TSTP Solution File: PRO004+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : PRO004+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 May 21 02:23:19 EDT 2024

% Result   : Theorem 3.78s 0.91s
% Output   : Refutation 3.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  248 (  77 unt;   0 def)
%            Number of atoms       :  762 (  21 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  798 ( 284   ~; 258   |; 189   &)
%                                         (  22 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   22 (  20 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  533 ( 461   !;  72   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f29450,plain,
    $false,
    inference(subsumption_resolution,[],[f29424,f13693]) ).

fof(f13693,plain,
    ~ occurrence_of(sK11(sK7(sK5)),tptp3),
    inference(unit_resulting_resolution,[],[f278,f13587,f355]) ).

fof(f355,plain,
    ! [X2,X0,X1] :
      ( ~ occurrence_of(X0,X2)
      | X1 = X2
      | ~ occurrence_of(X0,X1) ),
    inference(cnf_transformation,[],[f168]) ).

fof(f168,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ occurrence_of(X0,X2)
      | ~ occurrence_of(X0,X1) ),
    inference(flattening,[],[f167]) ).

fof(f167,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ occurrence_of(X0,X2)
      | ~ occurrence_of(X0,X1) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ( occurrence_of(X0,X2)
        & occurrence_of(X0,X1) )
     => X1 = X2 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X4,X5,X6] :
      ( ( occurrence_of(X4,X6)
        & occurrence_of(X4,X5) )
     => X5 = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).

fof(f13587,plain,
    occurrence_of(sK11(sK7(sK5)),tptp1),
    inference(unit_resulting_resolution,[],[f503,f6048,f5814,f5815,f305]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( ~ subactivity_occurrence(X0,X1)
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | occurrence_of(sK11(X0),tptp1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(cnf_transformation,[],[f223]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ( next_subocc(X0,sK11(X0),tptp0)
        & occurrence_of(sK11(X0),tptp1) )
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f141,f222]) ).

fof(f222,plain,
    ! [X0] :
      ( ? [X2] :
          ( next_subocc(X0,X2,tptp0)
          & occurrence_of(X2,tptp1) )
     => ( next_subocc(X0,sK11(X0),tptp0)
        & occurrence_of(sK11(X0),tptp1) ) ),
    introduced(choice_axiom,[]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( next_subocc(X0,X2,tptp0)
          & occurrence_of(X2,tptp1) )
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(flattening,[],[f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( next_subocc(X0,X2,tptp0)
          & occurrence_of(X2,tptp1) )
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( ~ leaf_occ(X0,X1)
        & arboreal(X0)
        & subactivity_occurrence(X0,X1)
        & occurrence_of(X1,tptp0) )
     => ? [X2] :
          ( next_subocc(X0,X2,tptp0)
          & occurrence_of(X2,tptp1) ) ),
    inference(rectify,[],[f65]) ).

fof(f65,axiom,
    ! [X168,X169] :
      ( ( ~ leaf_occ(X168,X169)
        & arboreal(X168)
        & subactivity_occurrence(X168,X169)
        & occurrence_of(X169,tptp0) )
     => ? [X170] :
          ( next_subocc(X168,X170,tptp0)
          & occurrence_of(X170,tptp1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_64) ).

fof(f5815,plain,
    occurrence_of(sK20(sK14(tptp0,sK7(sK5)),sK7(sK5),tptp0),tptp0),
    inference(unit_resulting_resolution,[],[f5706,f341]) ).

fof(f341,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X0,X1,X2)
      | occurrence_of(sK20(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ! [X0,X1,X2] :
      ( ( subactivity_occurrence(X0,sK20(X0,X1,X2))
        & subactivity_occurrence(X1,sK20(X0,X1,X2))
        & occurrence_of(sK20(X0,X1,X2),X2) )
      | ~ sP2(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f252,f253]) ).

fof(f253,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( subactivity_occurrence(X0,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X2) )
     => ( subactivity_occurrence(X0,sK20(X0,X1,X2))
        & subactivity_occurrence(X1,sK20(X0,X1,X2))
        & occurrence_of(sK20(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( subactivity_occurrence(X0,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X2) )
      | ~ sP2(X0,X1,X2) ),
    inference(rectify,[],[f251]) ).

fof(f251,plain,
    ! [X2,X1,X0] :
      ( ? [X3] :
          ( subactivity_occurrence(X2,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X0) )
      | ~ sP2(X2,X1,X0) ),
    inference(nnf_transformation,[],[f204]) ).

fof(f204,plain,
    ! [X2,X1,X0] :
      ( ? [X3] :
          ( subactivity_occurrence(X2,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X0) )
      | ~ sP2(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f5706,plain,
    sP2(sK14(tptp0,sK7(sK5)),sK7(sK5),tptp0),
    inference(unit_resulting_resolution,[],[f5523,f344]) ).

fof(f344,plain,
    ! [X2,X0,X1] :
      ( ~ min_precedes(X1,X2,X0)
      | sP2(X2,X1,X0) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f205,plain,
    ! [X0,X1,X2] :
      ( sP2(X2,X1,X0)
      | ~ min_precedes(X1,X2,X0) ),
    inference(definition_folding,[],[f155,f204]) ).

fof(f155,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( subactivity_occurrence(X2,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X0) )
      | ~ min_precedes(X1,X2,X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( min_precedes(X1,X2,X0)
     => ? [X3] :
          ( subactivity_occurrence(X2,X3)
          & subactivity_occurrence(X1,X3)
          & occurrence_of(X3,X0) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,axiom,
    ! [X69,X70,X71] :
      ( min_precedes(X70,X71,X69)
     => ? [X72] :
          ( subactivity_occurrence(X71,X72)
          & subactivity_occurrence(X70,X72)
          & occurrence_of(X72,X69) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_25) ).

fof(f5523,plain,
    min_precedes(sK7(sK5),sK14(tptp0,sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f628,f800,f314]) ).

fof(f314,plain,
    ! [X0,X1] :
      ( ~ root(X1,X0)
      | min_precedes(X1,sK14(X0,X1),X0)
      | sP1(X0,X1) ),
    inference(cnf_transformation,[],[f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | min_precedes(X1,sK14(X0,X1),X0)
        | ( ! [X3] : ~ min_precedes(X3,X1,X0)
          & ~ root(X1,X0) ) )
      & ( ( ! [X4] : ~ min_precedes(X1,X4,X0)
          & ( min_precedes(sK15(X0,X1),X1,X0)
            | root(X1,X0) ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f230,f232,f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( ? [X2] : min_precedes(X1,X2,X0)
     => min_precedes(X1,sK14(X0,X1),X0) ),
    introduced(choice_axiom,[]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( ? [X5] : min_precedes(X5,X1,X0)
     => min_precedes(sK15(X0,X1),X1,X0) ),
    introduced(choice_axiom,[]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ( sP1(X0,X1)
        | ? [X2] : min_precedes(X1,X2,X0)
        | ( ! [X3] : ~ min_precedes(X3,X1,X0)
          & ~ root(X1,X0) ) )
      & ( ( ! [X4] : ~ min_precedes(X1,X4,X0)
          & ( ? [X5] : min_precedes(X5,X1,X0)
            | root(X1,X0) ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f229]) ).

fof(f229,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ? [X2] : min_precedes(X0,X2,X1)
        | ( ! [X3] : ~ min_precedes(X3,X0,X1)
          & ~ root(X0,X1) ) )
      & ( ( ! [X2] : ~ min_precedes(X0,X2,X1)
          & ( ? [X3] : min_precedes(X3,X0,X1)
            | root(X0,X1) ) )
        | ~ sP1(X1,X0) ) ),
    inference(flattening,[],[f228]) ).

fof(f228,plain,
    ! [X1,X0] :
      ( ( sP1(X1,X0)
        | ? [X2] : min_precedes(X0,X2,X1)
        | ( ! [X3] : ~ min_precedes(X3,X0,X1)
          & ~ root(X0,X1) ) )
      & ( ( ! [X2] : ~ min_precedes(X0,X2,X1)
          & ( ? [X3] : min_precedes(X3,X0,X1)
            | root(X0,X1) ) )
        | ~ sP1(X1,X0) ) ),
    inference(nnf_transformation,[],[f202]) ).

fof(f202,plain,
    ! [X1,X0] :
      ( sP1(X1,X0)
    <=> ( ! [X2] : ~ min_precedes(X0,X2,X1)
        & ( ? [X3] : min_precedes(X3,X0,X1)
          | root(X0,X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f800,plain,
    root(sK7(sK5),tptp0),
    inference(superposition,[],[f563,f725]) ).

fof(f725,plain,
    tptp0 = sK17(sK7(sK5),sK5),
    inference(unit_resulting_resolution,[],[f267,f545,f355]) ).

fof(f545,plain,
    occurrence_of(sK5,sK17(sK7(sK5),sK5)),
    inference(unit_resulting_resolution,[],[f442,f325]) ).

fof(f325,plain,
    ! [X0,X1] :
      ( ~ root_occ(X0,X1)
      | occurrence_of(X1,sK17(X0,X1)) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f244,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ root(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ( root(X0,sK17(X0,X1))
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,sK17(X0,X1)) )
        | ~ root_occ(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f242,f243]) ).

fof(f243,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( root(X0,X3)
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,X3) )
     => ( root(X0,sK17(X0,X1))
        & subactivity_occurrence(X0,X1)
        & occurrence_of(X1,sK17(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ root(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ? [X3] :
            ( root(X0,X3)
            & subactivity_occurrence(X0,X1)
            & occurrence_of(X1,X3) )
        | ~ root_occ(X0,X1) ) ),
    inference(rectify,[],[f241]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( ( root_occ(X0,X1)
        | ! [X2] :
            ( ~ root(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ? [X2] :
            ( root(X0,X2)
            & subactivity_occurrence(X0,X1)
            & occurrence_of(X1,X2) )
        | ~ root_occ(X0,X1) ) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( root_occ(X0,X1)
    <=> ? [X2] :
          ( root(X0,X2)
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,X2) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X99,X100] :
      ( root_occ(X99,X100)
    <=> ? [X101] :
          ( root(X99,X101)
          & subactivity_occurrence(X99,X100)
          & occurrence_of(X100,X101) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).

fof(f442,plain,
    root_occ(sK7(sK5),sK5),
    inference(unit_resulting_resolution,[],[f400,f285]) ).

fof(f285,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | root_occ(sK7(X0),X0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f216,plain,
    ! [X0] :
      ( ( next_subocc(sK7(X0),sK8(X0),tptp0)
        & leaf_occ(sK8(X0),X0)
        & occurrence_of(sK8(X0),tptp3)
        & root_occ(sK7(X0),X0)
        & occurrence_of(sK7(X0),tptp4) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f214,f215]) ).

fof(f215,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( next_subocc(X1,X2,tptp0)
          & leaf_occ(X2,X0)
          & occurrence_of(X2,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X1,tptp4) )
     => ( next_subocc(sK7(X0),sK8(X0),tptp0)
        & leaf_occ(sK8(X0),X0)
        & occurrence_of(sK8(X0),tptp3)
        & root_occ(sK7(X0),X0)
        & occurrence_of(sK7(X0),tptp4) ) ),
    introduced(choice_axiom,[]) ).

fof(f214,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( next_subocc(X1,X2,tptp0)
          & leaf_occ(X2,X0)
          & occurrence_of(X2,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X1,tptp4) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f200]) ).

fof(f200,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( next_subocc(X1,X2,tptp0)
          & leaf_occ(X2,X0)
          & occurrence_of(X2,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X1,tptp4) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f400,plain,
    sP0(sK5),
    inference(unit_resulting_resolution,[],[f267,f289]) ).

fof(f289,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | sP0(X0) ),
    inference(cnf_transformation,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ occurrence_of(X0,tptp0) ),
    inference(definition_folding,[],[f125,f200]) ).

fof(f125,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( next_subocc(X1,X2,tptp0)
          & leaf_occ(X2,X0)
          & occurrence_of(X2,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X1,tptp4) )
      | ~ occurrence_of(X0,tptp0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( occurrence_of(X0,tptp0)
     => ? [X1,X2] :
          ( next_subocc(X1,X2,tptp0)
          & leaf_occ(X2,X0)
          & occurrence_of(X2,tptp3)
          & root_occ(X1,X0)
          & occurrence_of(X1,tptp4) ) ),
    inference(rectify,[],[f50]) ).

fof(f50,axiom,
    ! [X161] :
      ( occurrence_of(X161,tptp0)
     => ? [X162,X163] :
          ( next_subocc(X162,X163,tptp0)
          & leaf_occ(X163,X161)
          & occurrence_of(X163,tptp3)
          & root_occ(X162,X161)
          & occurrence_of(X162,tptp4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_49) ).

fof(f267,plain,
    occurrence_of(sK5,tptp0),
    inference(cnf_transformation,[],[f211]) ).

fof(f211,plain,
    occurrence_of(sK5,tptp0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f69,f210]) ).

fof(f210,plain,
    ( ? [X0] : occurrence_of(X0,tptp0)
   => occurrence_of(sK5,tptp0) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ? [X0] : occurrence_of(X0,tptp0),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ~ ~ ? [X0] : occurrence_of(X0,tptp0),
    inference(rectify,[],[f67]) ).

fof(f67,negated_conjecture,
    ~ ~ ? [X171] : occurrence_of(X171,tptp0),
    inference(negated_conjecture,[],[f66]) ).

fof(f66,conjecture,
    ~ ? [X171] : occurrence_of(X171,tptp0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f563,plain,
    root(sK7(sK5),sK17(sK7(sK5),sK5)),
    inference(unit_resulting_resolution,[],[f442,f327]) ).

fof(f327,plain,
    ! [X0,X1] :
      ( ~ root_occ(X0,X1)
      | root(X0,sK17(X0,X1)) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f628,plain,
    ~ sP1(tptp0,sK7(sK5)),
    inference(unit_resulting_resolution,[],[f626,f313]) ).

fof(f313,plain,
    ! [X0,X1,X4] :
      ( ~ min_precedes(X1,X4,X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f233]) ).

fof(f626,plain,
    min_precedes(sK7(sK5),sK8(sK5),tptp0),
    inference(unit_resulting_resolution,[],[f624,f356]) ).

fof(f356,plain,
    ! [X2,X0,X1] :
      ( ~ sP4(X0,X1,X2)
      | min_precedes(X2,X1,X0) ),
    inference(cnf_transformation,[],[f263]) ).

fof(f263,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ( min_precedes(sK23(X0,X1,X2),X1,X0)
          & min_precedes(X2,sK23(X0,X1,X2),X0) )
        | ~ min_precedes(X2,X1,X0) )
      & ( ( ! [X4] :
              ( ~ min_precedes(X4,X1,X0)
              | ~ min_precedes(X2,X4,X0) )
          & min_precedes(X2,X1,X0) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f261,f262]) ).

fof(f262,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( min_precedes(X3,X1,X0)
          & min_precedes(X2,X3,X0) )
     => ( min_precedes(sK23(X0,X1,X2),X1,X0)
        & min_precedes(X2,sK23(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f261,plain,
    ! [X0,X1,X2] :
      ( ( sP4(X0,X1,X2)
        | ? [X3] :
            ( min_precedes(X3,X1,X0)
            & min_precedes(X2,X3,X0) )
        | ~ min_precedes(X2,X1,X0) )
      & ( ( ! [X4] :
              ( ~ min_precedes(X4,X1,X0)
              | ~ min_precedes(X2,X4,X0) )
          & min_precedes(X2,X1,X0) )
        | ~ sP4(X0,X1,X2) ) ),
    inference(rectify,[],[f260]) ).

fof(f260,plain,
    ! [X2,X1,X0] :
      ( ( sP4(X2,X1,X0)
        | ? [X3] :
            ( min_precedes(X3,X1,X2)
            & min_precedes(X0,X3,X2) )
        | ~ min_precedes(X0,X1,X2) )
      & ( ( ! [X3] :
              ( ~ min_precedes(X3,X1,X2)
              | ~ min_precedes(X0,X3,X2) )
          & min_precedes(X0,X1,X2) )
        | ~ sP4(X2,X1,X0) ) ),
    inference(flattening,[],[f259]) ).

fof(f259,plain,
    ! [X2,X1,X0] :
      ( ( sP4(X2,X1,X0)
        | ? [X3] :
            ( min_precedes(X3,X1,X2)
            & min_precedes(X0,X3,X2) )
        | ~ min_precedes(X0,X1,X2) )
      & ( ( ! [X3] :
              ( ~ min_precedes(X3,X1,X2)
              | ~ min_precedes(X0,X3,X2) )
          & min_precedes(X0,X1,X2) )
        | ~ sP4(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f208]) ).

fof(f208,plain,
    ! [X2,X1,X0] :
      ( sP4(X2,X1,X0)
    <=> ( ! [X3] :
            ( ~ min_precedes(X3,X1,X2)
            | ~ min_precedes(X0,X3,X2) )
        & min_precedes(X0,X1,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f624,plain,
    sP4(tptp0,sK8(sK5),sK7(sK5)),
    inference(unit_resulting_resolution,[],[f539,f360]) ).

fof(f360,plain,
    ! [X2,X0,X1] :
      ( ~ next_subocc(X0,X1,X2)
      | sP4(X2,X1,X0) ),
    inference(cnf_transformation,[],[f264]) ).

fof(f264,plain,
    ! [X0,X1,X2] :
      ( ( next_subocc(X0,X1,X2)
        | ~ sP4(X2,X1,X0) )
      & ( sP4(X2,X1,X0)
        | ~ next_subocc(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f209]) ).

fof(f209,plain,
    ! [X0,X1,X2] :
      ( next_subocc(X0,X1,X2)
    <=> sP4(X2,X1,X0) ),
    inference(definition_folding,[],[f169,f208]) ).

fof(f169,plain,
    ! [X0,X1,X2] :
      ( next_subocc(X0,X1,X2)
    <=> ( ! [X3] :
            ( ~ min_precedes(X3,X1,X2)
            | ~ min_precedes(X0,X3,X2) )
        & min_precedes(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( next_subocc(X0,X1,X2)
    <=> ( ~ ? [X3] :
              ( min_precedes(X3,X1,X2)
              & min_precedes(X0,X3,X2) )
        & min_precedes(X0,X1,X2) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X60,X61,X62] :
      ( next_subocc(X60,X61,X62)
    <=> ( ~ ? [X63] :
              ( min_precedes(X63,X61,X62)
              & min_precedes(X60,X63,X62) )
        & min_precedes(X60,X61,X62) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_22) ).

fof(f539,plain,
    next_subocc(sK7(sK5),sK8(sK5),tptp0),
    inference(unit_resulting_resolution,[],[f400,f288]) ).

fof(f288,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | next_subocc(sK7(X0),sK8(X0),tptp0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f5814,plain,
    subactivity_occurrence(sK7(sK5),sK20(sK14(tptp0,sK7(sK5)),sK7(sK5),tptp0)),
    inference(unit_resulting_resolution,[],[f5706,f342]) ).

fof(f342,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X0,X1,X2)
      | subactivity_occurrence(X1,sK20(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f6048,plain,
    ~ leaf_occ(sK7(sK5),sK20(sK14(tptp0,sK7(sK5)),sK7(sK5),tptp0)),
    inference(unit_resulting_resolution,[],[f636,f5815,f381]) ).

fof(f381,plain,
    ! [X2,X0,X1] :
      ( ~ sP26(X2,X1)
      | ~ occurrence_of(X0,X2)
      | ~ leaf_occ(X1,X0) ),
    inference(general_splitting,[],[f354,f380_D]) ).

fof(f380,plain,
    ! [X2,X3,X1] :
      ( ~ min_precedes(X1,X3,X2)
      | sP26(X2,X1) ),
    inference(cnf_transformation,[],[f380_D]) ).

fof(f380_D,plain,
    ! [X1,X2] :
      ( ! [X3] : ~ min_precedes(X1,X3,X2)
    <=> ~ sP26(X2,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).

fof(f354,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X1,X3,X2)
      | ~ leaf_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(cnf_transformation,[],[f166]) ).

fof(f166,plain,
    ! [X0,X1,X2] :
      ( ! [X3] : ~ min_precedes(X1,X3,X2)
      | ~ leaf_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(flattening,[],[f165]) ).

fof(f165,plain,
    ! [X0,X1,X2] :
      ( ! [X3] : ~ min_precedes(X1,X3,X2)
      | ~ leaf_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(ennf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ( leaf_occ(X1,X0)
        & occurrence_of(X0,X2) )
     => ~ ? [X3] : min_precedes(X1,X3,X2) ),
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X113,X114,X115] :
      ( ( leaf_occ(X114,X113)
        & occurrence_of(X113,X115) )
     => ~ ? [X116] : min_precedes(X114,X116,X115) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_37) ).

fof(f636,plain,
    sP26(tptp0,sK7(sK5)),
    inference(unit_resulting_resolution,[],[f626,f380]) ).

fof(f503,plain,
    arboreal(sK7(sK5)),
    inference(unit_resulting_resolution,[],[f272,f420,f299]) ).

fof(f299,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X0,X1)
      | ~ atomic(X1)
      | arboreal(X0) ),
    inference(cnf_transformation,[],[f219]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ( ( arboreal(X0)
          | ~ atomic(X1) )
        & ( atomic(X1)
          | ~ arboreal(X0) ) )
      | ~ occurrence_of(X0,X1) ),
    inference(nnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ( arboreal(X0)
      <=> atomic(X1) )
      | ~ occurrence_of(X0,X1) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( occurrence_of(X0,X1)
     => ( arboreal(X0)
      <=> atomic(X1) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X16,X17] :
      ( occurrence_of(X16,X17)
     => ( arboreal(X16)
      <=> atomic(X17) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).

fof(f420,plain,
    occurrence_of(sK7(sK5),tptp4),
    inference(unit_resulting_resolution,[],[f400,f284]) ).

fof(f284,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | occurrence_of(sK7(X0),tptp4) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f272,plain,
    atomic(tptp4),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,axiom,
    atomic(tptp4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_52) ).

fof(f278,plain,
    tptp3 != tptp1,
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    tptp3 != tptp1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_59) ).

fof(f29424,plain,
    occurrence_of(sK11(sK7(sK5)),tptp3),
    inference(superposition,[],[f25844,f29402]) ).

fof(f29402,plain,
    sK11(sK7(sK5)) = sK8(sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f25652,f26712,f26916,f25600,f25843,f393]) ).

fof(f393,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP32(X0,X2,X1)
      | X2 = X4
      | ~ subactivity_occurrence(X2,X1)
      | ~ leaf_occ(X4,X1)
      | ~ occurrence_of(X1,X0)
      | min_precedes(X2,X4,X0) ),
    inference(general_splitting,[],[f375,f392_D]) ).

fof(f392,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X3,X2,X0)
      | ~ root_occ(X3,X1)
      | sP32(X0,X2,X1) ),
    inference(cnf_transformation,[],[f392_D]) ).

fof(f392_D,plain,
    ! [X1,X2,X0] :
      ( ! [X3] :
          ( ~ min_precedes(X3,X2,X0)
          | ~ root_occ(X3,X1) )
    <=> ~ sP32(X0,X2,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP32])]) ).

fof(f375,plain,
    ! [X2,X3,X0,X1,X4] :
      ( min_precedes(X2,X4,X0)
      | X2 = X4
      | ~ min_precedes(X3,X2,X0)
      | ~ subactivity_occurrence(X2,X1)
      | ~ leaf_occ(X4,X1)
      | ~ root_occ(X3,X1)
      | ~ occurrence_of(X1,X0) ),
    inference(cnf_transformation,[],[f195]) ).

fof(f195,plain,
    ! [X0,X1,X2,X3,X4] :
      ( min_precedes(X2,X4,X0)
      | X2 = X4
      | ~ min_precedes(X3,X2,X0)
      | ~ subactivity_occurrence(X2,X1)
      | ~ leaf_occ(X4,X1)
      | ~ root_occ(X3,X1)
      | ~ occurrence_of(X1,X0) ),
    inference(flattening,[],[f194]) ).

fof(f194,plain,
    ! [X0,X1,X2,X3,X4] :
      ( min_precedes(X2,X4,X0)
      | X2 = X4
      | ~ min_precedes(X3,X2,X0)
      | ~ subactivity_occurrence(X2,X1)
      | ~ leaf_occ(X4,X1)
      | ~ root_occ(X3,X1)
      | ~ occurrence_of(X1,X0) ),
    inference(ennf_transformation,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( X2 != X4
        & min_precedes(X3,X2,X0)
        & subactivity_occurrence(X2,X1)
        & leaf_occ(X4,X1)
        & root_occ(X3,X1)
        & occurrence_of(X1,X0) )
     => min_precedes(X2,X4,X0) ),
    inference(rectify,[],[f49]) ).

fof(f49,axiom,
    ! [X156,X157,X158,X159,X160] :
      ( ( X158 != X160
        & min_precedes(X159,X158,X156)
        & subactivity_occurrence(X158,X157)
        & leaf_occ(X160,X157)
        & root_occ(X159,X157)
        & occurrence_of(X157,X156) )
     => min_precedes(X158,X160,X156) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_48) ).

fof(f25843,plain,
    leaf_occ(sK8(sK12(sK11(sK7(sK5)),tptp0)),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f25693,f287]) ).

fof(f287,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | leaf_occ(sK8(X0),X0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f25693,plain,
    sP0(sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f25652,f289]) ).

fof(f25600,plain,
    ! [X0] : ~ min_precedes(sK11(sK7(sK5)),X0,tptp0),
    inference(unit_resulting_resolution,[],[f25590,f380]) ).

fof(f25590,plain,
    ~ sP26(tptp0,sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f22264,f25449,f381]) ).

fof(f25449,plain,
    leaf_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0)),
    inference(subsumption_resolution,[],[f25448,f22264]) ).

fof(f25448,plain,
    ( leaf_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0))
    | ~ occurrence_of(sK20(sK11(sK7(sK5)),sK7(sK5),tptp0),tptp0) ),
    inference(subsumption_resolution,[],[f25447,f23068]) ).

fof(f23068,plain,
    ~ root_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0)),
    inference(unit_resulting_resolution,[],[f22015,f22264,f379]) ).

fof(f379,plain,
    ! [X2,X0,X1] :
      ( ~ sP25(X2,X1)
      | ~ occurrence_of(X0,X2)
      | ~ root_occ(X1,X0) ),
    inference(general_splitting,[],[f353,f378_D]) ).

fof(f378,plain,
    ! [X2,X3,X1] :
      ( ~ min_precedes(X3,X1,X2)
      | sP25(X2,X1) ),
    inference(cnf_transformation,[],[f378_D]) ).

fof(f378_D,plain,
    ! [X1,X2] :
      ( ! [X3] : ~ min_precedes(X3,X1,X2)
    <=> ~ sP25(X2,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP25])]) ).

fof(f353,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X3,X1,X2)
      | ~ root_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(cnf_transformation,[],[f164]) ).

fof(f164,plain,
    ! [X0,X1,X2] :
      ( ! [X3] : ~ min_precedes(X3,X1,X2)
      | ~ root_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(flattening,[],[f163]) ).

fof(f163,plain,
    ! [X0,X1,X2] :
      ( ! [X3] : ~ min_precedes(X3,X1,X2)
      | ~ root_occ(X1,X0)
      | ~ occurrence_of(X0,X2) ),
    inference(ennf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ( root_occ(X1,X0)
        & occurrence_of(X0,X2) )
     => ~ ? [X3] : min_precedes(X3,X1,X2) ),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X117,X118,X119] :
      ( ( root_occ(X118,X117)
        & occurrence_of(X117,X119) )
     => ~ ? [X120] : min_precedes(X120,X118,X119) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_38) ).

fof(f22015,plain,
    sP25(tptp0,sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f21991,f378]) ).

fof(f21991,plain,
    min_precedes(sK7(sK5),sK11(sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f21972,f356]) ).

fof(f21972,plain,
    sP4(tptp0,sK11(sK7(sK5)),sK7(sK5)),
    inference(unit_resulting_resolution,[],[f21849,f360]) ).

fof(f21849,plain,
    next_subocc(sK7(sK5),sK11(sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f503,f6048,f5814,f5815,f306]) ).

fof(f306,plain,
    ! [X0,X1] :
      ( ~ subactivity_occurrence(X0,X1)
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | next_subocc(X0,sK11(X0),tptp0)
      | ~ occurrence_of(X1,tptp0) ),
    inference(cnf_transformation,[],[f223]) ).

fof(f25447,plain,
    ( leaf_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0))
    | root_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0))
    | ~ occurrence_of(sK20(sK11(sK7(sK5)),sK7(sK5),tptp0),tptp0) ),
    inference(subsumption_resolution,[],[f25437,f13687]) ).

fof(f13687,plain,
    arboreal(sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f271,f13587,f299]) ).

fof(f271,plain,
    atomic(tptp1),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,axiom,
    atomic(tptp1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_55) ).

fof(f25437,plain,
    ( leaf_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0))
    | ~ arboreal(sK11(sK7(sK5)))
    | root_occ(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0))
    | ~ occurrence_of(sK20(sK11(sK7(sK5)),sK7(sK5),tptp0),tptp0) ),
    inference(resolution,[],[f22262,f303]) ).

fof(f303,plain,
    ! [X0,X1] :
      ( ~ subactivity_occurrence(X0,X1)
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | root_occ(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( root_occ(X0,X1)
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(flattening,[],[f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( root_occ(X0,X1)
      | leaf_occ(X0,X1)
      | ~ arboreal(X0)
      | ~ subactivity_occurrence(X0,X1)
      | ~ occurrence_of(X1,tptp0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( ~ leaf_occ(X0,X1)
        & arboreal(X0)
        & subactivity_occurrence(X0,X1)
        & occurrence_of(X1,tptp0) )
     => root_occ(X0,X1) ),
    inference(rectify,[],[f64]) ).

fof(f64,axiom,
    ! [X166,X167] :
      ( ( ~ leaf_occ(X166,X167)
        & arboreal(X166)
        & subactivity_occurrence(X166,X167)
        & occurrence_of(X167,tptp0) )
     => root_occ(X166,X167) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_63) ).

fof(f22262,plain,
    subactivity_occurrence(sK11(sK7(sK5)),sK20(sK11(sK7(sK5)),sK7(sK5),tptp0)),
    inference(unit_resulting_resolution,[],[f22005,f343]) ).

fof(f343,plain,
    ! [X2,X0,X1] :
      ( ~ sP2(X0,X1,X2)
      | subactivity_occurrence(X0,sK20(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f22005,plain,
    sP2(sK11(sK7(sK5)),sK7(sK5),tptp0),
    inference(unit_resulting_resolution,[],[f21991,f344]) ).

fof(f22264,plain,
    occurrence_of(sK20(sK11(sK7(sK5)),sK7(sK5),tptp0),tptp0),
    inference(unit_resulting_resolution,[],[f22005,f341]) ).

fof(f26916,plain,
    sP32(tptp0,sK11(sK7(sK5)),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f21991,f26876,f392]) ).

fof(f26876,plain,
    root_occ(sK7(sK5),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f800,f25652,f26868,f328]) ).

fof(f328,plain,
    ! [X2,X0,X1] :
      ( ~ subactivity_occurrence(X0,X1)
      | ~ root(X0,X2)
      | root_occ(X0,X1)
      | ~ occurrence_of(X1,X2) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f26868,plain,
    subactivity_occurrence(sK7(sK5),sK12(sK11(sK7(sK5)),tptp0)),
    inference(forward_demodulation,[],[f26851,f23880]) ).

fof(f23880,plain,
    sK7(sK5) = sK19(sK11(sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f22079,f23848,f23850,f23861,f351]) ).

fof(f351,plain,
    ! [X2,X0,X1] :
      ( ~ earlier(X2,X1)
      | earlier(X0,X2)
      | earlier(X2,X0)
      | X0 = X2
      | ~ earlier(X0,X1) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0,X1,X2] :
      ( X0 = X2
      | earlier(X0,X2)
      | earlier(X2,X0)
      | ~ earlier(X2,X1)
      | ~ earlier(X0,X1) ),
    inference(flattening,[],[f159]) ).

fof(f159,plain,
    ! [X0,X1,X2] :
      ( X0 = X2
      | earlier(X0,X2)
      | earlier(X2,X0)
      | ~ earlier(X2,X1)
      | ~ earlier(X0,X1) ),
    inference(ennf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ( earlier(X2,X1)
        & earlier(X0,X1) )
     => ( X0 = X2
        | earlier(X0,X2)
        | earlier(X2,X0) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X13,X14,X15] :
      ( ( earlier(X15,X14)
        & earlier(X13,X14) )
     => ( X13 = X15
        | earlier(X13,X15)
        | earlier(X15,X13) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).

fof(f23861,plain,
    earlier(sK19(sK11(sK7(sK5)),tptp0),sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f23779,f318]) ).

fof(f318,plain,
    ! [X0,X1] :
      ( ~ precedes(X0,X1)
      | earlier(X0,X1) ),
    inference(cnf_transformation,[],[f236]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( ( precedes(X0,X1)
        | ~ legal(X1)
        | ~ earlier(X0,X1) )
      & ( ( legal(X1)
          & earlier(X0,X1) )
        | ~ precedes(X0,X1) ) ),
    inference(flattening,[],[f235]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ( precedes(X0,X1)
        | ~ legal(X1)
        | ~ earlier(X0,X1) )
      & ( ( legal(X1)
          & earlier(X0,X1) )
        | ~ precedes(X0,X1) ) ),
    inference(nnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( precedes(X0,X1)
    <=> ( legal(X1)
        & earlier(X0,X1) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X21,X22] :
      ( precedes(X21,X22)
    <=> ( legal(X22)
        & earlier(X21,X22) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).

fof(f23779,plain,
    precedes(sK19(sK11(sK7(sK5)),tptp0),sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f22004,f338]) ).

fof(f338,plain,
    ! [X2,X0,X1] :
      ( ~ min_precedes(X0,X1,X2)
      | precedes(X0,X1) ),
    inference(cnf_transformation,[],[f153]) ).

fof(f153,plain,
    ! [X0,X1,X2] :
      ( precedes(X0,X1)
      | ~ min_precedes(X0,X1,X2) ),
    inference(ennf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( min_precedes(X0,X1,X2)
     => precedes(X0,X1) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X38,X39,X40] :
      ( min_precedes(X38,X39,X40)
     => precedes(X38,X39) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_15) ).

fof(f22004,plain,
    min_precedes(sK19(sK11(sK7(sK5)),tptp0),sK11(sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f21991,f340]) ).

fof(f340,plain,
    ! [X2,X0,X1] :
      ( ~ min_precedes(X0,X1,X2)
      | min_precedes(sK19(X1,X2),X1,X2) ),
    inference(cnf_transformation,[],[f250]) ).

fof(f250,plain,
    ! [X0,X1,X2] :
      ( ( min_precedes(sK19(X1,X2),X1,X2)
        & root(sK19(X1,X2),X2) )
      | ~ min_precedes(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f154,f249]) ).

fof(f249,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( min_precedes(X3,X1,X2)
          & root(X3,X2) )
     => ( min_precedes(sK19(X1,X2),X1,X2)
        & root(sK19(X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f154,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( min_precedes(X3,X1,X2)
          & root(X3,X2) )
      | ~ min_precedes(X0,X1,X2) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2] :
      ( min_precedes(X0,X1,X2)
     => ? [X3] :
          ( min_precedes(X3,X1,X2)
          & root(X3,X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X31,X32,X33] :
      ( min_precedes(X31,X32,X33)
     => ? [X34] :
          ( min_precedes(X34,X32,X33)
          & root(X34,X33) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).

fof(f23850,plain,
    ~ earlier(sK7(sK5),sK19(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f22211,f23789,f320]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( ~ earlier(X0,X1)
      | ~ legal(X1)
      | precedes(X0,X1) ),
    inference(cnf_transformation,[],[f236]) ).

fof(f23789,plain,
    ~ precedes(sK7(sK5),sK19(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f21991,f22216,f22004,f374]) ).

fof(f374,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X2,X0,X3)
      | ~ precedes(X1,X2)
      | min_precedes(X1,X2,X3)
      | ~ min_precedes(X1,X0,X3) ),
    inference(cnf_transformation,[],[f193]) ).

fof(f193,plain,
    ! [X0,X1,X2,X3] :
      ( min_precedes(X1,X2,X3)
      | ~ precedes(X1,X2)
      | ~ min_precedes(X2,X0,X3)
      | ~ min_precedes(X1,X0,X3) ),
    inference(flattening,[],[f192]) ).

fof(f192,plain,
    ! [X0,X1,X2,X3] :
      ( min_precedes(X1,X2,X3)
      | ~ precedes(X1,X2)
      | ~ min_precedes(X2,X0,X3)
      | ~ min_precedes(X1,X0,X3) ),
    inference(ennf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1,X2,X3] :
      ( ( precedes(X1,X2)
        & min_precedes(X2,X0,X3)
        & min_precedes(X1,X0,X3) )
     => min_precedes(X1,X2,X3) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X52,X53,X54,X55] :
      ( ( precedes(X53,X54)
        & min_precedes(X54,X52,X55)
        & min_precedes(X53,X52,X55) )
     => min_precedes(X53,X54,X55) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_20) ).

fof(f22216,plain,
    ! [X0] : ~ min_precedes(X0,sK19(sK11(sK7(sK5)),tptp0),tptp0),
    inference(unit_resulting_resolution,[],[f22003,f337]) ).

fof(f337,plain,
    ! [X2,X0,X1] :
      ( ~ min_precedes(X0,X1,X2)
      | ~ root(X1,X2) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0,X1,X2] :
      ( ~ root(X1,X2)
      | ~ min_precedes(X0,X1,X2) ),
    inference(ennf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( min_precedes(X0,X1,X2)
     => ~ root(X1,X2) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X35,X36,X37] :
      ( min_precedes(X35,X36,X37)
     => ~ root(X36,X37) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).

fof(f22003,plain,
    root(sK19(sK11(sK7(sK5)),tptp0),tptp0),
    inference(unit_resulting_resolution,[],[f21991,f339]) ).

fof(f339,plain,
    ! [X2,X0,X1] :
      ( ~ min_precedes(X0,X1,X2)
      | root(sK19(X1,X2),X2) ),
    inference(cnf_transformation,[],[f250]) ).

fof(f22211,plain,
    legal(sK19(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f22003,f290]) ).

fof(f290,plain,
    ! [X0,X1] :
      ( ~ root(X0,X1)
      | legal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( legal(X0)
      | ~ root(X0,X1) ),
    inference(ennf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( root(X0,X1)
     => legal(X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X41,X42] :
      ( root(X41,X42)
     => legal(X41) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_16) ).

fof(f23848,plain,
    ~ earlier(sK19(sK11(sK7(sK5)),tptp0),sK7(sK5)),
    inference(unit_resulting_resolution,[],[f569,f23787,f320]) ).

fof(f23787,plain,
    ~ precedes(sK19(sK11(sK7(sK5)),tptp0),sK7(sK5)),
    inference(unit_resulting_resolution,[],[f21991,f801,f22004,f374]) ).

fof(f801,plain,
    ! [X0] : ~ min_precedes(X0,sK7(sK5),tptp0),
    inference(superposition,[],[f568,f725]) ).

fof(f568,plain,
    ! [X0] : ~ min_precedes(X0,sK7(sK5),sK17(sK7(sK5),sK5)),
    inference(unit_resulting_resolution,[],[f563,f337]) ).

fof(f569,plain,
    legal(sK7(sK5)),
    inference(unit_resulting_resolution,[],[f563,f290]) ).

fof(f22079,plain,
    earlier(sK7(sK5),sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f22002,f318]) ).

fof(f22002,plain,
    precedes(sK7(sK5),sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f21991,f338]) ).

fof(f26851,plain,
    subactivity_occurrence(sK19(sK11(sK7(sK5)),tptp0),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f22004,f25652,f26712,f372]) ).

fof(f372,plain,
    ! [X2,X3,X0,X1] :
      ( ~ min_precedes(X0,X1,X2)
      | ~ subactivity_occurrence(X1,X3)
      | ~ occurrence_of(X3,X2)
      | subactivity_occurrence(X0,X3) ),
    inference(cnf_transformation,[],[f189]) ).

fof(f189,plain,
    ! [X0,X1,X2,X3] :
      ( subactivity_occurrence(X0,X3)
      | ~ subactivity_occurrence(X1,X3)
      | ~ occurrence_of(X3,X2)
      | ~ min_precedes(X0,X1,X2) ),
    inference(flattening,[],[f188]) ).

fof(f188,plain,
    ! [X0,X1,X2,X3] :
      ( subactivity_occurrence(X0,X3)
      | ~ subactivity_occurrence(X1,X3)
      | ~ occurrence_of(X3,X2)
      | ~ min_precedes(X0,X1,X2) ),
    inference(ennf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0,X1,X2,X3] :
      ( ( subactivity_occurrence(X1,X3)
        & occurrence_of(X3,X2)
        & min_precedes(X0,X1,X2) )
     => subactivity_occurrence(X0,X3) ),
    inference(rectify,[],[f30]) ).

fof(f30,axiom,
    ! [X83,X84,X85,X86] :
      ( ( subactivity_occurrence(X84,X86)
        & occurrence_of(X86,X85)
        & min_precedes(X83,X84,X85) )
     => subactivity_occurrence(X83,X86) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_29) ).

fof(f26712,plain,
    subactivity_occurrence(sK11(sK7(sK5)),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f25651,f330]) ).

fof(f330,plain,
    ! [X0,X1] :
      ( ~ leaf_occ(X0,X1)
      | subactivity_occurrence(X0,X1) ),
    inference(cnf_transformation,[],[f248]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( ( leaf_occ(X0,X1)
        | ! [X2] :
            ( ~ leaf(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ( leaf(X0,sK18(X0,X1))
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,sK18(X0,X1)) )
        | ~ leaf_occ(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f246,f247]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( leaf(X0,X3)
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,X3) )
     => ( leaf(X0,sK18(X0,X1))
        & subactivity_occurrence(X0,X1)
        & occurrence_of(X1,sK18(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ( leaf_occ(X0,X1)
        | ! [X2] :
            ( ~ leaf(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ? [X3] :
            ( leaf(X0,X3)
            & subactivity_occurrence(X0,X1)
            & occurrence_of(X1,X3) )
        | ~ leaf_occ(X0,X1) ) ),
    inference(rectify,[],[f245]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ( leaf_occ(X0,X1)
        | ! [X2] :
            ( ~ leaf(X0,X2)
            | ~ subactivity_occurrence(X0,X1)
            | ~ occurrence_of(X1,X2) ) )
      & ( ? [X2] :
            ( leaf(X0,X2)
            & subactivity_occurrence(X0,X1)
            & occurrence_of(X1,X2) )
        | ~ leaf_occ(X0,X1) ) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( leaf_occ(X0,X1)
    <=> ? [X2] :
          ( leaf(X0,X2)
          & subactivity_occurrence(X0,X1)
          & occurrence_of(X1,X2) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X102,X103] :
      ( leaf_occ(X102,X103)
    <=> ? [X104] :
          ( leaf(X102,X104)
          & subactivity_occurrence(X102,X103)
          & occurrence_of(X103,X104) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_34) ).

fof(f25651,plain,
    leaf_occ(sK11(sK7(sK5)),sK12(sK11(sK7(sK5)),tptp0)),
    inference(unit_resulting_resolution,[],[f268,f25647,f308]) ).

fof(f308,plain,
    ! [X0,X1] :
      ( ~ leaf(X0,X1)
      | atomic(X1)
      | leaf_occ(X0,sK12(X0,X1)) ),
    inference(cnf_transformation,[],[f225]) ).

fof(f225,plain,
    ! [X0,X1] :
      ( ( leaf_occ(X0,sK12(X0,X1))
        & occurrence_of(sK12(X0,X1),X1) )
      | atomic(X1)
      | ~ leaf(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f143,f224]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( leaf_occ(X0,X2)
          & occurrence_of(X2,X1) )
     => ( leaf_occ(X0,sK12(X0,X1))
        & occurrence_of(sK12(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( leaf_occ(X0,X2)
          & occurrence_of(X2,X1) )
      | atomic(X1)
      | ~ leaf(X0,X1) ),
    inference(flattening,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( leaf_occ(X0,X2)
          & occurrence_of(X2,X1) )
      | atomic(X1)
      | ~ leaf(X0,X1) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( ~ atomic(X1)
        & leaf(X0,X1) )
     => ? [X2] :
          ( leaf_occ(X0,X2)
          & occurrence_of(X2,X1) ) ),
    inference(rectify,[],[f46]) ).

fof(f46,axiom,
    ! [X145,X146] :
      ( ( ~ atomic(X146)
        & leaf(X145,X146) )
     => ? [X147] :
          ( leaf_occ(X145,X147)
          & occurrence_of(X147,X146) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_45) ).

fof(f25647,plain,
    leaf(sK11(sK7(sK5)),tptp0),
    inference(unit_resulting_resolution,[],[f25607,f317]) ).

fof(f317,plain,
    ! [X0,X1] :
      ( ~ sP1(X1,X0)
      | leaf(X0,X1) ),
    inference(cnf_transformation,[],[f234]) ).

fof(f234,plain,
    ! [X0,X1] :
      ( ( leaf(X0,X1)
        | ~ sP1(X1,X0) )
      & ( sP1(X1,X0)
        | ~ leaf(X0,X1) ) ),
    inference(nnf_transformation,[],[f203]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( leaf(X0,X1)
    <=> sP1(X1,X0) ),
    inference(definition_folding,[],[f148,f202]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( leaf(X0,X1)
    <=> ( ! [X2] : ~ min_precedes(X0,X2,X1)
        & ( ? [X3] : min_precedes(X3,X0,X1)
          | root(X0,X1) ) ) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( leaf(X0,X1)
    <=> ( ~ ? [X2] : min_precedes(X0,X2,X1)
        & ( ? [X3] : min_precedes(X3,X0,X1)
          | root(X0,X1) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X56,X57] :
      ( leaf(X56,X57)
    <=> ( ~ ? [X59] : min_precedes(X56,X59,X57)
        & ( ? [X58] : min_precedes(X58,X56,X57)
          | root(X56,X57) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_21) ).

fof(f25607,plain,
    sP1(tptp0,sK11(sK7(sK5))),
    inference(unit_resulting_resolution,[],[f21991,f25600,f315]) ).

fof(f315,plain,
    ! [X3,X0,X1] :
      ( ~ min_precedes(X3,X1,X0)
      | min_precedes(X1,sK14(X0,X1),X0)
      | sP1(X0,X1) ),
    inference(cnf_transformation,[],[f233]) ).

fof(f268,plain,
    ~ atomic(tptp0),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,axiom,
    ~ atomic(tptp0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_51) ).

fof(f25652,plain,
    occurrence_of(sK12(sK11(sK7(sK5)),tptp0),tptp0),
    inference(unit_resulting_resolution,[],[f268,f25647,f307]) ).

fof(f307,plain,
    ! [X0,X1] :
      ( ~ leaf(X0,X1)
      | atomic(X1)
      | occurrence_of(sK12(X0,X1),X1) ),
    inference(cnf_transformation,[],[f225]) ).

fof(f25844,plain,
    occurrence_of(sK8(sK12(sK11(sK7(sK5)),tptp0)),tptp3),
    inference(unit_resulting_resolution,[],[f25693,f286]) ).

fof(f286,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | occurrence_of(sK8(X0),tptp3) ),
    inference(cnf_transformation,[],[f216]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PRO004+3 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 03:57:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (19936)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.36  % (19942)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)
% 0.20/0.37  % (19939)WARNING: value z3 for option sas not known
% 0.20/0.37  % (19937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  % (19939)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)
% 0.20/0.37  % (19940)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (19941)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)
% 0.20/0.37  % (19943)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)
% 0.20/0.37  % (19938)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  Detected minimum model sizes of [4]
% 0.20/0.37  Detected maximum model sizes of [max]
% 0.20/0.37  Detected minimum model sizes of [4]
% 0.20/0.37  Detected maximum model sizes of [max]
% 0.20/0.37  TRYING [4]
% 0.20/0.37  TRYING [4]
% 0.20/0.39  TRYING [5]
% 0.20/0.40  TRYING [5]
% 0.20/0.44  TRYING [6]
% 0.20/0.46  TRYING [6]
% 0.20/0.51  TRYING [7]
% 0.20/0.54  TRYING [7]
% 2.06/0.65  TRYING [8]
% 2.25/0.71  TRYING [8]
% 3.78/0.91  % (19943)First to succeed.
% 3.78/0.91  % (19943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19936"
% 3.78/0.91  % (19943)Refutation found. Thanks to Tanya!
% 3.78/0.91  % SZS status Theorem for theBenchmark
% 3.78/0.91  % SZS output start Proof for theBenchmark
% See solution above
% 3.78/0.92  % (19943)------------------------------
% 3.78/0.92  % (19943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.78/0.92  % (19943)Termination reason: Refutation
% 3.78/0.92  
% 3.78/0.92  % (19943)Memory used [KB]: 10917
% 3.78/0.92  % (19943)Time elapsed: 0.546 s
% 3.78/0.92  % (19943)Instructions burned: 1845 (million)
% 3.78/0.92  % (19936)Success in time 0.556 s
%------------------------------------------------------------------------------