & subset(X0,X1) )
     => proper_subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( proper_subset(X0,X1)
    <=> ( X0 != X1
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).

fof(f127,plain,
    sK1 != sK2,
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ~ proper_subset(sK2,sK1)
    & sK1 != sK2
    & ~ proper_subset(sK1,sK2)
    & ordinal(sK2)
    & ordinal(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f58,f89,f88]) ).

fof(f88,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ proper_subset(X1,X0)
            & X0 != X1
            & ~ proper_subset(X0,X1)
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ~ proper_subset(X1,sK1)
          & sK1 != X1
          & ~ proper_subset(sK1,X1)
          & ordinal(X1) )
      & ordinal(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ( ? [X1] :
        ( ~ proper_subset(X1,sK1)
        & sK1 != X1
        & ~ proper_subset(sK1,X1)
        & ordinal(X1) )
   => ( ~ proper_subset(sK2,sK1)
      & sK1 != sK2
      & ~ proper_subset(sK1,sK2)
      & ordinal(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ proper_subset(X1,X0)
          & X0 != X1
          & ~ proper_subset(X0,X1)
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ proper_subset(X1,X0)
          & X0 != X1
          & ~ proper_subset(X0,X1)
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ~ ( ~ proper_subset(X1,X0)
                & X0 != X1
                & ~ proper_subset(X0,X1) ) ) ),
    inference(negated_conjecture,[],[f38]) ).

fof(f38,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ~ ( ~ proper_subset(X1,X0)
              & X0 != X1
              & ~ proper_subset(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_ordinal1) ).

fof(f126,plain,
    ~ proper_subset(sK1,sK2),
    inference(cnf_transformation,[],[f90]) ).

fof(f125,plain,
    ordinal(sK2),
    inference(cnf_transformation,[],[f90]) ).

fof(f124,plain,
    ordinal(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f729,plain,
    ordinal_subset(sK1,sK2),
    inference(subsumption_resolution,[],[f728,f125]) ).

fof(f728,plain,
    ( ~ ordinal(sK2)
    | ordinal_subset(sK1,sK2) ),
    inference(subsumption_resolution,[],[f727,f124]) ).

fof(f727,plain,
    ( ~ ordinal(sK1)
    | ~ ordinal(sK2)
    | ordinal_subset(sK1,sK2) ),
    inference(subsumption_resolution,[],[f709,f587]) ).

fof(f587,plain,
    ~ subset(sK2,sK1),
    inference(unit_resulting_resolution,[],[f128,f127,f163]) ).

fof(f128,plain,
    ~ proper_subset(sK2,sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f709,plain,
    ( subset(sK2,sK1)
    | ~ ordinal(sK1)
    | ~ ordinal(sK2)
    | ordinal_subset(sK1,sK2) ),
    inference(resolution,[],[f161,f613]) ).

fof(f613,plain,
    ( ordinal_subset(sK2,sK1)
    | ordinal_subset(sK1,sK2) ),
    inference(resolution,[],[f595,f125]) ).

fof(f595,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | ordinal_subset(sK1,X0)
      | ordinal_subset(X0,sK1) ),
    inference(resolution,[],[f160,f124]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ~ ordinal(X1)
      | ordinal_subset(X0,X1)
      | ordinal_subset(X1,X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ordinal_subset(X1,X0)
      | ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ordinal_subset(X1,X0)
      | ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X1,X0)
        | ordinal_subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n014.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Apr 29 23:16:19 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (546)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (553)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 theBenchmark for (497ds/0Mi)
% 0.14/0.38  % (549)WARNING: value z3 for option sas not known
% 0.22/0.38  % (548)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38  % (550)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38  % (549)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 theBenchmark for (569ds/0Mi)
% 0.22/0.38  % (551)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 theBenchmark for (531ds/0Mi)
% 0.22/0.38  % (552)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 theBenchmark for (522ds/0Mi)
% 0.22/0.38  % (547)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38  % (553)First to succeed.
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [3]
% 0.22/0.38  % (553)Refutation found. Thanks to Tanya!
% 0.22/0.38  % SZS status Theorem for theBenchmark
% 0.22/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (553)------------------------------
% 0.22/0.38  % (553)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (553)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (553)Memory used [KB]: 933
% 0.22/0.38  % (553)Time elapsed: 0.007 s
% 0.22/0.38  % (553)Instructions burned: 15 (million)
% 0.22/0.38  % (553)------------------------------
% 0.22/0.38  % (553)------------------------------
% 0.22/0.38  % (546)Success in time 0.02 s
%------------------------------------------------------------------------------