TSTP Solution File: PRO009+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:36:43 EDT 2024

% Result   : Theorem 0.17s 0.45s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   55 (   3 unt;   0 def)
%            Number of atoms       :  213 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  264 ( 106   ~;  97   |;  51   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   5 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   94 (  76   !;  18   ?)

% 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') ).

fof(f5,axiom,
    ! [X15,X16,X17] :
      ( next_subocc(X15,X16,X17)
    <=> ( min_precedes(X15,X16,X17)
        & ~ ? [X18] :
              ( min_precedes(X15,X18,X17)
              & min_precedes(X18,X16,X17) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,axiom,
    ! [X95] :
      ( occurrence_of(X95,tptp0)
     => ? [X96,X97,X98] :
          ( occurrence_of(X96,tptp3)
          & root_occ(X96,X95)
          & occurrence_of(X97,tptp4)
          & next_subocc(X96,X97,tptp0)
          & ( occurrence_of(X98,tptp2)
            | occurrence_of(X98,tptp1) )
          & next_subocc(X97,X98,tptp0)
          & leaf_occ(X98,X95) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,conjecture,
    ! [X99] :
      ( occurrence_of(X99,tptp0)
     => ? [X100,X101] :
          ( occurrence_of(X100,tptp3)
          & root_occ(X100,X99)
          & ( occurrence_of(X101,tptp2)
            | occurrence_of(X101,tptp1) )
          & min_precedes(X100,X101,tptp0)
          & leaf_occ(X101,X99) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f47,negated_conjecture,
    ~ ! [X99] :
        ( occurrence_of(X99,tptp0)
       => ? [X100,X101] :
            ( occurrence_of(X100,tptp3)
            & root_occ(X100,X99)
            & ( occurrence_of(X101,tptp2)
              | occurrence_of(X101,tptp1) )
            & min_precedes(X100,X101,tptp0)
            & leaf_occ(X101,X99) ) ),
    inference(negated_conjecture,[status(cth)],[f46]) ).

fof(f48,plain,
    ! [X0,X1,X2,X3] :
      ( ~ min_precedes(X0,X1,X3)
      | ~ min_precedes(X1,X2,X3)
      | min_precedes(X0,X2,X3) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f49,plain,
    ! [X0,X2,X3] :
      ( ! [X1] :
          ( ~ min_precedes(X0,X1,X3)
          | ~ min_precedes(X1,X2,X3) )
      | min_precedes(X0,X2,X3) ),
    inference(miniscoping,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3] :
      ( ~ min_precedes(X0,X1,X2)
      | ~ min_precedes(X1,X3,X2)
      | min_precedes(X0,X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f60,plain,
    ! [X15,X16,X17] :
      ( next_subocc(X15,X16,X17)
    <=> ( min_precedes(X15,X16,X17)
        & ! [X18] :
            ( ~ min_precedes(X15,X18,X17)
            | ~ min_precedes(X18,X16,X17) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f61,plain,
    ! [X15,X16,X17] :
      ( ( ~ next_subocc(X15,X16,X17)
        | ( min_precedes(X15,X16,X17)
          & ! [X18] :
              ( ~ min_precedes(X15,X18,X17)
              | ~ min_precedes(X18,X16,X17) ) ) )
      & ( next_subocc(X15,X16,X17)
        | ~ min_precedes(X15,X16,X17)
        | ? [X18] :
            ( min_precedes(X15,X18,X17)
            & min_precedes(X18,X16,X17) ) ) ),
    inference(NNF_transformation,[status(esa)],[f60]) ).

fof(f62,plain,
    ( ! [X15,X16,X17] :
        ( ~ next_subocc(X15,X16,X17)
        | ( min_precedes(X15,X16,X17)
          & ! [X18] :
              ( ~ min_precedes(X15,X18,X17)
              | ~ min_precedes(X18,X16,X17) ) ) )
    & ! [X15,X16,X17] :
        ( next_subocc(X15,X16,X17)
        | ~ min_precedes(X15,X16,X17)
        | ? [X18] :
            ( min_precedes(X15,X18,X17)
            & min_precedes(X18,X16,X17) ) ) ),
    inference(miniscoping,[status(esa)],[f61]) ).

fof(f63,plain,
    ( ! [X15,X16,X17] :
        ( ~ next_subocc(X15,X16,X17)
        | ( min_precedes(X15,X16,X17)
          & ! [X18] :
              ( ~ min_precedes(X15,X18,X17)
              | ~ min_precedes(X18,X16,X17) ) ) )
    & ! [X15,X16,X17] :
        ( next_subocc(X15,X16,X17)
        | ~ min_precedes(X15,X16,X17)
        | ( min_precedes(X15,sk0_0(X17,X16,X15),X17)
          & min_precedes(sk0_0(X17,X16,X15),X16,X17) ) ) ),
    inference(skolemization,[status(esa)],[f62]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ~ next_subocc(X0,X1,X2)
      | min_precedes(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f63]) ).

fof(f177,plain,
    ! [X95] :
      ( ~ occurrence_of(X95,tptp0)
      | ? [X96,X97,X98] :
          ( occurrence_of(X96,tptp3)
          & root_occ(X96,X95)
          & occurrence_of(X97,tptp4)
          & next_subocc(X96,X97,tptp0)
          & ( occurrence_of(X98,tptp2)
            | occurrence_of(X98,tptp1) )
          & next_subocc(X97,X98,tptp0)
          & leaf_occ(X98,X95) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f178,plain,
    ! [X95] :
      ( ~ occurrence_of(X95,tptp0)
      | ? [X98] :
          ( ? [X97] :
              ( ? [X96] :
                  ( occurrence_of(X96,tptp3)
                  & root_occ(X96,X95)
                  & occurrence_of(X97,tptp4)
                  & next_subocc(X96,X97,tptp0) )
              & ( occurrence_of(X98,tptp2)
                | occurrence_of(X98,tptp1) )
              & next_subocc(X97,X98,tptp0) )
          & leaf_occ(X98,X95) ) ),
    inference(miniscoping,[status(esa)],[f177]) ).

fof(f179,plain,
    ! [X95] :
      ( ~ occurrence_of(X95,tptp0)
      | ( occurrence_of(sk0_16(X95),tptp3)
        & root_occ(sk0_16(X95),X95)
        & occurrence_of(sk0_15(X95),tptp4)
        & next_subocc(sk0_16(X95),sk0_15(X95),tptp0)
        & ( occurrence_of(sk0_14(X95),tptp2)
          | occurrence_of(sk0_14(X95),tptp1) )
        & next_subocc(sk0_15(X95),sk0_14(X95),tptp0)
        & leaf_occ(sk0_14(X95),X95) ) ),
    inference(skolemization,[status(esa)],[f178]) ).

fof(f180,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | occurrence_of(sk0_16(X0),tptp3) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f181,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | root_occ(sk0_16(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | next_subocc(sk0_16(X0),sk0_15(X0),tptp0) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | occurrence_of(sk0_14(X0),tptp2)
      | occurrence_of(sk0_14(X0),tptp1) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | next_subocc(sk0_15(X0),sk0_14(X0),tptp0) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f186,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | leaf_occ(sk0_14(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f179]) ).

fof(f199,plain,
    ? [X99] :
      ( occurrence_of(X99,tptp0)
      & ! [X100,X101] :
          ( ~ occurrence_of(X100,tptp3)
          | ~ root_occ(X100,X99)
          | ( ~ occurrence_of(X101,tptp2)
            & ~ occurrence_of(X101,tptp1) )
          | ~ min_precedes(X100,X101,tptp0)
          | ~ leaf_occ(X101,X99) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f47]) ).

fof(f200,plain,
    ? [X99] :
      ( occurrence_of(X99,tptp0)
      & ! [X101] :
          ( ! [X100] :
              ( ~ occurrence_of(X100,tptp3)
              | ~ root_occ(X100,X99)
              | ( ~ occurrence_of(X101,tptp2)
                & ~ occurrence_of(X101,tptp1) )
              | ~ min_precedes(X100,X101,tptp0) )
          | ~ leaf_occ(X101,X99) ) ),
    inference(miniscoping,[status(esa)],[f199]) ).

fof(f201,plain,
    ( occurrence_of(sk0_17,tptp0)
    & ! [X101] :
        ( ! [X100] :
            ( ~ occurrence_of(X100,tptp3)
            | ~ root_occ(X100,sk0_17)
            | ( ~ occurrence_of(X101,tptp2)
              & ~ occurrence_of(X101,tptp1) )
            | ~ min_precedes(X100,X101,tptp0) )
        | ~ leaf_occ(X101,sk0_17) ) ),
    inference(skolemization,[status(esa)],[f200]) ).

fof(f202,plain,
    occurrence_of(sk0_17,tptp0),
    inference(cnf_transformation,[status(esa)],[f201]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X0,tptp3)
      | ~ root_occ(X0,sk0_17)
      | ~ occurrence_of(X1,tptp2)
      | ~ min_precedes(X0,X1,tptp0)
      | ~ leaf_occ(X1,sk0_17) ),
    inference(cnf_transformation,[status(esa)],[f201]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X0,tptp3)
      | ~ root_occ(X0,sk0_17)
      | ~ occurrence_of(X1,tptp1)
      | ~ min_precedes(X0,X1,tptp0)
      | ~ leaf_occ(X1,sk0_17) ),
    inference(cnf_transformation,[status(esa)],[f201]) ).

fof(f309,plain,
    ! [X0] :
      ( min_precedes(sk0_15(X0),sk0_14(X0),tptp0)
      | ~ occurrence_of(X0,tptp0) ),
    inference(resolution,[status(thm)],[f64,f185]) ).

fof(f310,plain,
    ! [X0] :
      ( min_precedes(sk0_16(X0),sk0_15(X0),tptp0)
      | ~ occurrence_of(X0,tptp0) ),
    inference(resolution,[status(thm)],[f64,f183]) ).

fof(f328,plain,
    ! [X0,X1] :
      ( ~ occurrence_of(X0,tptp0)
      | ~ min_precedes(X1,sk0_15(X0),tptp0)
      | min_precedes(X1,sk0_14(X0),tptp0) ),
    inference(resolution,[status(thm)],[f309,f50]) ).

fof(f348,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | min_precedes(sk0_16(X0),sk0_14(X0),tptp0)
      | ~ occurrence_of(X0,tptp0) ),
    inference(resolution,[status(thm)],[f328,f310]) ).

fof(f349,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | min_precedes(sk0_16(X0),sk0_14(X0),tptp0) ),
    inference(duplicate_literals_removal,[status(esa)],[f348]) ).

fof(f356,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | ~ occurrence_of(sk0_16(X0),tptp3)
      | ~ root_occ(sk0_16(X0),sk0_17)
      | ~ occurrence_of(sk0_14(X0),tptp1)
      | ~ leaf_occ(sk0_14(X0),sk0_17) ),
    inference(resolution,[status(thm)],[f349,f204]) ).

fof(f357,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | ~ root_occ(sk0_16(X0),sk0_17)
      | ~ occurrence_of(sk0_14(X0),tptp1)
      | ~ leaf_occ(sk0_14(X0),sk0_17) ),
    inference(forward_subsumption_resolution,[status(thm)],[f356,f180]) ).

fof(f358,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | ~ occurrence_of(sk0_16(X0),tptp3)
      | ~ root_occ(sk0_16(X0),sk0_17)
      | ~ occurrence_of(sk0_14(X0),tptp2)
      | ~ leaf_occ(sk0_14(X0),sk0_17) ),
    inference(resolution,[status(thm)],[f349,f203]) ).

fof(f359,plain,
    ! [X0] :
      ( ~ occurrence_of(X0,tptp0)
      | ~ root_occ(sk0_16(X0),sk0_17)
      | ~ occurrence_of(sk0_14(X0),tptp2)
      | ~ leaf_occ(sk0_14(X0),sk0_17) ),
    inference(forward_subsumption_resolution,[status(thm)],[f358,f180]) ).

fof(f378,plain,
    ( spl0_6
  <=> occurrence_of(sk0_17,tptp0) ),
    introduced(split_symbol_definition) ).

fof(f380,plain,
    ( ~ occurrence_of(sk0_17,tptp0)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f378]) ).

fof(f381,plain,
    ( spl0_7
  <=> root_occ(sk0_16(sk0_17),sk0_17) ),
    introduced(split_symbol_definition) ).

fof(f383,plain,
    ( ~ root_occ(sk0_16(sk0_17),sk0_17)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f381]) ).

fof(f384,plain,
    ( spl0_8
  <=> occurrence_of(sk0_14(sk0_17),tptp1) ),
    introduced(split_symbol_definition) ).

fof(f386,plain,
    ( ~ occurrence_of(sk0_14(sk0_17),tptp1)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f384]) ).

fof(f387,plain,
    ( ~ occurrence_of(sk0_17,tptp0)
    | ~ root_occ(sk0_16(sk0_17),sk0_17)
    | ~ occurrence_of(sk0_14(sk0_17),tptp1)
    | ~ occurrence_of(sk0_17,tptp0) ),
    inference(resolution,[status(thm)],[f357,f186]) ).

fof(f388,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f387,f378,f381,f384]) ).

fof(f389,plain,
    ( spl0_9
  <=> occurrence_of(sk0_14(sk0_17),tptp2) ),
    introduced(split_symbol_definition) ).

fof(f392,plain,
    ( ~ occurrence_of(sk0_17,tptp0)
    | ~ root_occ(sk0_16(sk0_17),sk0_17)
    | ~ occurrence_of(sk0_14(sk0_17),tptp2)
    | ~ occurrence_of(sk0_17,tptp0) ),
    inference(resolution,[status(thm)],[f359,f186]) ).

fof(f393,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f392,f378,f381,f389]) ).

fof(f569,plain,
    ( ~ occurrence_of(sk0_17,tptp0)
    | occurrence_of(sk0_14(sk0_17),tptp2)
    | spl0_8 ),
    inference(resolution,[status(thm)],[f386,f184]) ).

fof(f570,plain,
    ( ~ spl0_6
    | spl0_9
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f569,f378,f389,f384]) ).

fof(f571,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f380,f202]) ).

fof(f572,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f571]) ).

fof(f573,plain,
    ( ~ occurrence_of(sk0_17,tptp0)
    | spl0_7 ),
    inference(resolution,[status(thm)],[f383,f181]) ).

fof(f574,plain,
    ( ~ spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f573,f378,f381]) ).

fof(f575,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f388,f393,f570,f572,f574]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : PRO009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n007.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Apr 30 00:06:32 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.17/0.45  % Refutation found
% 0.17/0.45  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.46  % Elapsed time: 0.128473 seconds
% 0.17/0.46  % CPU time: 0.918406 seconds
% 0.17/0.46  % Total memory used: 60.917 MB
% 0.17/0.46  % Net memory used: 60.186 MB
%------------------------------------------------------------------------------