TSTP Solution File: NUM460+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 : Fri May  3 02:49:23 EDT 2024

% Result   : Theorem 69.42s 10.27s
% Output   : CNFRefutation 69.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  136 (  40 unt;   0 def)
%            Number of atoms       :  434 ( 133 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  549 ( 251   ~; 245   |;  36   &)
%                                         (   6 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  142 (   0 sgn  91   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
          | sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
       => ! [X2] :
            ( sdtmndt0(X1,X0) = X2
          <=> ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

fof(f22,axiom,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xn)
    & aNaturalNumber0(xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).

fof(f23,conjecture,
    ( ( sdtlseqdt0(xn,xl)
      & sdtlseqdt0(xm,xn) )
   => sdtlseqdt0(xm,xl) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f24,negated_conjecture,
    ~ ( ( sdtlseqdt0(xn,xl)
        & sdtlseqdt0(xm,xn) )
     => sdtlseqdt0(xm,xl) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f26]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f32]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
        & sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f43]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f51]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f53]) ).

fof(f58,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & sdtlseqdt0(xn,xl)
    & sdtlseqdt0(xm,xn) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f59,plain,
    ( ~ sdtlseqdt0(xm,xl)
    & sdtlseqdt0(xn,xl)
    & sdtlseqdt0(xm,xn) ),
    inference(flattening,[],[f58]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtpldt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f60]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtpldt0(X0,sK0(X0,X1)) = X1
        & aNaturalNumber0(sK0(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
            & aNaturalNumber0(sK0(X0,X1)) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f61,f62]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f64]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f72,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sK0(X0,X1))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sK0(X0,X1)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sdtpldt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f93,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f94,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(X0,X2) = X1
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f98,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f22]) ).

fof(f99,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f22]) ).

fof(f100,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f22]) ).

fof(f101,plain,
    sdtlseqdt0(xm,xn),
    inference(cnf_transformation,[],[f59]) ).

fof(f102,plain,
    sdtlseqdt0(xn,xl),
    inference(cnf_transformation,[],[f59]) ).

fof(f103,plain,
    ~ sdtlseqdt0(xm,xl),
    inference(cnf_transformation,[],[f59]) ).

fof(f104,plain,
    ! [X2,X0] :
      ( sdtlseqdt0(X0,sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f92]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f94]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtmndt0(X1,X0))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f93]) ).

cnf(c_52,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_54,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_55,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_67,plain,
    ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 = X2 ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_73,plain,
    ( ~ aNaturalNumber0(sdtpldt0(X0,X1))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_74,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,sK0(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_75,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sK0(X0,X1)) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_77,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_78,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtmndt0(X1,X0)) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_81,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f100]) ).

cnf(c_82,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_83,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f98]) ).

cnf(c_84,negated_conjecture,
    ~ sdtlseqdt0(xm,xl),
    inference(cnf_transformation,[],[f103]) ).

cnf(c_85,negated_conjecture,
    sdtlseqdt0(xn,xl),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_86,negated_conjecture,
    sdtlseqdt0(xm,xn),
    inference(cnf_transformation,[],[f101]) ).

cnf(c_139,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
    inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).

cnf(c_3656,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | sdtpldt0(xn,sK0(xn,xl)) = xl ),
    inference(superposition,[status(thm)],[c_85,c_74]) ).

cnf(c_3657,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | sdtpldt0(xm,sK0(xm,xn)) = xn ),
    inference(superposition,[status(thm)],[c_86,c_74]) ).

cnf(c_3687,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | sdtpldt0(xn,sdtmndt0(xl,xn)) = xl ),
    inference(superposition,[status(thm)],[c_85,c_77]) ).

cnf(c_3688,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | sdtpldt0(xm,sdtmndt0(xn,xm)) = xn ),
    inference(superposition,[status(thm)],[c_86,c_77]) ).

cnf(c_4730,plain,
    sdtpldt0(xn,sK0(xn,xl)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).

cnf(c_4732,plain,
    sdtpldt0(xm,sK0(xm,xn)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).

cnf(c_4744,plain,
    sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).

cnf(c_4746,plain,
    sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).

cnf(c_5871,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xn)
    | sK0(xn,xl) = X0 ),
    inference(superposition,[status(thm)],[c_4730,c_67]) ).

cnf(c_5872,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | sK0(xm,xn) = X0 ),
    inference(superposition,[status(thm)],[c_4732,c_67]) ).

cnf(c_6125,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xn,xl))
    | sdtpldt0(xn,X0) != xl
    | sK0(xn,xl) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_5871,c_82,c_5871]) ).

cnf(c_6126,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | sK0(xn,xl) = X0 ),
    inference(renaming,[status(thm)],[c_6125]) ).

cnf(c_6132,plain,
    ( ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(superposition,[status(thm)],[c_4744,c_6126]) ).

cnf(c_6317,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | ~ sdtlseqdt0(xn,xl)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(superposition,[status(thm)],[c_75,c_6132]) ).

cnf(c_6318,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xm,xn))
    | sdtpldt0(xm,X0) != xn
    | sK0(xm,xn) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_5872,c_83,c_5872]) ).

cnf(c_6319,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | sK0(xm,xn) = X0 ),
    inference(renaming,[status(thm)],[c_6318]) ).

cnf(c_6327,plain,
    ( ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_4746,c_6319]) ).

cnf(c_6328,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ sdtlseqdt0(xm,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_75,c_6327]) ).

cnf(c_7367,plain,
    sdtpldt0(xn,sK0(xn,xl)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).

cnf(c_7369,plain,
    sdtpldt0(xm,sK0(xm,xn)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).

cnf(c_7371,plain,
    sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).

cnf(c_7373,plain,
    sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).

cnf(c_8296,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xn)
    | sK0(xn,xl) = X0 ),
    inference(superposition,[status(thm)],[c_7367,c_67]) ).

cnf(c_8297,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | sK0(xm,xn) = X0 ),
    inference(superposition,[status(thm)],[c_7369,c_67]) ).

cnf(c_8625,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xn,xl))
    | sdtpldt0(xn,X0) != xl
    | sK0(xn,xl) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_8296,c_82,c_5871]) ).

cnf(c_8626,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | sK0(xn,xl) = X0 ),
    inference(renaming,[status(thm)],[c_8625]) ).

cnf(c_8631,plain,
    ( ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(superposition,[status(thm)],[c_7371,c_8626]) ).

cnf(c_8632,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(global_subsumption_just,[status(thm)],[c_8631,c_82,c_81,c_85,c_6317]) ).

cnf(c_8634,plain,
    ( ~ sdtlseqdt0(xn,xl)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(superposition,[status(thm)],[c_78,c_8632]) ).

cnf(c_8635,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xm,xn))
    | sdtpldt0(xm,X0) != xn
    | sK0(xm,xn) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_8297,c_83,c_5872]) ).

cnf(c_8636,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | sK0(xm,xn) = X0 ),
    inference(renaming,[status(thm)],[c_8635]) ).

cnf(c_8643,plain,
    ( ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_7373,c_8636]) ).

cnf(c_8644,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(global_subsumption_just,[status(thm)],[c_8643,c_83,c_82,c_86,c_6328]) ).

cnf(c_8646,plain,
    ( ~ sdtlseqdt0(xm,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_78,c_8644]) ).

cnf(c_8975,plain,
    sK0(xn,xl) = sdtmndt0(xl,xn),
    inference(global_subsumption_just,[status(thm)],[c_8634,c_82,c_81,c_85,c_8634]) ).

cnf(c_8977,plain,
    ( ~ sdtlseqdt0(xn,xl)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | aNaturalNumber0(sdtmndt0(xl,xn)) ),
    inference(superposition,[status(thm)],[c_8975,c_75]) ).

cnf(c_8981,plain,
    sK0(xm,xn) = sdtmndt0(xn,xm),
    inference(global_subsumption_just,[status(thm)],[c_8646,c_83,c_82,c_86,c_8646]) ).

cnf(c_8983,plain,
    ( ~ sdtlseqdt0(xm,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_8981,c_75]) ).

cnf(c_9334,plain,
    aNaturalNumber0(sdtmndt0(xl,xn)),
    inference(global_subsumption_just,[status(thm)],[c_8977,c_82,c_81,c_85,c_8977]) ).

cnf(c_9342,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
    inference(superposition,[status(thm)],[c_9334,c_54]) ).

cnf(c_9360,plain,
    aNaturalNumber0(sdtmndt0(xn,xm)),
    inference(global_subsumption_just,[status(thm)],[c_8983,c_83,c_82,c_86,c_8983]) ).

cnf(c_10466,plain,
    sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
    inference(superposition,[status(thm)],[c_9360,c_9342]) ).

cnf(c_10799,plain,
    ( ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) ),
    inference(superposition,[status(thm)],[c_10466,c_52]) ).

cnf(c_35012,plain,
    sdtpldt0(xn,sK0(xn,xl)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3656,c_82,c_81,c_3656]) ).

cnf(c_35014,plain,
    sdtpldt0(xm,sK0(xm,xn)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3657,c_83,c_82,c_3657]) ).

cnf(c_35016,plain,
    sdtpldt0(xn,sdtmndt0(xl,xn)) = xl,
    inference(global_subsumption_just,[status(thm)],[c_3687,c_82,c_81,c_3687]) ).

cnf(c_35018,plain,
    sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
    inference(global_subsumption_just,[status(thm)],[c_3688,c_83,c_82,c_3688]) ).

cnf(c_35929,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xn)
    | sK0(xn,xl) = X0 ),
    inference(superposition,[status(thm)],[c_35012,c_67]) ).

cnf(c_35930,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(xm)
    | sK0(xm,xn) = X0 ),
    inference(superposition,[status(thm)],[c_35014,c_67]) ).

cnf(c_36120,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xn,xl))
    | sdtpldt0(xn,X0) != xl
    | sK0(xn,xl) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_35929,c_82,c_5871]) ).

cnf(c_36121,plain,
    ( sdtpldt0(xn,X0) != xl
    | ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(X0)
    | sK0(xn,xl) = X0 ),
    inference(renaming,[status(thm)],[c_36120]) ).

cnf(c_36126,plain,
    ( ~ aNaturalNumber0(sK0(xn,xl))
    | ~ aNaturalNumber0(sdtmndt0(xl,xn))
    | sK0(xn,xl) = sdtmndt0(xl,xn) ),
    inference(superposition,[status(thm)],[c_35016,c_36121]) ).

cnf(c_36127,plain,
    sK0(xn,xl) = sdtmndt0(xl,xn),
    inference(global_subsumption_just,[status(thm)],[c_36126,c_82,c_81,c_85,c_8634]) ).

cnf(c_36129,plain,
    ( ~ sdtlseqdt0(xn,xl)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | aNaturalNumber0(sdtmndt0(xl,xn)) ),
    inference(superposition,[status(thm)],[c_36127,c_75]) ).

cnf(c_36132,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(sK0(xm,xn))
    | sdtpldt0(xm,X0) != xn
    | sK0(xm,xn) = X0 ),
    inference(global_subsumption_just,[status(thm)],[c_35930,c_83,c_5872]) ).

cnf(c_36133,plain,
    ( sdtpldt0(xm,X0) != xn
    | ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(X0)
    | sK0(xm,xn) = X0 ),
    inference(renaming,[status(thm)],[c_36132]) ).

cnf(c_36140,plain,
    ( ~ aNaturalNumber0(sK0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | sK0(xm,xn) = sdtmndt0(xn,xm) ),
    inference(superposition,[status(thm)],[c_35018,c_36133]) ).

cnf(c_36141,plain,
    sK0(xm,xn) = sdtmndt0(xn,xm),
    inference(global_subsumption_just,[status(thm)],[c_36140,c_83,c_82,c_86,c_8646]) ).

cnf(c_36143,plain,
    ( ~ sdtlseqdt0(xm,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm)
    | aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(superposition,[status(thm)],[c_36141,c_75]) ).

cnf(c_36536,plain,
    aNaturalNumber0(sdtmndt0(xl,xn)),
    inference(global_subsumption_just,[status(thm)],[c_36129,c_82,c_81,c_85,c_8977]) ).

cnf(c_36544,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(sdtmndt0(xl,xn),X0) = sdtpldt0(X0,sdtmndt0(xl,xn)) ),
    inference(superposition,[status(thm)],[c_36536,c_54]) ).

cnf(c_36606,plain,
    aNaturalNumber0(sdtmndt0(xn,xm)),
    inference(global_subsumption_just,[status(thm)],[c_36143,c_83,c_82,c_86,c_8983]) ).

cnf(c_36611,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),X1) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),X1)) ),
    inference(superposition,[status(thm)],[c_36606,c_55]) ).

cnf(c_37527,plain,
    sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)),
    inference(superposition,[status(thm)],[c_36606,c_36544]) ).

cnf(c_39489,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(sdtpldt0(X0,sdtmndt0(xn,xm)),sdtmndt0(xl,xn)) = sdtpldt0(X0,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) ),
    inference(superposition,[status(thm)],[c_36536,c_36611]) ).

cnf(c_39996,plain,
    sdtpldt0(sdtpldt0(xm,sdtmndt0(xn,xm)),sdtmndt0(xl,xn)) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))),
    inference(superposition,[status(thm)],[c_83,c_39489]) ).

cnf(c_59045,plain,
    sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
    inference(superposition,[status(thm)],[c_35018,c_39996]) ).

cnf(c_59057,plain,
    sdtpldt0(xm,sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm))) = sdtpldt0(xn,sdtmndt0(xl,xn)),
    inference(superposition,[status(thm)],[c_37527,c_59045]) ).

cnf(c_59062,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
    inference(superposition,[status(thm)],[c_59045,c_139]) ).

cnf(c_59074,plain,
    ( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xl,xn),sdtmndt0(xn,xm)))
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))) ),
    inference(superposition,[status(thm)],[c_59057,c_139]) ).

cnf(c_59086,plain,
    sdtlseqdt0(xm,sdtpldt0(xn,sdtmndt0(xl,xn))),
    inference(global_subsumption_just,[status(thm)],[c_59062,c_83,c_82,c_81,c_86,c_85,c_8977,c_8983,c_10799,c_59074]) ).

cnf(c_59088,plain,
    sdtlseqdt0(xm,xl),
    inference(superposition,[status(thm)],[c_35016,c_59086]) ).

cnf(c_59092,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_59088,c_84]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 19:43:27 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 69.42/10.27  % SZS status Started for theBenchmark.p
% 69.42/10.27  % SZS status Theorem for theBenchmark.p
% 69.42/10.27  
% 69.42/10.27  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 69.42/10.27  
% 69.42/10.27  ------  iProver source info
% 69.42/10.27  
% 69.42/10.27  git: date: 2024-05-02 19:28:25 +0000
% 69.42/10.27  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 69.42/10.27  git: non_committed_changes: false
% 69.42/10.27  
% 69.42/10.27  ------ Parsing...
% 69.42/10.27  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 69.42/10.27  
% 69.42/10.27  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 69.42/10.27  
% 69.42/10.27  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 69.42/10.27  
% 69.42/10.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 69.42/10.27  ------ Proving...
% 69.42/10.27  ------ Problem Properties 
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  clauses                                 38
% 69.42/10.27  conjectures                             3
% 69.42/10.27  EPR                                     11
% 69.42/10.27  Horn                                    35
% 69.42/10.27  unary                                   9
% 69.42/10.27  binary                                  7
% 69.42/10.27  lits                                    113
% 69.42/10.27  lits eq                                 34
% 69.42/10.27  fd_pure                                 0
% 69.42/10.27  fd_pseudo                               0
% 69.42/10.27  fd_cond                                 3
% 69.42/10.27  fd_pseudo_cond                          5
% 69.42/10.27  AC symbols                              0
% 69.42/10.27  
% 69.42/10.27  ------ Input Options Time Limit: Unbounded
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  ------ 
% 69.42/10.27  Current options:
% 69.42/10.27  ------ 
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  ------ Proving...
% 69.42/10.27  
% 69.42/10.27  
% 69.42/10.27  % SZS status Theorem for theBenchmark.p
% 69.42/10.27  
% 69.42/10.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.42/10.27  
% 69.42/10.28  
%------------------------------------------------------------------------------