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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : PRO012+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 12:30:38 PM UTC 2026

% Result   : Theorem 0.11s 0.45s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   95 (  21 unt;   6 def)
%            Number of atoms       :  286 (  16 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  321 ( 130   ~; 124   |;  53   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   7 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  115 (   0 sgn  95   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1,X2,X3] :
      ( ( min_precedes(X0,X1,X3)
        & min_precedes(X1,X2,X3) )
     => min_precedes(X0,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).

fof(f3,axiom,
    ! [X0,X1,X2,X3] :
      ( ( occurrence_of(X2,X3)
        & root_occ(X0,X2)
        & root_occ(X1,X2) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( root_occ(X0,X1)
    <=> ? [X2] :
          ( occurrence_of(X1,X2)
          & subactivity_occurrence(X0,X1)
          & root(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( occurrence_of(X1,X0)
        & ~ atomic(X0) )
     => ? [X2] :
          ( root(X2,X0)
          & subactivity_occurrence(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_30) ).

fof(f33,axiom,
    ! [X0] :
      ( occurrence_of(X0,tptp0)
     => ? [X1,X2,X3] :
          ( occurrence_of(X1,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X2,tptp4)
          & min_precedes(X1,X2,tptp0)
          & ( occurrence_of(X3,tptp2)
            | occurrence_of(X3,tptp1) )
          & min_precedes(X2,X3,tptp0)
          & ! [X4] :
              ( min_precedes(X1,X4,tptp0)
             => ( X4 = X2
                | X4 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_32) ).

fof(f35,axiom,
    ~ atomic(tptp0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_34) ).

fof(f46,conjecture,
    ! [X0] :
      ( occurrence_of(X0,tptp0)
     => ? [X1,X2] :
          ( occurrence_of(X1,tptp3)
          & root_occ(X1,X0)
          & ( occurrence_of(X2,tptp2)
            | occurrence_of(X2,tptp1) )
          & min_precedes(X1,X2,tptp0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f47,negated_conjecture,
    ~ ! [X0] :
        ( occurrence_of(X0,tptp0)
       => ? [X1,X2] :
            ( occurrence_of(X1,tptp3)
            & root_occ(X1,X0)
            & ( occurrence_of(X2,tptp2)
              | occurrence_of(X2,tptp1) )
            & min_precedes(X1,X2,tptp0) ) ),
    inference(negated_conjecture,[status(cth)],[f46]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3] :
      ( min_precedes(X0,X2,X3)
      | ~ min_precedes(X0,X1,X3)
      | ~ min_precedes(X1,X2,X3) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( min_precedes(X0,X2,X3)
      | ~ min_precedes(X0,X1,X3)
      | ~ min_precedes(X1,X2,X3) ),
    inference(flattening,[],[f50]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | ~ occurrence_of(X2,X3)
      | ~ root_occ(X0,X2)
      | ~ root_occ(X1,X2) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | ~ occurrence_of(X2,X3)
      | ~ root_occ(X0,X2)
      | ~ root_occ(X1,X2) ),
    inference(flattening,[],[f54]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( root(X2,X0)
          & subactivity_occurrence(X2,X1) )
      | ~ occurrence_of(X1,X0)
      | atomic(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( root(X2,X0)
          & subactivity_occurrence(X2,X1) )
      | ~ occurrence_of(X1,X0)
      | atomic(X0) ),
    inference(flattening,[],[f89]) ).

fof(f92,plain,
    ! [X0] :
      ( ? [X1,X2,X3] :
          ( occurrence_of(X1,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X2,tptp4)
          & min_precedes(X1,X2,tptp0)
          & ( occurrence_of(X3,tptp2)
            | occurrence_of(X3,tptp1) )
          & min_precedes(X2,X3,tptp0)
          & ! [X4] :
              ( X4 = X2
              | X4 = X3
              | ~ min_precedes(X1,X4,tptp0) ) )
      | ~ occurrence_of(X0,tptp0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f93,plain,
    ! [X0] :
      ( ? [X1,X2,X3] :
          ( occurrence_of(X1,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X2,tptp4)
          & min_precedes(X1,X2,tptp0)
          & ( occurrence_of(X3,tptp2)
            | occurrence_of(X3,tptp1) )
          & min_precedes(X2,X3,tptp0)
          & ! [X4] :
              ( X4 = X2
              | X4 = X3
              | ~ min_precedes(X1,X4,tptp0) ) )
      | ~ occurrence_of(X0,tptp0) ),
    inference(flattening,[],[f92]) ).

fof(f94,plain,
    ? [X0] :
      ( ! [X1,X2] :
          ( ~ occurrence_of(X1,tptp3)
          | ~ root_occ(X1,X0)
          | ( ~ occurrence_of(X2,tptp2)
            & ~ occurrence_of(X2,tptp1) )
          | ~ min_precedes(X1,X2,tptp0) )
      & occurrence_of(X0,tptp0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ occurrence_of(X1,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ root(X0,X2) ) )
      & ( ? [X2] :
            ( occurrence_of(X1,X2)
            & subactivity_occurrence(X0,X1)
            & root(X0,X2) )
        | ~ root_occ(X0,X1) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ occurrence_of(X1,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ root(X0,X2) ) )
      & ( ? [X3] :
            ( occurrence_of(X1,X3)
            & subactivity_occurrence(X0,X1)
            & root(X0,X3) )
        | ~ root_occ(X0,X1) ) ),
    inference(rectify,[],[f96]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ occurrence_of(X1,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ root(X0,X2) ) )
      & ( ( occurrence_of(X1,sK1(X0,X1))
          & subactivity_occurrence(X0,X1)
          & root(X0,sK1(X0,X1)) )
        | ~ root_occ(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f97]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ( root(sK13(X0,X1),X0)
        & subactivity_occurrence(sK13(X0,X1),X1) )
      | ~ occurrence_of(X1,X0)
      | atomic(X0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f90]) ).

fof(f117,plain,
    ! [X0] :
      ( ( occurrence_of(sK14(X0),tptp3)
        & root_occ(sK14(X0),X0)
        & occurrence_of(sK15(X0),tptp4)
        & min_precedes(sK14(X0),sK15(X0),tptp0)
        & ( occurrence_of(sK16(X0),tptp2)
          | occurrence_of(sK16(X0),tptp1) )
        & min_precedes(sK15(X0),sK16(X0),tptp0)
        & ! [X4] :
            ( sK15(X0) = X4
            | sK16(X0) = X4
            | ~ min_precedes(sK14(X0),X4,tptp0) ) )
      | ~ occurrence_of(X0,tptp0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f93]) ).

fof(f118,plain,
    ( ! [X1,X2] :
        ( ~ occurrence_of(X1,tptp3)
        | ~ root_occ(X1,sK17)
        | ( ~ occurrence_of(X2,tptp2)
          & ~ occurrence_of(X2,tptp1) )
        | ~ min_precedes(X1,X2,tptp0) )
    & occurrence_of(sK17,tptp0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f94]) ).

fof(f119,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X0,X1,X3)
      | min_precedes(X0,X2,X3)
      | ~ min_precedes(X1,X2,X3) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f121,plain,
    ! [X2,X3,X0,X1] :
      ( ~ root_occ(X0,X2)
      | ~ occurrence_of(X2,X3)
      | X0 = X1
      | ~ root_occ(X1,X2) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f135,plain,
    ! [X2,X0,X1] :
      ( ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,X2)
      | root_occ(X0,X1)
      | ~ root(X0,X2) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X1,X0)
      | subactivity_occurrence(sK13(X0,X1),X1)
      | atomic(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X1,X0)
      | root(sK13(X0,X1),X0)
      | atomic(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f180,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | min_precedes(sK15(X0),sK16(X0),tptp0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f181,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | occurrence_of(sK16(X0),tptp1)
      | occurrence_of(sK16(X0),tptp2) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f182,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | min_precedes(sK14(X0),sK15(X0),tptp0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | root_occ(sK14(X0),X0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | occurrence_of(sK14(X0),tptp3) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f187,plain,
    ~ atomic(tptp0),
    inference(cnf_transformation,[],[f35]) ).

fof(f198,plain,
    occurrence_of(sK17,tptp0),
    inference(cnf_transformation,[],[f118]) ).

fof(f199,plain,
    ! [X2,X1] :
      ( ~ root_occ(X1,sK17)
      | ~ occurrence_of(X1,tptp3)
      | ~ occurrence_of(X2,tptp1)
      | ~ min_precedes(X1,X2,tptp0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f200,plain,
    ! [X2,X1] :
      ( ~ root_occ(X1,sK17)
      | ~ occurrence_of(X1,tptp3)
      | ~ occurrence_of(X2,tptp2)
      | ~ min_precedes(X1,X2,tptp0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f217,plain,
    root_occ(sK14(sK17),sK17),
    inference(resolution,[],[f184,f198]) ).

fof(f219,plain,
    occurrence_of(sK14(sK17),tptp3),
    inference(resolution,[],[f185,f198]) ).

fof(f223,plain,
    ! [X0] :
      ( ~ occurrence_of(sK14(sK17),tptp3)
      | ~ occurrence_of(X0,tptp2)
      | ~ min_precedes(sK14(sK17),X0,tptp0) ),
    inference(resolution,[],[f217,f200]) ).

fof(f224,plain,
    ! [X0] :
      ( ~ occurrence_of(sK14(sK17),tptp3)
      | ~ occurrence_of(X0,tptp1)
      | ~ min_precedes(sK14(sK17),X0,tptp0) ),
    inference(resolution,[],[f217,f199]) ).

fof(f228,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp1)
      | ~ min_precedes(sK14(sK17),X0,tptp0) ),
    inference(forward_subsumption_resolution,[],[f224,f219]) ).

fof(f229,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp2)
      | ~ min_precedes(sK14(sK17),X0,tptp0) ),
    inference(forward_subsumption_resolution,[],[f223,f219]) ).

fof(f245,plain,
    min_precedes(sK15(sK17),sK16(sK17),tptp0),
    inference(resolution,[],[f180,f198]) ).

fof(f248,plain,
    min_precedes(sK14(sK17),sK15(sK17),tptp0),
    inference(resolution,[],[f182,f198]) ).

fof(f288,plain,
    ( subactivity_occurrence(sK13(tptp0,sK17),sK17)
    | atomic(tptp0) ),
    inference(resolution,[],[f176,f198]) ).

fof(f295,plain,
    subactivity_occurrence(sK13(tptp0,sK17),sK17),
    inference(forward_subsumption_resolution,[],[f288,f187]) ).

fof(f300,plain,
    ( root(sK13(tptp0,sK17),tptp0)
    | atomic(tptp0) ),
    inference(resolution,[],[f177,f198]) ).

fof(f307,plain,
    root(sK13(tptp0,sK17),tptp0),
    inference(forward_subsumption_resolution,[],[f300,f187]) ).

fof(f320,plain,
    ( occurrence_of(sK16(sK17),tptp1)
    | occurrence_of(sK16(sK17),tptp2) ),
    inference(resolution,[],[f181,f198]) ).

fof(f322,definition,
    ( spl18_1
  <=> occurrence_of(sK16(sK17),tptp2) ),
    introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).

fof(f324,plain,
    ( occurrence_of(sK16(sK17),tptp2)
    | ~ spl18_1 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f326,definition,
    ( spl18_2
  <=> occurrence_of(sK16(sK17),tptp1) ),
    introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).

fof(f328,plain,
    ( occurrence_of(sK16(sK17),tptp1)
    | ~ spl18_2 ),
    inference(avatar_component_clause,[],[f326]) ).

fof(f329,plain,
    ( spl18_1
    | spl18_2 ),
    inference(avatar_split_clause,[],[f320,f326,f322]) ).

fof(f336,plain,
    ! [X0] :
      ( ~ min_precedes(sK15(sK17),X0,tptp0)
      | min_precedes(sK14(sK17),X0,tptp0) ),
    inference(resolution,[],[f119,f248]) ).

fof(f338,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(sK17,X0)
      | sK14(sK17) = X1
      | ~ root_occ(X1,sK17) ),
    inference(resolution,[],[f121,f217]) ).

fof(f340,definition,
    ( spl18_3
  <=> ! [X1] :
        ( sK14(sK17) = X1
        | ~ root_occ(X1,sK17) ) ),
    introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).

fof(f341,plain,
    ( ! [X1] :
        ( ~ root_occ(X1,sK17)
        | sK14(sK17) = X1 )
    | ~ spl18_3 ),
    inference(avatar_component_clause,[],[f340]) ).

fof(f343,definition,
    ( spl18_4
  <=> ! [X0] : ~ occurrence_of(sK17,X0) ),
    introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).

fof(f344,plain,
    ( ! [X0] : ~ occurrence_of(sK17,X0)
    | ~ spl18_4 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f345,plain,
    ( spl18_3
    | spl18_4 ),
    inference(avatar_split_clause,[],[f338,f343,f340]) ).

fof(f349,plain,
    ! [X0] :
      ( ~ occurrence_of(sK17,X0)
      | root_occ(sK13(tptp0,sK17),sK17)
      | ~ root(sK13(tptp0,sK17),X0) ),
    inference(resolution,[],[f135,f295]) ).

fof(f351,definition,
    ( spl18_5
  <=> root_occ(sK13(tptp0,sK17),sK17) ),
    introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).

fof(f353,plain,
    ( root_occ(sK13(tptp0,sK17),sK17)
    | ~ spl18_5 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f355,definition,
    ( spl18_6
  <=> ! [X0] :
        ( ~ occurrence_of(sK17,X0)
        | ~ root(sK13(tptp0,sK17),X0) ) ),
    introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).

fof(f356,plain,
    ( ! [X0] :
        ( ~ root(sK13(tptp0,sK17),X0)
        | ~ occurrence_of(sK17,X0) )
    | ~ spl18_6 ),
    inference(avatar_component_clause,[],[f355]) ).

fof(f357,plain,
    ( spl18_5
    | spl18_6 ),
    inference(avatar_split_clause,[],[f349,f355,f351]) ).

fof(f415,plain,
    ( $false
    | ~ spl18_4 ),
    inference(resolution,[],[f344,f198]) ).

fof(f420,plain,
    ~ spl18_4,
    inference(avatar_contradiction_clause,[],[f415]) ).

fof(f646,plain,
    ( ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
    | ~ spl18_1 ),
    inference(resolution,[],[f324,f229]) ).

fof(f659,plain,
    ( ~ occurrence_of(sK17,tptp0)
    | ~ spl18_6 ),
    inference(resolution,[],[f356,f307]) ).

fof(f660,plain,
    ( $false
    | ~ spl18_6 ),
    inference(forward_subsumption_resolution,[],[f659,f198]) ).

fof(f661,plain,
    ~ spl18_6,
    inference(avatar_contradiction_clause,[],[f660]) ).

fof(f662,plain,
    ( sK14(sK17) = sK13(tptp0,sK17)
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(resolution,[],[f353,f341]) ).

fof(f918,plain,
    min_precedes(sK14(sK17),sK16(sK17),tptp0),
    inference(resolution,[],[f336,f245]) ).

fof(f921,plain,
    ( $false
    | ~ spl18_1 ),
    inference(forward_subsumption_resolution,[],[f918,f646]) ).

fof(f922,plain,
    ~ spl18_1,
    inference(avatar_contradiction_clause,[],[f921]) ).

fof(f923,plain,
    ( min_precedes(sK13(tptp0,sK17),sK16(sK17),tptp0)
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(forward_demodulation,[],[f918,f662]) ).

fof(f927,plain,
    ( ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
    | ~ spl18_2 ),
    inference(resolution,[],[f328,f228]) ).

fof(f934,plain,
    ( ~ min_precedes(sK13(tptp0,sK17),sK16(sK17),tptp0)
    | ~ spl18_2
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(forward_demodulation,[],[f927,f662]) ).

fof(f935,plain,
    ( $false
    | ~ spl18_2
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(forward_subsumption_resolution,[],[f934,f923]) ).

fof(f936,plain,
    ( ~ spl18_2
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(avatar_contradiction_clause,[],[f935]) ).

cnf(s1,plain,
    ( spl18_1
    | spl18_2 ),
    inference(sat_conversion,[],[f329]) ).

cnf(s2,plain,
    ( spl18_3
    | spl18_4 ),
    inference(sat_conversion,[],[f345]) ).

cnf(s3,plain,
    ( spl18_5
    | spl18_6 ),
    inference(sat_conversion,[],[f357]) ).

cnf(s12,plain,
    ~ spl18_4,
    inference(sat_conversion,[],[f420]) ).

cnf(s29,plain,
    ~ spl18_6,
    inference(sat_conversion,[],[f661]) ).

cnf(s45,plain,
    ~ spl18_1,
    inference(sat_conversion,[],[f922]) ).

cnf(s46,plain,
    ( ~ spl18_2
    | ~ spl18_3
    | ~ spl18_5 ),
    inference(sat_conversion,[],[f936]) ).

cnf(s49,plain,
    spl18_5,
    inference(rat,[],[s3,s29]) ).

cnf(s51,plain,
    spl18_3,
    inference(rat,[],[s2,s12]) ).

cnf(s52,plain,
    ~ spl18_2,
    inference(rat,[],[s46,s49,s51]) ).

cnf(s58,plain,
    $false,
    inference(rat,[],[s1,s52,s45]) ).

fof(f937,plain,
    $false,
    inference(avatar_sat_refutation,[],[s58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : PRO012+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37  % Computer : n013.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.38  % CPULimit : 300
% 0.11/0.38  % WCLimit  : 300
% 0.11/0.38  % DateTime : Sun Sep 27 22:21:36 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41  Running first-order model finding
% 0.11/0.41  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45  % (609441)Will run a generic schedule for satisfiability detection.
% 0.11/0.45  % (609451)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2083957043:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45  % (609447)% WARNING: option uhcvi not known.
% 0.11/0.45  % (609446)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=540834684_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45  % (609450)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1517866454:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45  % (609449)dis+10_1_sil=32000:sp=arity:random_seed=2567473817:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45  % (609448)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1068852727:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45  % (609452)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=896066906:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45  % (609447)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1888471783:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45  % (609451) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-609441-609451"...
% 0.11/0.45  % (609451)...printing done.
% 0.11/0.45  % Detected minimum model sizes of [4]
% 0.11/0.45  % Detected maximum model sizes of [max]
% 0.11/0.45  % (609451)Refutation found. Thanks to Tanya!
% 0.11/0.45  % SZS status Theorem for theBenchmark
% 0.11/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45  % (609451)------------------------------
% 0.11/0.45  % (609451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45  % (609451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45  % (609451)CaDiCaL version: 2.1.3
% 0.11/0.45  % (609451)Termination reason: Refutation
% 0.11/0.45  % (609451)Time elapsed: 0.010 s
% 0.11/0.45  % (609451)Peak memory usage: 13 MB
% 0.11/0.45  % (609451)Instructions burned: 23 (million)
% 0.11/0.45  % (609441)Success in time 0.035 s
% 0.11/0.45  % Vampire exiting
%------------------------------------------------------------------------------