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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 01:07:53 PM UTC 2026

% Result   : Theorem 25.64s 3.67s
% Output   : CNFRefutation 14.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  104 (  58 unt;   0 def)
%            Number of atoms       :  192 (  10 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  152 (  64   ~;  61   |;  18   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   10 (   8 usr;   8 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :  194 ( 182   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ( modus_ponens
  <=> ! [X,Y] :
        ( ( is_a_theorem(implies(X,Y))
          & is_a_theorem(X) )
       => is_a_theorem(Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ( and_2
  <=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ( kn1
  <=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ( kn2
  <=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ( kn3
  <=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    ( op_or
   => ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    kn1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f37,axiom,
    kn2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f38,axiom,
    kn3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,conjecture,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,negated_conjecture,
    ~ and_2,
    inference(negated_conjecture,[status(cth)],[f43]) ).

fof(f45,plain,
    ( modus_ponens
  <=> ! [X,Y] :
        ( is_a_theorem(Y)
        | ~ is_a_theorem(implies(X,Y))
        | ~ is_a_theorem(X) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f1]) ).

fof(f46,plain,
    ( ( ? [X,Y] :
          ( ~ is_a_theorem(Y)
          & is_a_theorem(implies(X,Y))
          & is_a_theorem(X) )
      | modus_ponens )
    & ( ! [X,Y] :
          ( is_a_theorem(Y)
          | ~ is_a_theorem(implies(X,Y))
          | ~ is_a_theorem(X) )
      | ~ modus_ponens ) ),
    inference(NNF_transformation,[status(thm)],[f45]) ).

fof(f47,plain,
    ( ( ? [Y] :
          ( ~ is_a_theorem(Y)
          & ? [X] :
              ( is_a_theorem(implies(X,Y))
              & is_a_theorem(X) ) )
      | modus_ponens )
    & ( ! [Y] :
          ( is_a_theorem(Y)
          | ! [X] :
              ( ~ is_a_theorem(implies(X,Y))
              | ~ is_a_theorem(X) ) )
      | ~ modus_ponens ) ),
    inference(miniscoping,[status(thm)],[f46]) ).

fof(f48,plain,
    ( ( ( ~ is_a_theorem(sK0_skl)
        & is_a_theorem(implies(sK1_skl,sK0_skl))
        & is_a_theorem(sK1_skl) )
      | modus_ponens )
    & ( ! [Y] :
          ( is_a_theorem(Y)
          | ! [X] :
              ( ~ is_a_theorem(implies(X,Y))
              | ~ is_a_theorem(X) ) )
      | ~ modus_ponens ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[status(thm)],[f48]) ).

fof(f79,plain,
    ( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
      | and_2 )
    & ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
      | ~ and_2 ) ),
    inference(NNF_transformation,[status(thm)],[f8]) ).

fof(f80,plain,
    ( ( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
      | and_2 )
    & ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
      | ~ and_2 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f79]) ).

fof(f82,plain,
    ( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
    | and_2 ),
    inference(cnf_transformation,[status(thm)],[f80]) ).

fof(f111,plain,
    ( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
      | kn1 )
    & ( ! [P] : is_a_theorem(implies(P,and(P,P)))
      | ~ kn1 ) ),
    inference(NNF_transformation,[status(thm)],[f16]) ).

fof(f112,plain,
    ( ( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
      | kn1 )
    & ( ! [P] : is_a_theorem(implies(P,and(P,P)))
      | ~ kn1 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111]) ).

fof(f113,plain,
    ! [X0] :
      ( is_a_theorem(implies(X0,and(X0,X0)))
      | ~ kn1 ),
    inference(cnf_transformation,[status(thm)],[f112]) ).

fof(f115,plain,
    ( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
      | kn2 )
    & ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
      | ~ kn2 ) ),
    inference(NNF_transformation,[status(thm)],[f17]) ).

fof(f116,plain,
    ( ( ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl))
      | kn2 )
    & ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
      | ~ kn2 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ kn2 ),
    inference(cnf_transformation,[status(thm)],[f116]) ).

fof(f119,plain,
    ( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
      | kn3 )
    & ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
      | ~ kn3 ) ),
    inference(NNF_transformation,[status(thm)],[f18]) ).

fof(f120,plain,
    ( ( ~ is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl)))))
      | kn3 )
    & ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
      | ~ kn3 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(P,sK35_skl),skolemize(Q,sK36_skl),skolemize(R,sK37_skl)],[f119]) ).

fof(f121,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(cnf_transformation,[status(thm)],[f120]) ).

fof(f155,plain,
    ( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
    | ~ op_or ),
    inference(pre_NNF_transformation,[status(thm)],[f27]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[status(thm)],[f155]) ).

fof(f159,plain,
    ( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
    | ~ op_implies_and ),
    inference(pre_NNF_transformation,[status(thm)],[f29]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[status(thm)],[f159]) ).

fof(f165,plain,
    op_or,
    inference(cnf_transformation,[status(thm)],[f32]) ).

fof(f166,plain,
    op_implies_and,
    inference(cnf_transformation,[status(thm)],[f33]) ).

fof(f168,plain,
    modus_ponens,
    inference(cnf_transformation,[status(thm)],[f35]) ).

fof(f169,plain,
    kn1,
    inference(cnf_transformation,[status(thm)],[f36]) ).

fof(f170,plain,
    kn2,
    inference(cnf_transformation,[status(thm)],[f37]) ).

fof(f171,plain,
    kn3,
    inference(cnf_transformation,[status(thm)],[f38]) ).

fof(f176,plain,
    ~ and_2,
    inference(cnf_transformation,[status(thm)],[f44]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f49,f168]) ).

fof(f179,plain,
    ! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
    inference(forward_subsumption_resolution,[status(thm)],[f113,f169]) ).

fof(f182,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f117,f170]) ).

fof(f186,plain,
    ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)),
    inference(forward_subsumption_resolution,[status(thm)],[f82,f176]) ).

fof(f187,plain,
    ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
    inference(forward_subsumption_resolution,[status(thm)],[f160,f166]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( or(X0,X1) = implies(not(X0),X1)
      | ~ op_or ),
    inference(forward_demodulation,[status(thm)],[f187,f156]) ).

fof(f196,plain,
    ! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
    inference(forward_subsumption_resolution,[status(thm)],[f189,f165]) ).

fof(f197,plain,
    ! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
    inference(paramodulation,[status(thm)],[f187,f196]) ).

fof(f198,plain,
    ! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
    inference(paramodulation,[status(thm)],[f196,f179]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(or(X0,X1))
      | ~ is_a_theorem(not(X0)) ),
    inference(paramodulation,[status(thm)],[f196,f177]) ).

fof(f402,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(forward_demodulation,[status(thm)],[f196,f121]) ).

fof(f403,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
    inference(forward_subsumption_resolution,[status(thm)],[f402,f171]) ).

fof(f404,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[f403,f177]) ).

fof(f406,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))),
    inference(paramodulation,[status(thm)],[f196,f403]) ).

fof(f417,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
    inference(forward_demodulation,[status(thm)],[f187,f406]) ).

fof(f422,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[f417,f177]) ).

fof(f425,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))),
    inference(paramodulation,[status(thm)],[f197,f417]) ).

fof(f432,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
    inference(forward_demodulation,[status(thm)],[f196,f425]) ).

fof(f438,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[f432,f177]) ).

fof(f448,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))),
    inference(resolution,[status(thm)],[f438,f198]) ).

fof(f471,plain,
    ! [X0,X1] :
      ( is_a_theorem(or(X1,X0))
      | ~ is_a_theorem(implies(and(not(X0),not(X0)),X1)) ),
    inference(resolution,[status(thm)],[f448,f177]) ).

fof(f487,plain,
    ! [X0] : is_a_theorem(or(not(X0),X0)),
    inference(resolution,[status(thm)],[f471,f182]) ).

fof(f499,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
    inference(resolution,[status(thm)],[f487,f438]) ).

fof(f501,plain,
    ! [X0] :
      ( is_a_theorem(X0)
      | ~ is_a_theorem(not(not(X0))) ),
    inference(resolution,[status(thm)],[f487,f199]) ).

fof(f507,plain,
    ! [X0,X1] :
      ( is_a_theorem(or(X1,not(X0)))
      | ~ is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[f499,f177]) ).

fof(f551,plain,
    ! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
    inference(resolution,[status(thm)],[f507,f182]) ).

fof(f552,plain,
    ! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
    inference(resolution,[status(thm)],[f507,f179]) ).

fof(f556,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X0))),
    inference(resolution,[status(thm)],[f551,f438]) ).

fof(f562,plain,
    ! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
    inference(paramodulation,[status(thm)],[f187,f551]) ).

fof(f566,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X0))),
    inference(forward_demodulation,[status(thm)],[f196,f556]) ).

fof(f568,plain,
    ! [X0,X1,X2] : is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))),
    inference(resolution,[status(thm)],[f562,f422]) ).

fof(f576,plain,
    ! [X0] :
      ( is_a_theorem(not(X0))
      | ~ is_a_theorem(not(and(X0,X0))) ),
    inference(resolution,[status(thm)],[f552,f199]) ).

fof(f603,plain,
    ! [X0] :
      ( is_a_theorem(not(not(X0)))
      | ~ is_a_theorem(implies(not(X0),X0)) ),
    inference(paramodulation,[status(thm)],[f187,f576]) ).

fof(f605,plain,
    ! [X0] :
      ( is_a_theorem(not(not(X0)))
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(forward_demodulation,[status(thm)],[f196,f603]) ).

fof(f676,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(or(X2,X0))
      | ~ is_a_theorem(or(and(X0,X1),X2)) ),
    inference(resolution,[status(thm)],[f566,f177]) ).

fof(f758,plain,
    ! [X0,X1,X2] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
    inference(resolution,[status(thm)],[f676,f568]) ).

fof(f785,plain,
    ! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
    inference(resolution,[status(thm)],[f758,f605]) ).

fof(f795,plain,
    ! [X0] : is_a_theorem(implies(X0,X0)),
    inference(resolution,[status(thm)],[f785,f501]) ).

fof(f803,plain,
    ! [X0] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
    inference(resolution,[status(thm)],[f795,f471]) ).

fof(f804,plain,
    ! [X0,X1] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
    inference(resolution,[status(thm)],[f795,f404]) ).

fof(f805,plain,
    ! [X0] : is_a_theorem(or(X0,not(X0))),
    inference(resolution,[status(thm)],[f795,f507]) ).

fof(f810,plain,
    ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
    inference(forward_demodulation,[status(thm)],[f197,f803]) ).

fof(f811,plain,
    ! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
    inference(forward_demodulation,[status(thm)],[f196,f810]) ).

fof(f818,plain,
    ! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))),
    inference(resolution,[status(thm)],[f805,f438]) ).

fof(f825,plain,
    ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f196,f818]) ).

fof(f839,plain,
    ! [X0] :
      ( is_a_theorem(X0)
      | ~ is_a_theorem(or(X0,X0)) ),
    inference(resolution,[status(thm)],[f811,f177]) ).

fof(f1042,plain,
    ! [X0,X1] :
      ( is_a_theorem(or(X1,X0))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[f825,f177]) ).

fof(f1491,plain,
    ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X1)),
    inference(resolution,[status(thm)],[f804,f676]) ).

fof(f1526,plain,
    ! [X0,X1] : is_a_theorem(or(X0,not(and(X1,X0)))),
    inference(resolution,[status(thm)],[f1491,f1042]) ).

fof(f1532,plain,
    ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1))),
    inference(paramodulation,[status(thm)],[f187,f1491]) ).

fof(f1541,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X1))),
    inference(resolution,[status(thm)],[f1526,f438]) ).

fof(f1554,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X1))),
    inference(forward_demodulation,[status(thm)],[f196,f1541]) ).

fof(f1556,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(implies(not(X0),X1),or(X1,implies(X2,X0)))),
    inference(resolution,[status(thm)],[f1532,f438]) ).

fof(f1564,plain,
    ! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(X1,implies(X2,X0)))),
    inference(forward_demodulation,[status(thm)],[f196,f1556]) ).

fof(f5124,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(or(X2,X1))
      | ~ is_a_theorem(or(and(X0,X1),X2)) ),
    inference(resolution,[status(thm)],[f1554,f177]) ).

fof(f5138,plain,
    ! [X0,X1,X2] :
      ( is_a_theorem(or(X1,implies(X2,X0)))
      | ~ is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[f1564,f177]) ).

fof(f16114,plain,
    ! [X0,X1,X2] : is_a_theorem(or(implies(and(X0,X1),X2),X1)),
    inference(resolution,[status(thm)],[f5124,f562]) ).

fof(f16480,plain,
    ! [X0,X1,X2] : is_a_theorem(or(X0,implies(and(X1,X0),X2))),
    inference(resolution,[status(thm)],[f16114,f1042]) ).

fof(f18036,plain,
    ! [X0,X1,X2,X3] : is_a_theorem(or(implies(and(X0,X1),X2),implies(X3,X1))),
    inference(resolution,[status(thm)],[f5138,f16480]) ).

fof(f41384,plain,
    ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
    inference(resolution,[status(thm)],[f18036,f839]) ).

fof(f41419,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f186,f41384]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n005.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Mon Sep 21 00:35:48 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.38  % Drodi V4.1.1
% 25.64/3.67  % Refutation found
% 25.64/3.67  % SZS status Theorem for theBenchmark: Theorem is valid
% 25.64/3.67  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.04/3.79  % Elapsed time: 3.408482 seconds
% 14.04/3.79  % CPU time: 26.474524 seconds
% 14.04/3.79  % Total memory used: 503.525 MB
% 14.04/3.79  % Net memory used: 481.553 MB
%------------------------------------------------------------------------------