TSTP Solution File: GEO118+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 : Wed May 31 12:07:50 EDT 2023

% Result   : Theorem 0.20s 0.37s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   5 unt;   0 def)
%            Number of atoms       :  132 (   8 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  168 (  61   ~;  57   |;  44   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-5 aty)
%            Number of variables   :  115 (; 104   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ! [C,P,Q,R] :
      ( between_c(C,P,Q,R)
    <=> ( P != R
        & ? [Cpp] :
            ( part_of(Cpp,C)
            & end_point(P,Cpp)
            & end_point(R,Cpp)
            & inner_point(Q,Cpp) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [O,P,Q,R] :
      ( between_o(O,P,Q,R)
    <=> ( ( ordered_by(O,P,Q)
          & ordered_by(O,Q,R) )
        | ( ordered_by(O,R,Q)
          & ordered_by(O,Q,P) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [P,Q,R,O] :
      ( between_o(O,P,Q,R)
    <=> ? [C] :
          ( ! [P] :
              ( incident_o(P,O)
            <=> incident_c(P,C) )
          & between_c(C,P,Q,R) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,conjecture,
    ! [O,P,Q] :
      ( ordered_by(O,P,Q)
     => ~ ordered_by(O,Q,P) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,negated_conjecture,
    ~ ! [O,P,Q] :
        ( ordered_by(O,P,Q)
       => ~ ordered_by(O,Q,P) ),
    inference(negated_conjecture,[status(cth)],[f28]) ).

fof(f115,plain,
    ! [C,P,Q,R] :
      ( ( ~ between_c(C,P,Q,R)
        | ( P != R
          & ? [Cpp] :
              ( part_of(Cpp,C)
              & end_point(P,Cpp)
              & end_point(R,Cpp)
              & inner_point(Q,Cpp) ) ) )
      & ( between_c(C,P,Q,R)
        | P = R
        | ! [Cpp] :
            ( ~ part_of(Cpp,C)
            | ~ end_point(P,Cpp)
            | ~ end_point(R,Cpp)
            | ~ inner_point(Q,Cpp) ) ) ),
    inference(NNF_transformation,[status(esa)],[f17]) ).

fof(f116,plain,
    ( ! [C,P,Q,R] :
        ( ~ between_c(C,P,Q,R)
        | ( P != R
          & ? [Cpp] :
              ( part_of(Cpp,C)
              & end_point(P,Cpp)
              & end_point(R,Cpp)
              & inner_point(Q,Cpp) ) ) )
    & ! [C,P,Q,R] :
        ( between_c(C,P,Q,R)
        | P = R
        | ! [Cpp] :
            ( ~ part_of(Cpp,C)
            | ~ end_point(P,Cpp)
            | ~ end_point(R,Cpp)
            | ~ inner_point(Q,Cpp) ) ) ),
    inference(miniscoping,[status(esa)],[f115]) ).

fof(f117,plain,
    ( ! [C,P,Q,R] :
        ( ~ between_c(C,P,Q,R)
        | ( P != R
          & part_of(sk0_13(R,Q,P,C),C)
          & end_point(P,sk0_13(R,Q,P,C))
          & end_point(R,sk0_13(R,Q,P,C))
          & inner_point(Q,sk0_13(R,Q,P,C)) ) )
    & ! [C,P,Q,R] :
        ( between_c(C,P,Q,R)
        | P = R
        | ! [Cpp] :
            ( ~ part_of(Cpp,C)
            | ~ end_point(P,Cpp)
            | ~ end_point(R,Cpp)
            | ~ inner_point(Q,Cpp) ) ) ),
    inference(skolemization,[status(esa)],[f116]) ).

fof(f118,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between_c(X0,X1,X2,X3)
      | X1 != X3 ),
    inference(cnf_transformation,[status(esa)],[f117]) ).

fof(f124,plain,
    ! [O,P,Q,R] :
      ( ( ~ between_o(O,P,Q,R)
        | ( ordered_by(O,P,Q)
          & ordered_by(O,Q,R) )
        | ( ordered_by(O,R,Q)
          & ordered_by(O,Q,P) ) )
      & ( between_o(O,P,Q,R)
        | ( ( ~ ordered_by(O,P,Q)
            | ~ ordered_by(O,Q,R) )
          & ( ~ ordered_by(O,R,Q)
            | ~ ordered_by(O,Q,P) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f18]) ).

fof(f125,plain,
    ( ! [O,P,Q,R] :
        ( ~ between_o(O,P,Q,R)
        | ( ordered_by(O,P,Q)
          & ordered_by(O,Q,R) )
        | ( ordered_by(O,R,Q)
          & ordered_by(O,Q,P) ) )
    & ! [O,P,Q,R] :
        ( between_o(O,P,Q,R)
        | ( ( ~ ordered_by(O,P,Q)
            | ~ ordered_by(O,Q,R) )
          & ( ~ ordered_by(O,R,Q)
            | ~ ordered_by(O,Q,P) ) ) ) ),
    inference(miniscoping,[status(esa)],[f124]) ).

fof(f131,plain,
    ! [X0,X1,X2,X3] :
      ( between_o(X0,X1,X2,X3)
      | ~ ordered_by(X0,X3,X2)
      | ~ ordered_by(X0,X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f125]) ).

fof(f159,plain,
    ! [P,Q,R,O] :
      ( ( ~ between_o(O,P,Q,R)
        | ? [C] :
            ( ! [P] :
                ( ( ~ incident_o(P,O)
                  | incident_c(P,C) )
                & ( incident_o(P,O)
                  | ~ incident_c(P,C) ) )
            & between_c(C,P,Q,R) ) )
      & ( between_o(O,P,Q,R)
        | ! [C] :
            ( ? [P] :
                ( ( ~ incident_o(P,O)
                  | ~ incident_c(P,C) )
                & ( incident_o(P,O)
                  | incident_c(P,C) ) )
            | ~ between_c(C,P,Q,R) ) ) ),
    inference(NNF_transformation,[status(esa)],[f23]) ).

fof(f160,plain,
    ( ! [P,Q,R,O] :
        ( ~ between_o(O,P,Q,R)
        | ? [C] :
            ( ! [P] :
                ( ~ incident_o(P,O)
                | incident_c(P,C) )
            & ! [P] :
                ( incident_o(P,O)
                | ~ incident_c(P,C) )
            & between_c(C,P,Q,R) ) )
    & ! [P,Q,R,O] :
        ( between_o(O,P,Q,R)
        | ! [C] :
            ( ? [P] :
                ( ( ~ incident_o(P,O)
                  | ~ incident_c(P,C) )
                & ( incident_o(P,O)
                  | incident_c(P,C) ) )
            | ~ between_c(C,P,Q,R) ) ) ),
    inference(miniscoping,[status(esa)],[f159]) ).

fof(f161,plain,
    ( ! [P,Q,R,O] :
        ( ~ between_o(O,P,Q,R)
        | ( ! [P] :
              ( ~ incident_o(P,O)
              | incident_c(P,sk0_17(O,R,Q,P)) )
          & ! [P] :
              ( incident_o(P,O)
              | ~ incident_c(P,sk0_17(O,R,Q,P)) )
          & between_c(sk0_17(O,R,Q,P),P,Q,R) ) )
    & ! [P,Q,R,O] :
        ( between_o(O,P,Q,R)
        | ! [C] :
            ( ( ( ~ incident_o(sk0_18(C,O,R,Q,P),O)
                | ~ incident_c(sk0_18(C,O,R,Q,P),C) )
              & ( incident_o(sk0_18(C,O,R,Q,P),O)
                | incident_c(sk0_18(C,O,R,Q,P),C) ) )
            | ~ between_c(C,P,Q,R) ) ) ),
    inference(skolemization,[status(esa)],[f160]) ).

fof(f164,plain,
    ! [X0,X1,X2,X3] :
      ( ~ between_o(X0,X1,X2,X3)
      | between_c(sk0_17(X0,X3,X2,X1),X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f161]) ).

fof(f188,plain,
    ? [O,P,Q] :
      ( ordered_by(O,P,Q)
      & ordered_by(O,Q,P) ),
    inference(pre_NNF_transformation,[status(esa)],[f29]) ).

fof(f189,plain,
    ( ordered_by(sk0_24,sk0_25,sk0_26)
    & ordered_by(sk0_24,sk0_26,sk0_25) ),
    inference(skolemization,[status(esa)],[f188]) ).

fof(f190,plain,
    ordered_by(sk0_24,sk0_25,sk0_26),
    inference(cnf_transformation,[status(esa)],[f189]) ).

fof(f191,plain,
    ordered_by(sk0_24,sk0_26,sk0_25),
    inference(cnf_transformation,[status(esa)],[f189]) ).

fof(f196,plain,
    ! [X0,X1,X2] : ~ between_c(X0,X1,X2,X1),
    inference(destructive_equality_resolution,[status(esa)],[f118]) ).

fof(f220,plain,
    ! [X0,X1,X2,X3] :
      ( between_c(sk0_17(X0,X1,X2,X3),X3,X2,X1)
      | ~ ordered_by(X0,X1,X2)
      | ~ ordered_by(X0,X2,X3) ),
    inference(resolution,[status(thm)],[f164,f131]) ).

fof(f232,plain,
    ! [X0,X1,X2] :
      ( ~ ordered_by(X0,X1,X2)
      | ~ ordered_by(X0,X2,X1) ),
    inference(resolution,[status(thm)],[f220,f196]) ).

fof(f248,plain,
    ~ ordered_by(sk0_24,sk0_25,sk0_26),
    inference(resolution,[status(thm)],[f232,f191]) ).

fof(f249,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f248,f190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n001.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 : Tue May 30 12:30:30 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.37  % Refutation found
% 0.20/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38  % Elapsed time: 0.036154 seconds
% 0.20/0.38  % CPU time: 0.126159 seconds
% 0.20/0.38  % Memory used: 12.937 MB
%------------------------------------------------------------------------------