TSTP Solution File: PRO011+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PRO011+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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  : 600s
% DateTime : Mon Jul 18 17:50:17 EDT 2022

% Result   : Theorem 8.35s 8.52s
% Output   : CNFRefutation 8.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   72 (  13 unt;   1 def)
%            Number of atoms       :  289 (  18 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  324 ( 107   ~; 105   |;  93   &)
%                                         (   8 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  135 (   2 sgn  71   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(sos_02,axiom,
    ! [X4,X5,X6] :
      ( ( occurrence_of(X4,X5)
        & occurrence_of(X4,X6) )
     => X5 = X6 ) ).

fof(sos_21,axiom,
    ! [X56,X57] :
      ( leaf(X56,X57)
    <=> ( ( root(X56,X57)
          | ? [X58] : min_precedes(X58,X56,X57) )
        & ~ ? [X59] : min_precedes(X56,X59,X57) ) ) ).

fof(sos_34,axiom,
    ! [X102,X103] :
      ( leaf_occ(X102,X103)
    <=> ? [X104] :
          ( occurrence_of(X103,X104)
          & subactivity_occurrence(X102,X103)
          & leaf(X102,X104) ) ) ).

fof(sos_35,axiom,
    ! [X105] :
      ( occurrence_of(X105,tptp0)
     => ? [X106,X107,X108] :
          ( occurrence_of(X106,tptp3)
          & root_occ(X106,X105)
          & occurrence_of(X107,tptp4)
          & next_subocc(X106,X107,tptp0)
          & ( occurrence_of(X108,tptp1)
            | occurrence_of(X108,tptp2) )
          & next_subocc(X107,X108,tptp0)
          & leaf_occ(X108,X105) ) ) ).

fof(goals,conjecture,
    ! [X109] :
      ( occurrence_of(X109,tptp0)
     => ? [X110,X111] :
          ( leaf_occ(X111,X109)
          & ( occurrence_of(X111,tptp1)
           => ~ ? [X112] :
                  ( occurrence_of(X112,tptp2)
                  & subactivity_occurrence(X112,X109)
                  & min_precedes(X110,X112,tptp0) ) )
          & ( occurrence_of(X111,tptp2)
           => ~ ? [X113] :
                  ( occurrence_of(X113,tptp1)
                  & subactivity_occurrence(X113,X109)
                  & min_precedes(X110,X113,tptp0) ) ) ) ) ).

fof(definition_0,definition,
    ! [X110,X111] :
      ( definitionFOFtoCNF_0(X110,X111)
    <=> ( occurrence_of(X111,tptp1)
        & ? [X112] :
            ( min_precedes(X110,X112,tptp0)
            & occurrence_of(X112,tptp2)
            & subactivity_occurrence(X112,skolemFOFtoCNF_X109) ) ) ) ).

fof(subgoal_0,plain,
    ! [X109] :
      ( occurrence_of(X109,tptp0)
     => ? [X110,X111] :
          ( leaf_occ(X111,X109)
          & ( occurrence_of(X111,tptp1)
           => ~ ? [X112] :
                  ( occurrence_of(X112,tptp2)
                  & subactivity_occurrence(X112,X109)
                  & min_precedes(X110,X112,tptp0) ) )
          & ( occurrence_of(X111,tptp2)
           => ~ ? [X113] :
                  ( occurrence_of(X113,tptp1)
                  & subactivity_occurrence(X113,X109)
                  & min_precedes(X110,X113,tptp0) ) ) ) ),
    inference(strip,[],[goals]) ).

fof(negate_0_0,plain,
    ~ ! [X109] :
        ( occurrence_of(X109,tptp0)
       => ? [X110,X111] :
            ( leaf_occ(X111,X109)
            & ( occurrence_of(X111,tptp1)
             => ~ ? [X112] :
                    ( occurrence_of(X112,tptp2)
                    & subactivity_occurrence(X112,X109)
                    & min_precedes(X110,X112,tptp0) ) )
            & ( occurrence_of(X111,tptp2)
             => ~ ? [X113] :
                    ( occurrence_of(X113,tptp1)
                    & subactivity_occurrence(X113,X109)
                    & min_precedes(X110,X113,tptp0) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X56,X57] :
      ( ~ leaf(X56,X57)
    <=> ( ( ~ root(X56,X57)
          & ! [X58] : ~ min_precedes(X58,X56,X57) )
        | ? [X59] : min_precedes(X56,X59,X57) ) ),
    inference(canonicalize,[],[sos_21]) ).

fof(normalize_0_1,plain,
    ! [X56,X57] :
      ( ~ leaf(X56,X57)
    <=> ( ( ~ root(X56,X57)
          & ! [X58] : ~ min_precedes(X58,X56,X57) )
        | ? [X59] : min_precedes(X56,X59,X57) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X56,X57,X58,X59] :
      ( ( ~ leaf(X56,X57)
        | ~ min_precedes(X56,X59,X57) )
      & ( ~ leaf(X56,X57)
        | min_precedes(skolemFOFtoCNF_X58(X56,X57),X56,X57)
        | root(X56,X57) )
      & ( ~ min_precedes(X58,X56,X57)
        | leaf(X56,X57)
        | min_precedes(X56,skolemFOFtoCNF_X59(X56,X57),X57) )
      & ( ~ root(X56,X57)
        | leaf(X56,X57)
        | min_precedes(X56,skolemFOFtoCNF_X59(X56,X57),X57) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X56,X57,X59] :
      ( ~ leaf(X56,X57)
      | ~ min_precedes(X56,X59,X57) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X110,X111] :
      ( ~ definitionFOFtoCNF_0(X110,X111)
    <=> ( ~ occurrence_of(X111,tptp1)
        | ! [X112] :
            ( ~ min_precedes(X110,X112,tptp0)
            | ~ occurrence_of(X112,tptp2)
            | ~ subactivity_occurrence(X112,skolemFOFtoCNF_X109) ) ) ),
    inference(canonicalize,[],[definition_0]) ).

fof(normalize_0_5,plain,
    ! [X110,X111,X112] :
      ( ( ~ definitionFOFtoCNF_0(X110,X111)
        | min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0) )
      & ( ~ definitionFOFtoCNF_0(X110,X111)
        | occurrence_of(X111,tptp1) )
      & ( ~ definitionFOFtoCNF_0(X110,X111)
        | occurrence_of(skolemFOFtoCNF_X112(X110),tptp2) )
      & ( ~ definitionFOFtoCNF_0(X110,X111)
        | subactivity_occurrence(skolemFOFtoCNF_X112(X110),skolemFOFtoCNF_X109) )
      & ( ~ min_precedes(X110,X112,tptp0)
        | ~ occurrence_of(X111,tptp1)
        | ~ occurrence_of(X112,tptp2)
        | ~ subactivity_occurrence(X112,skolemFOFtoCNF_X109)
        | definitionFOFtoCNF_0(X110,X111) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X110,X111] :
      ( ~ definitionFOFtoCNF_0(X110,X111)
      | min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ? [X109] :
      ( occurrence_of(X109,tptp0)
      & ! [X110,X111] :
          ( ~ leaf_occ(X111,X109)
          | ( occurrence_of(X111,tptp1)
            & ? [X112] :
                ( min_precedes(X110,X112,tptp0)
                & occurrence_of(X112,tptp2)
                & subactivity_occurrence(X112,X109) ) )
          | ( occurrence_of(X111,tptp2)
            & ? [X113] :
                ( min_precedes(X110,X113,tptp0)
                & occurrence_of(X113,tptp1)
                & subactivity_occurrence(X113,X109) ) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_8,plain,
    ( occurrence_of(skolemFOFtoCNF_X109,tptp0)
    & ! [X110,X111] :
        ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
        | ( occurrence_of(X111,tptp1)
          & ? [X112] :
              ( min_precedes(X110,X112,tptp0)
              & occurrence_of(X112,tptp2)
              & subactivity_occurrence(X112,skolemFOFtoCNF_X109) ) )
        | ( occurrence_of(X111,tptp2)
          & ? [X113] :
              ( min_precedes(X110,X113,tptp0)
              & occurrence_of(X113,tptp1)
              & subactivity_occurrence(X113,skolemFOFtoCNF_X109) ) ) ) ),
    inference(skolemize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    occurrence_of(skolemFOFtoCNF_X109,tptp0),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X105] :
      ( ~ occurrence_of(X105,tptp0)
      | ? [X106,X107,X108] :
          ( leaf_occ(X108,X105)
          & next_subocc(X106,X107,tptp0)
          & next_subocc(X107,X108,tptp0)
          & occurrence_of(X106,tptp3)
          & occurrence_of(X107,tptp4)
          & root_occ(X106,X105)
          & ( occurrence_of(X108,tptp1)
            | occurrence_of(X108,tptp2) ) ) ),
    inference(canonicalize,[],[sos_35]) ).

fof(normalize_0_11,plain,
    ! [X105] :
      ( ~ occurrence_of(X105,tptp0)
      | ? [X106,X107,X108] :
          ( leaf_occ(X108,X105)
          & next_subocc(X106,X107,tptp0)
          & next_subocc(X107,X108,tptp0)
          & occurrence_of(X106,tptp3)
          & occurrence_of(X107,tptp4)
          & root_occ(X106,X105)
          & ( occurrence_of(X108,tptp1)
            | occurrence_of(X108,tptp2) ) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X105] :
      ( ( ~ occurrence_of(X105,tptp0)
        | leaf_occ(skolemFOFtoCNF_X108(X105),X105) )
      & ( ~ occurrence_of(X105,tptp0)
        | next_subocc(skolemFOFtoCNF_X106(X105),skolemFOFtoCNF_X107(X105),tptp0) )
      & ( ~ occurrence_of(X105,tptp0)
        | next_subocc(skolemFOFtoCNF_X107(X105),skolemFOFtoCNF_X108(X105),tptp0) )
      & ( ~ occurrence_of(X105,tptp0)
        | occurrence_of(skolemFOFtoCNF_X106(X105),tptp3) )
      & ( ~ occurrence_of(X105,tptp0)
        | occurrence_of(skolemFOFtoCNF_X107(X105),tptp4) )
      & ( ~ occurrence_of(X105,tptp0)
        | root_occ(skolemFOFtoCNF_X106(X105),X105) )
      & ( ~ occurrence_of(X105,tptp0)
        | occurrence_of(skolemFOFtoCNF_X108(X105),tptp1)
        | occurrence_of(skolemFOFtoCNF_X108(X105),tptp2) ) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X105] :
      ( ~ occurrence_of(X105,tptp0)
      | leaf_occ(skolemFOFtoCNF_X108(X105),X105) ),
    inference(conjunct,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [X110,X111] :
      ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
      | ( occurrence_of(X111,tptp1)
        & ? [X112] :
            ( min_precedes(X110,X112,tptp0)
            & occurrence_of(X112,tptp2)
            & subactivity_occurrence(X112,skolemFOFtoCNF_X109) ) )
      | ( occurrence_of(X111,tptp2)
        & ? [X113] :
            ( min_precedes(X110,X113,tptp0)
            & occurrence_of(X113,tptp1)
            & subactivity_occurrence(X113,skolemFOFtoCNF_X109) ) ) ),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_15,plain,
    ! [X110,X111] :
      ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
      | ( occurrence_of(X111,tptp1)
        & ? [X112] :
            ( min_precedes(X110,X112,tptp0)
            & occurrence_of(X112,tptp2)
            & subactivity_occurrence(X112,skolemFOFtoCNF_X109) ) )
      | ( occurrence_of(X111,tptp2)
        & ? [X113] :
            ( min_precedes(X110,X113,tptp0)
            & occurrence_of(X113,tptp1)
            & subactivity_occurrence(X113,skolemFOFtoCNF_X109) ) ) ),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [X110,X111] :
      ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
      | definitionFOFtoCNF_0(X110,X111)
      | ( occurrence_of(X111,tptp2)
        & ? [X113] :
            ( min_precedes(X110,X113,tptp0)
            & occurrence_of(X113,tptp1)
            & subactivity_occurrence(X113,skolemFOFtoCNF_X109) ) ) ),
    inference(simplify,[],[normalize_0_15,normalize_0_4]) ).

fof(normalize_0_17,plain,
    ! [X110,X111] :
      ( ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
        | definitionFOFtoCNF_0(X110,X111)
        | min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0) )
      & ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
        | definitionFOFtoCNF_0(X110,X111)
        | occurrence_of(X111,tptp2) )
      & ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
        | definitionFOFtoCNF_0(X110,X111)
        | occurrence_of(skolemFOFtoCNF_X113(X110),tptp1) )
      & ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
        | definitionFOFtoCNF_0(X110,X111)
        | subactivity_occurrence(skolemFOFtoCNF_X113(X110),skolemFOFtoCNF_X109) ) ),
    inference(clausify,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    ! [X110,X111] :
      ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
      | definitionFOFtoCNF_0(X110,X111)
      | min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0) ),
    inference(conjunct,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [X102,X103] :
      ( ~ leaf_occ(X102,X103)
    <=> ! [X104] :
          ( ~ leaf(X102,X104)
          | ~ occurrence_of(X103,X104)
          | ~ subactivity_occurrence(X102,X103) ) ),
    inference(canonicalize,[],[sos_34]) ).

fof(normalize_0_20,plain,
    ! [X102,X103] :
      ( ~ leaf_occ(X102,X103)
    <=> ! [X104] :
          ( ~ leaf(X102,X104)
          | ~ occurrence_of(X103,X104)
          | ~ subactivity_occurrence(X102,X103) ) ),
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [X102,X103,X104] :
      ( ( ~ leaf_occ(X102,X103)
        | leaf(X102,skolemFOFtoCNF_X104(X102,X103)) )
      & ( ~ leaf_occ(X102,X103)
        | occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) )
      & ( ~ leaf_occ(X102,X103)
        | subactivity_occurrence(X102,X103) )
      & ( ~ leaf(X102,X104)
        | ~ occurrence_of(X103,X104)
        | ~ subactivity_occurrence(X102,X103)
        | leaf_occ(X102,X103) ) ),
    inference(clausify,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [X102,X103] :
      ( ~ leaf_occ(X102,X103)
      | leaf(X102,skolemFOFtoCNF_X104(X102,X103)) ),
    inference(conjunct,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
    ! [X102,X103] :
      ( ~ leaf_occ(X102,X103)
      | occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) ),
    inference(conjunct,[],[normalize_0_21]) ).

fof(normalize_0_24,plain,
    ! [X4,X5,X6] :
      ( ~ occurrence_of(X4,X5)
      | ~ occurrence_of(X4,X6)
      | X5 = X6 ),
    inference(canonicalize,[],[sos_02]) ).

fof(normalize_0_25,plain,
    ! [X4,X5,X6] :
      ( ~ occurrence_of(X4,X5)
      | ~ occurrence_of(X4,X6)
      | X5 = X6 ),
    inference(specialize,[],[normalize_0_24]) ).

cnf(refute_0_0,plain,
    ( ~ leaf(X56,X57)
    | ~ min_precedes(X56,X59,X57) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0)
    | ~ min_precedes(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X112(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),tptp0) ),
    inference(subst,[],[refute_0_0:[bind(X56,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X57,$fot(tptp0)),bind(X59,$fot(skolemFOFtoCNF_X112(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))))]]) ).

cnf(refute_0_2,plain,
    ( ~ definitionFOFtoCNF_0(X110,X111)
    | min_precedes(X110,skolemFOFtoCNF_X112(X110),tptp0) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))
    | min_precedes(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X112(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),tptp0) ),
    inference(subst,[],[refute_0_2:[bind(X110,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X111,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).

cnf(refute_0_4,plain,
    ( ~ leaf(X_262,tptp0)
    | ~ min_precedes(X_262,skolemFOFtoCNF_X113(X_262),tptp0) ),
    inference(subst,[],[refute_0_0:[bind(X56,$fot(X_262)),bind(X57,$fot(tptp0)),bind(X59,$fot(skolemFOFtoCNF_X113(X_262)))]]) ).

cnf(refute_0_5,plain,
    occurrence_of(skolemFOFtoCNF_X109,tptp0),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_6,plain,
    ( ~ occurrence_of(X105,tptp0)
    | leaf_occ(skolemFOFtoCNF_X108(X105),X105) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_7,plain,
    ( ~ occurrence_of(skolemFOFtoCNF_X109,tptp0)
    | leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) ),
    inference(subst,[],[refute_0_6:[bind(X105,$fot(skolemFOFtoCNF_X109))]]) ).

cnf(refute_0_8,plain,
    leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),
    inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,tptp0) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( ~ leaf_occ(X111,skolemFOFtoCNF_X109)
    | definitionFOFtoCNF_0(X110,X111)
    | min_precedes(X110,skolemFOFtoCNF_X113(X110),tptp0) ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_10,plain,
    ( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
    | definitionFOFtoCNF_0(X_260,skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))
    | min_precedes(X_260,skolemFOFtoCNF_X113(X_260),tptp0) ),
    inference(subst,[],[refute_0_9:[bind(X110,$fot(X_260)),bind(X111,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).

cnf(refute_0_11,plain,
    ( definitionFOFtoCNF_0(X_260,skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))
    | min_precedes(X_260,skolemFOFtoCNF_X113(X_260),tptp0) ),
    inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_8,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( definitionFOFtoCNF_0(X_262,skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))
    | min_precedes(X_262,skolemFOFtoCNF_X113(X_262),tptp0) ),
    inference(subst,[],[refute_0_11:[bind(X_260,$fot(X_262))]]) ).

cnf(refute_0_13,plain,
    ( ~ leaf(X_262,tptp0)
    | definitionFOFtoCNF_0(X_262,skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) ),
    inference(resolve,[$cnf( min_precedes(X_262,skolemFOFtoCNF_X113(X_262),tptp0) )],[refute_0_12,refute_0_4]) ).

cnf(refute_0_14,plain,
    ( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0)
    | definitionFOFtoCNF_0(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) ),
    inference(subst,[],[refute_0_13:[bind(X_262,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)))]]) ).

cnf(refute_0_15,plain,
    ( ~ leaf_occ(X102,X103)
    | leaf(X102,skolemFOFtoCNF_X104(X102,X103)) ),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_16,plain,
    ( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
    | leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),
    inference(subst,[],[refute_0_15:[bind(X102,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X103,$fot(skolemFOFtoCNF_X109))]]) ).

cnf(refute_0_17,plain,
    leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)),
    inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_8,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( ~ leaf_occ(X102,X103)
    | occurrence_of(X103,skolemFOFtoCNF_X104(X102,X103)) ),
    inference(canonicalize,[],[normalize_0_23]) ).

cnf(refute_0_19,plain,
    ( ~ leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
    | occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),
    inference(subst,[],[refute_0_18:[bind(X102,$fot(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109))),bind(X103,$fot(skolemFOFtoCNF_X109))]]) ).

cnf(refute_0_20,plain,
    occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)),
    inference(resolve,[$cnf( leaf_occ(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) )],[refute_0_8,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ occurrence_of(X4,X5)
    | ~ occurrence_of(X4,X6)
    | X5 = X6 ),
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_22,plain,
    ( ~ occurrence_of(skolemFOFtoCNF_X109,X_391)
    | ~ occurrence_of(skolemFOFtoCNF_X109,tptp0)
    | tptp0 = X_391 ),
    inference(subst,[],[refute_0_21:[bind(X4,$fot(skolemFOFtoCNF_X109)),bind(X5,$fot(tptp0)),bind(X6,$fot(X_391))]]) ).

cnf(refute_0_23,plain,
    ( ~ occurrence_of(skolemFOFtoCNF_X109,X_391)
    | tptp0 = X_391 ),
    inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,tptp0) )],[refute_0_5,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
    | tptp0 = skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) ),
    inference(subst,[],[refute_0_23:[bind(X_391,$fot(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)))]]) ).

cnf(refute_0_25,plain,
    tptp0 = skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),
    inference(resolve,[$cnf( occurrence_of(skolemFOFtoCNF_X109,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_20,refute_0_24]) ).

cnf(refute_0_26,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_27,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_28,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( tptp0 != skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)
    | skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) = tptp0 ),
    inference(subst,[],[refute_0_28:[bind(X,$fot(tptp0)),bind(Y,$fot(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)))]]) ).

cnf(refute_0_30,plain,
    skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) = tptp0,
    inference(resolve,[$cnf( $equal(tptp0,skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_25,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109) != tptp0
    | ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
    | leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) ),
    introduced(tautology,[equality,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) ),[1],$fot(tptp0)]]) ).

cnf(refute_0_32,plain,
    ( ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109))
    | leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109),tptp0) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0),
    inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X104(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X109)) )],[refute_0_17,refute_0_32]) ).

cnf(refute_0_34,plain,
    definitionFOFtoCNF_0(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),
    inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) )],[refute_0_33,refute_0_14]) ).

cnf(refute_0_35,plain,
    min_precedes(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X112(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),tptp0),
    inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)) )],[refute_0_34,refute_0_3]) ).

cnf(refute_0_36,plain,
    ~ leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0),
    inference(resolve,[$cnf( min_precedes(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),skolemFOFtoCNF_X112(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109)),tptp0) )],[refute_0_35,refute_0_1]) ).

cnf(refute_0_37,plain,
    $false,
    inference(resolve,[$cnf( leaf(skolemFOFtoCNF_X108(skolemFOFtoCNF_X109),tptp0) )],[refute_0_33,refute_0_36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : PRO011+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 01:09:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.35/8.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.35/8.52  
% 8.35/8.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.35/8.53  
%------------------------------------------------------------------------------