TSTP Solution File: COM020+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 Aug 30 18:42:07 EDT 2023

% Result   : Theorem 7.31s 1.65s
% Output   : CNFRefutation 7.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  113 (  26 unt;   0 def)
%            Number of atoms       :  854 (  66 equ)
%            Maximal formula atoms :   33 (   7 avg)
%            Number of connectives : 1028 ( 287   ~; 332   |; 387   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;  12 con; 0-2 aty)
%            Number of variables   :  253 (   0 sgn; 139   !;  71   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0,X1] :
      ( ( aRewritingSystem0(X1)
        & aElement0(X0) )
     => ! [X2] :
          ( aReductOfIn0(X2,X0,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( ( aElement0(X3)
        & aElement0(X2)
        & aRewritingSystem0(X1)
        & aElement0(X0) )
     => ( ( sdtmndtasgtdt0(X2,X1,X3)
          & sdtmndtasgtdt0(X0,X1,X2) )
       => sdtmndtasgtdt0(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).

fof(f15,axiom,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).

fof(f16,axiom,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X0,X1,X2] :
        ( ( aReductOfIn0(X2,X0,xR)
          & aReductOfIn0(X1,X0,xR)
          & aElement0(X2)
          & aElement0(X1)
          & aElement0(X0) )
       => ? [X3] :
            ( sdtmndtasgtdt0(X2,xR,X3)
            & ( ( sdtmndtplgtdt0(X2,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X2,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X2,xR) ) )
              | X2 = X3 )
            & sdtmndtasgtdt0(X1,xR,X3)
            & ( ( sdtmndtplgtdt0(X1,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X1,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X1,xR) ) )
              | X1 = X3 )
            & aElement0(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).

fof(f17,axiom,
    ( aElement0(xc)
    & aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).

fof(f18,axiom,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,xR,X2)
          | sdtmndtplgtdt0(X0,xR,X2)
          | ? [X3] :
              ( sdtmndtplgtdt0(X3,xR,X2)
              & aReductOfIn0(X3,X0,xR)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,xR)
          | X0 = X2 )
        & ( sdtmndtasgtdt0(X0,xR,X1)
          | sdtmndtplgtdt0(X0,xR,X1)
          | ? [X3] :
              ( sdtmndtplgtdt0(X3,xR,X1)
              & aReductOfIn0(X3,X0,xR)
              & aElement0(X3) )
          | aReductOfIn0(X1,X0,xR)
          | X0 = X1 )
        & aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => ( iLess0(X0,xa)
       => ? [X3] :
            ( sdtmndtasgtdt0(X2,xR,X3)
            & ( ( sdtmndtplgtdt0(X2,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X2,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X2,xR) ) )
              | X2 = X3 )
            & sdtmndtasgtdt0(X1,xR,X3)
            & ( ( sdtmndtplgtdt0(X1,xR,X3)
                & ( ? [X4] :
                      ( sdtmndtplgtdt0(X4,xR,X3)
                      & aReductOfIn0(X4,X1,xR)
                      & aElement0(X4) )
                  | aReductOfIn0(X3,X1,xR) ) )
              | X1 = X3 )
            & aElement0(X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).

fof(f20,axiom,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xb)
              & aReductOfIn0(X0,xu,xR)
              & aElement0(X0) )
          | aReductOfIn0(xb,xu,xR) ) )
      | xb = xu )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).

fof(f22,axiom,
    ( sdtmndtasgtdt0(xv,xR,xw)
    & ( ( sdtmndtplgtdt0(xv,xR,xw)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xw)
              & aReductOfIn0(X0,xv,xR)
              & aElement0(X0) )
          | aReductOfIn0(xw,xv,xR) ) )
      | xv = xw )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( ( sdtmndtplgtdt0(xu,xR,xw)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xw)
              & aReductOfIn0(X0,xu,xR)
              & aElement0(X0) )
          | aReductOfIn0(xw,xu,xR) ) )
      | xu = xw )
    & aElement0(xw) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).

fof(f23,axiom,
    ( aNormalFormOfIn0(xd,xw,xR)
    & ~ ? [X0] : aReductOfIn0(X0,xd,xR)
    & sdtmndtasgtdt0(xw,xR,xd)
    & ( ( sdtmndtplgtdt0(xw,xR,xd)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xd)
              & aReductOfIn0(X0,xw,xR)
              & aElement0(X0) )
          | aReductOfIn0(xd,xw,xR) ) )
      | xw = xd )
    & aElement0(xd) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).

fof(f24,conjecture,
    ? [X0] :
      ( ( sdtmndtasgtdt0(xd,xR,X0)
        | sdtmndtplgtdt0(xd,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xd,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xd,xR)
        | xd = X0 )
      & ( sdtmndtasgtdt0(xb,xR,X0)
        | sdtmndtplgtdt0(xb,xR,X0)
        | ? [X1] :
            ( sdtmndtplgtdt0(X1,xR,X0)
            & aReductOfIn0(X1,xb,xR)
            & aElement0(X1) )
        | aReductOfIn0(X0,xb,xR)
        | xb = X0 )
      & aElement0(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f25,negated_conjecture,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xd,xR,X0)
          | sdtmndtplgtdt0(xd,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xd,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xd,xR)
          | xd = X0 )
        & ( sdtmndtasgtdt0(xb,xR,X0)
          | sdtmndtplgtdt0(xb,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xb,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xb,xR)
          | xb = X0 )
        & aElement0(X0) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f30,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( ( aElement0(X1)
          & aElement0(X0) )
       => ( ( sdtmndtplgtdt0(X0,xR,X1)
            | ? [X2] :
                ( sdtmndtplgtdt0(X2,xR,X1)
                & aReductOfIn0(X2,X0,xR)
                & aElement0(X2) )
            | aReductOfIn0(X1,X0,xR) )
         => iLess0(X1,X0) ) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ( aReductOfIn0(X5,X3,xR)
          & aReductOfIn0(X4,X3,xR)
          & aElement0(X5)
          & aElement0(X4)
          & aElement0(X3) )
       => ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) ) ) ),
    inference(rectify,[],[f16]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( ( sdtmndtasgtdt0(X0,xR,X2)
          | sdtmndtplgtdt0(X0,xR,X2)
          | ? [X3] :
              ( sdtmndtplgtdt0(X3,xR,X2)
              & aReductOfIn0(X3,X0,xR)
              & aElement0(X3) )
          | aReductOfIn0(X2,X0,xR)
          | X0 = X2 )
        & ( sdtmndtasgtdt0(X0,xR,X1)
          | sdtmndtplgtdt0(X0,xR,X1)
          | ? [X4] :
              ( sdtmndtplgtdt0(X4,xR,X1)
              & aReductOfIn0(X4,X0,xR)
              & aElement0(X4) )
          | aReductOfIn0(X1,X0,xR)
          | X0 = X1 )
        & aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => ( iLess0(X0,xa)
       => ? [X5] :
            ( sdtmndtasgtdt0(X2,xR,X5)
            & ( ( sdtmndtplgtdt0(X2,xR,X5)
                & ( ? [X6] :
                      ( sdtmndtplgtdt0(X6,xR,X5)
                      & aReductOfIn0(X6,X2,xR)
                      & aElement0(X6) )
                  | aReductOfIn0(X5,X2,xR) ) )
              | X2 = X5 )
            & sdtmndtasgtdt0(X1,xR,X5)
            & ( ( sdtmndtplgtdt0(X1,xR,X5)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X5)
                      & aReductOfIn0(X7,X1,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X5,X1,xR) ) )
              | X1 = X5 )
            & aElement0(X5) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f33,plain,
    ( sdtmndtasgtdt0(xv,xR,xw)
    & ( ( sdtmndtplgtdt0(xv,xR,xw)
        & ( ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xw)
              & aReductOfIn0(X0,xv,xR)
              & aElement0(X0) )
          | aReductOfIn0(xw,xv,xR) ) )
      | xv = xw )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( ( sdtmndtplgtdt0(xu,xR,xw)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xw)
              & aReductOfIn0(X1,xu,xR)
              & aElement0(X1) )
          | aReductOfIn0(xw,xu,xR) ) )
      | xu = xw )
    & aElement0(xw) ),
    inference(rectify,[],[f22]) ).

fof(f34,plain,
    ( aNormalFormOfIn0(xd,xw,xR)
    & ~ ? [X0] : aReductOfIn0(X0,xd,xR)
    & sdtmndtasgtdt0(xw,xR,xd)
    & ( ( sdtmndtplgtdt0(xw,xR,xd)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xd)
              & aReductOfIn0(X1,xw,xR)
              & aElement0(X1) )
          | aReductOfIn0(xd,xw,xR) ) )
      | xw = xd )
    & aElement0(xd) ),
    inference(rectify,[],[f23]) ).

fof(f35,plain,
    ~ ? [X0] :
        ( ( sdtmndtasgtdt0(xd,xR,X0)
          | sdtmndtplgtdt0(xd,xR,X0)
          | ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,X0)
              & aReductOfIn0(X1,xd,xR)
              & aElement0(X1) )
          | aReductOfIn0(X0,xd,xR)
          | xd = X0 )
        & ( sdtmndtasgtdt0(xb,xR,X0)
          | sdtmndtplgtdt0(xb,xR,X0)
          | ? [X2] :
              ( sdtmndtplgtdt0(X2,xR,X0)
              & aReductOfIn0(X2,xb,xR)
              & aElement0(X2) )
          | aReductOfIn0(X0,xb,xR)
          | xb = X0 )
        & aElement0(X0) ),
    inference(rectify,[],[f25]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aElement0(X2)
          | ~ aReductOfIn0(X2,X0,X1) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( aElement0(X2)
          | ~ aReductOfIn0(X2,X0,X1) )
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f36]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtasgtdt0(X0,X1,X3)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] :
      ( sdtmndtasgtdt0(X0,X1,X3)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f44]) ).

fof(f56,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f57,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & ( ( sdtmndtplgtdt0(X4,xR,X6)
                & ( ? [X8] :
                      ( sdtmndtplgtdt0(X8,xR,X6)
                      & aReductOfIn0(X8,X4,xR)
                      & aElement0(X8) )
                  | aReductOfIn0(X6,X4,xR) ) )
              | X4 = X6 )
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(flattening,[],[f56]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( sdtmndtasgtdt0(X2,xR,X5)
          & ( ( sdtmndtplgtdt0(X2,xR,X5)
              & ( ? [X6] :
                    ( sdtmndtplgtdt0(X6,xR,X5)
                    & aReductOfIn0(X6,X2,xR)
                    & aElement0(X6) )
                | aReductOfIn0(X5,X2,xR) ) )
            | X2 = X5 )
          & sdtmndtasgtdt0(X1,xR,X5)
          & ( ( sdtmndtplgtdt0(X1,xR,X5)
              & ( ? [X7] :
                    ( sdtmndtplgtdt0(X7,xR,X5)
                    & aReductOfIn0(X7,X1,xR)
                    & aElement0(X7) )
                | aReductOfIn0(X5,X1,xR) ) )
            | X1 = X5 )
          & aElement0(X5) )
      | ~ iLess0(X0,xa)
      | ( ~ sdtmndtasgtdt0(X0,xR,X2)
        & ~ sdtmndtplgtdt0(X0,xR,X2)
        & ! [X3] :
            ( ~ sdtmndtplgtdt0(X3,xR,X2)
            | ~ aReductOfIn0(X3,X0,xR)
            | ~ aElement0(X3) )
        & ~ aReductOfIn0(X2,X0,xR)
        & X0 != X2 )
      | ( ~ sdtmndtasgtdt0(X0,xR,X1)
        & ~ sdtmndtplgtdt0(X0,xR,X1)
        & ! [X4] :
            ( ~ sdtmndtplgtdt0(X4,xR,X1)
            | ~ aReductOfIn0(X4,X0,xR)
            | ~ aElement0(X4) )
        & ~ aReductOfIn0(X1,X0,xR)
        & X0 != X1 )
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( sdtmndtasgtdt0(X2,xR,X5)
          & ( ( sdtmndtplgtdt0(X2,xR,X5)
              & ( ? [X6] :
                    ( sdtmndtplgtdt0(X6,xR,X5)
                    & aReductOfIn0(X6,X2,xR)
                    & aElement0(X6) )
                | aReductOfIn0(X5,X2,xR) ) )
            | X2 = X5 )
          & sdtmndtasgtdt0(X1,xR,X5)
          & ( ( sdtmndtplgtdt0(X1,xR,X5)
              & ( ? [X7] :
                    ( sdtmndtplgtdt0(X7,xR,X5)
                    & aReductOfIn0(X7,X1,xR)
                    & aElement0(X7) )
                | aReductOfIn0(X5,X1,xR) ) )
            | X1 = X5 )
          & aElement0(X5) )
      | ~ iLess0(X0,xa)
      | ( ~ sdtmndtasgtdt0(X0,xR,X2)
        & ~ sdtmndtplgtdt0(X0,xR,X2)
        & ! [X3] :
            ( ~ sdtmndtplgtdt0(X3,xR,X2)
            | ~ aReductOfIn0(X3,X0,xR)
            | ~ aElement0(X3) )
        & ~ aReductOfIn0(X2,X0,xR)
        & X0 != X2 )
      | ( ~ sdtmndtasgtdt0(X0,xR,X1)
        & ~ sdtmndtplgtdt0(X0,xR,X1)
        & ! [X4] :
            ( ~ sdtmndtplgtdt0(X4,xR,X1)
            | ~ aReductOfIn0(X4,X0,xR)
            | ~ aElement0(X4) )
        & ~ aReductOfIn0(X1,X0,xR)
        & X0 != X1 )
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f58]) ).

fof(f60,plain,
    ( aNormalFormOfIn0(xd,xw,xR)
    & ! [X0] : ~ aReductOfIn0(X0,xd,xR)
    & sdtmndtasgtdt0(xw,xR,xd)
    & ( ( sdtmndtplgtdt0(xw,xR,xd)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xd)
              & aReductOfIn0(X1,xw,xR)
              & aElement0(X1) )
          | aReductOfIn0(xd,xw,xR) ) )
      | xw = xd )
    & aElement0(xd) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f61,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xd,xR,X0)
        & ~ sdtmndtplgtdt0(xd,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xd,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xd,xR)
        & xd != X0 )
      | ( ~ sdtmndtasgtdt0(xb,xR,X0)
        & ~ sdtmndtplgtdt0(xb,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xb,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xb,xR)
        & xb != X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f68,plain,
    ! [X6,X4] :
      ( ( sdtmndtplgtdt0(X4,xR,X6)
        & ( ? [X8] :
              ( sdtmndtplgtdt0(X8,xR,X6)
              & aReductOfIn0(X8,X4,xR)
              & aElement0(X8) )
          | aReductOfIn0(X6,X4,xR) ) )
      | X4 = X6
      | ~ sP4(X6,X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f69,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ? [X6] :
            ( sdtmndtasgtdt0(X5,xR,X6)
            & ( ( sdtmndtplgtdt0(X5,xR,X6)
                & ( ? [X7] :
                      ( sdtmndtplgtdt0(X7,xR,X6)
                      & aReductOfIn0(X7,X5,xR)
                      & aElement0(X7) )
                  | aReductOfIn0(X6,X5,xR) ) )
              | X5 = X6 )
            & sdtmndtasgtdt0(X4,xR,X6)
            & sP4(X6,X4)
            & aElement0(X6) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(definition_folding,[],[f57,f68]) ).

fof(f70,plain,
    ! [X5,X1] :
      ( ( sdtmndtplgtdt0(X1,xR,X5)
        & ( ? [X7] :
              ( sdtmndtplgtdt0(X7,xR,X5)
              & aReductOfIn0(X7,X1,xR)
              & aElement0(X7) )
          | aReductOfIn0(X5,X1,xR) ) )
      | X1 = X5
      | ~ sP5(X5,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f71,plain,
    ! [X2,X1] :
      ( ? [X5] :
          ( sdtmndtasgtdt0(X2,xR,X5)
          & ( ( sdtmndtplgtdt0(X2,xR,X5)
              & ( ? [X6] :
                    ( sdtmndtplgtdt0(X6,xR,X5)
                    & aReductOfIn0(X6,X2,xR)
                    & aElement0(X6) )
                | aReductOfIn0(X5,X2,xR) ) )
            | X2 = X5 )
          & sdtmndtasgtdt0(X1,xR,X5)
          & sP5(X5,X1)
          & aElement0(X5) )
      | ~ sP6(X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f72,plain,
    ! [X1,X0] :
      ( ( ~ sdtmndtasgtdt0(X0,xR,X1)
        & ~ sdtmndtplgtdt0(X0,xR,X1)
        & ! [X4] :
            ( ~ sdtmndtplgtdt0(X4,xR,X1)
            | ~ aReductOfIn0(X4,X0,xR)
            | ~ aElement0(X4) )
        & ~ aReductOfIn0(X1,X0,xR)
        & X0 != X1 )
      | ~ sP7(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( sP6(X2,X1)
      | ~ iLess0(X0,xa)
      | ( ~ sdtmndtasgtdt0(X0,xR,X2)
        & ~ sdtmndtplgtdt0(X0,xR,X2)
        & ! [X3] :
            ( ~ sdtmndtplgtdt0(X3,xR,X2)
            | ~ aReductOfIn0(X3,X0,xR)
            | ~ aElement0(X3) )
        & ~ aReductOfIn0(X2,X0,xR)
        & X0 != X2 )
      | sP7(X1,X0)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(definition_folding,[],[f59,f72,f71,f70]) ).

fof(f74,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xb,xR,X0)
        & ~ sdtmndtplgtdt0(xb,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xb,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xb,xR)
        & xb != X0 )
      | ~ sP8(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f75,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xd,xR,X0)
        & ~ sdtmndtplgtdt0(xd,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xd,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xd,xR)
        & xd != X0 )
      | sP8(X0)
      | ~ aElement0(X0) ),
    inference(definition_folding,[],[f61,f74]) ).

fof(f110,plain,
    ! [X4,X5] :
      ( ? [X6] :
          ( sdtmndtasgtdt0(X5,xR,X6)
          & ( ( sdtmndtplgtdt0(X5,xR,X6)
              & ( ? [X7] :
                    ( sdtmndtplgtdt0(X7,xR,X6)
                    & aReductOfIn0(X7,X5,xR)
                    & aElement0(X7) )
                | aReductOfIn0(X6,X5,xR) ) )
            | X5 = X6 )
          & sdtmndtasgtdt0(X4,xR,X6)
          & sP4(X6,X4)
          & aElement0(X6) )
     => ( sdtmndtasgtdt0(X5,xR,sK23(X4,X5))
        & ( ( sdtmndtplgtdt0(X5,xR,sK23(X4,X5))
            & ( ? [X7] :
                  ( sdtmndtplgtdt0(X7,xR,sK23(X4,X5))
                  & aReductOfIn0(X7,X5,xR)
                  & aElement0(X7) )
              | aReductOfIn0(sK23(X4,X5),X5,xR) ) )
          | sK23(X4,X5) = X5 )
        & sdtmndtasgtdt0(X4,xR,sK23(X4,X5))
        & sP4(sK23(X4,X5),X4)
        & aElement0(sK23(X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X4,X5] :
      ( ? [X7] :
          ( sdtmndtplgtdt0(X7,xR,sK23(X4,X5))
          & aReductOfIn0(X7,X5,xR)
          & aElement0(X7) )
     => ( sdtmndtplgtdt0(sK24(X4,X5),xR,sK23(X4,X5))
        & aReductOfIn0(sK24(X4,X5),X5,xR)
        & aElement0(sK24(X4,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ( isTerminating0(xR)
    & ! [X0,X1] :
        ( iLess0(X1,X0)
        | ( ~ sdtmndtplgtdt0(X0,xR,X1)
          & ! [X2] :
              ( ~ sdtmndtplgtdt0(X2,xR,X1)
              | ~ aReductOfIn0(X2,X0,xR)
              | ~ aElement0(X2) )
          & ~ aReductOfIn0(X1,X0,xR) )
        | ~ aElement0(X1)
        | ~ aElement0(X0) )
    & isLocallyConfluent0(xR)
    & ! [X3,X4,X5] :
        ( ( sdtmndtasgtdt0(X5,xR,sK23(X4,X5))
          & ( ( sdtmndtplgtdt0(X5,xR,sK23(X4,X5))
              & ( ( sdtmndtplgtdt0(sK24(X4,X5),xR,sK23(X4,X5))
                  & aReductOfIn0(sK24(X4,X5),X5,xR)
                  & aElement0(sK24(X4,X5)) )
                | aReductOfIn0(sK23(X4,X5),X5,xR) ) )
            | sK23(X4,X5) = X5 )
          & sdtmndtasgtdt0(X4,xR,sK23(X4,X5))
          & sP4(sK23(X4,X5),X4)
          & aElement0(sK23(X4,X5)) )
        | ~ aReductOfIn0(X5,X3,xR)
        | ~ aReductOfIn0(X4,X3,xR)
        | ~ aElement0(X5)
        | ~ aElement0(X4)
        | ~ aElement0(X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f69,f111,f110]) ).

fof(f113,plain,
    ! [X1,X0] :
      ( ( ~ sdtmndtasgtdt0(X0,xR,X1)
        & ~ sdtmndtplgtdt0(X0,xR,X1)
        & ! [X4] :
            ( ~ sdtmndtplgtdt0(X4,xR,X1)
            | ~ aReductOfIn0(X4,X0,xR)
            | ~ aElement0(X4) )
        & ~ aReductOfIn0(X1,X0,xR)
        & X0 != X1 )
      | ~ sP7(X1,X0) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ( ~ sdtmndtasgtdt0(X1,xR,X0)
        & ~ sdtmndtplgtdt0(X1,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,X1,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,X1,xR)
        & X0 != X1 )
      | ~ sP7(X0,X1) ),
    inference(rectify,[],[f113]) ).

fof(f115,plain,
    ! [X2,X1] :
      ( ? [X5] :
          ( sdtmndtasgtdt0(X2,xR,X5)
          & ( ( sdtmndtplgtdt0(X2,xR,X5)
              & ( ? [X6] :
                    ( sdtmndtplgtdt0(X6,xR,X5)
                    & aReductOfIn0(X6,X2,xR)
                    & aElement0(X6) )
                | aReductOfIn0(X5,X2,xR) ) )
            | X2 = X5 )
          & sdtmndtasgtdt0(X1,xR,X5)
          & sP5(X5,X1)
          & aElement0(X5) )
      | ~ sP6(X2,X1) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtmndtasgtdt0(X0,xR,X2)
          & ( ( sdtmndtplgtdt0(X0,xR,X2)
              & ( ? [X3] :
                    ( sdtmndtplgtdt0(X3,xR,X2)
                    & aReductOfIn0(X3,X0,xR)
                    & aElement0(X3) )
                | aReductOfIn0(X2,X0,xR) ) )
            | X0 = X2 )
          & sdtmndtasgtdt0(X1,xR,X2)
          & sP5(X2,X1)
          & aElement0(X2) )
      | ~ sP6(X0,X1) ),
    inference(rectify,[],[f115]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( sdtmndtasgtdt0(X0,xR,X2)
          & ( ( sdtmndtplgtdt0(X0,xR,X2)
              & ( ? [X3] :
                    ( sdtmndtplgtdt0(X3,xR,X2)
                    & aReductOfIn0(X3,X0,xR)
                    & aElement0(X3) )
                | aReductOfIn0(X2,X0,xR) ) )
            | X0 = X2 )
          & sdtmndtasgtdt0(X1,xR,X2)
          & sP5(X2,X1)
          & aElement0(X2) )
     => ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
        & ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
            & ( ? [X3] :
                  ( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
                  & aReductOfIn0(X3,X0,xR)
                  & aElement0(X3) )
              | aReductOfIn0(sK25(X0,X1),X0,xR) ) )
          | sK25(X0,X1) = X0 )
        & sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
        & sP5(sK25(X0,X1),X1)
        & aElement0(sK25(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtmndtplgtdt0(X3,xR,sK25(X0,X1))
          & aReductOfIn0(X3,X0,xR)
          & aElement0(X3) )
     => ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
        & aReductOfIn0(sK26(X0,X1),X0,xR)
        & aElement0(sK26(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
        & ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
            & ( ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
                & aReductOfIn0(sK26(X0,X1),X0,xR)
                & aElement0(sK26(X0,X1)) )
              | aReductOfIn0(sK25(X0,X1),X0,xR) ) )
          | sK25(X0,X1) = X0 )
        & sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
        & sP5(sK25(X0,X1),X1)
        & aElement0(sK25(X0,X1)) )
      | ~ sP6(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f116,f118,f117]) ).

fof(f127,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xb)
        & aReductOfIn0(X0,xu,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK30,xR,xb)
      & aReductOfIn0(sK30,xu,xR)
      & aElement0(sK30) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( sdtmndtasgtdt0(xu,xR,xb)
    & ( ( sdtmndtplgtdt0(xu,xR,xb)
        & ( ( sdtmndtplgtdt0(sK30,xR,xb)
            & aReductOfIn0(sK30,xu,xR)
            & aElement0(sK30) )
          | aReductOfIn0(xb,xu,xR) ) )
      | xb = xu )
    & aReductOfIn0(xu,xa,xR)
    & aElement0(xu) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f20,f127]) ).

fof(f131,plain,
    ( ? [X0] :
        ( sdtmndtplgtdt0(X0,xR,xw)
        & aReductOfIn0(X0,xv,xR)
        & aElement0(X0) )
   => ( sdtmndtplgtdt0(sK32,xR,xw)
      & aReductOfIn0(sK32,xv,xR)
      & aElement0(sK32) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X1] :
        ( sdtmndtplgtdt0(X1,xR,xw)
        & aReductOfIn0(X1,xu,xR)
        & aElement0(X1) )
   => ( sdtmndtplgtdt0(sK33,xR,xw)
      & aReductOfIn0(sK33,xu,xR)
      & aElement0(sK33) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( sdtmndtasgtdt0(xv,xR,xw)
    & ( ( sdtmndtplgtdt0(xv,xR,xw)
        & ( ( sdtmndtplgtdt0(sK32,xR,xw)
            & aReductOfIn0(sK32,xv,xR)
            & aElement0(sK32) )
          | aReductOfIn0(xw,xv,xR) ) )
      | xv = xw )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( ( sdtmndtplgtdt0(xu,xR,xw)
        & ( ( sdtmndtplgtdt0(sK33,xR,xw)
            & aReductOfIn0(sK33,xu,xR)
            & aElement0(sK33) )
          | aReductOfIn0(xw,xu,xR) ) )
      | xu = xw )
    & aElement0(xw) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f33,f132,f131]) ).

fof(f134,plain,
    ( ? [X1] :
        ( sdtmndtplgtdt0(X1,xR,xd)
        & aReductOfIn0(X1,xw,xR)
        & aElement0(X1) )
   => ( sdtmndtplgtdt0(sK34,xR,xd)
      & aReductOfIn0(sK34,xw,xR)
      & aElement0(sK34) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( aNormalFormOfIn0(xd,xw,xR)
    & ! [X0] : ~ aReductOfIn0(X0,xd,xR)
    & sdtmndtasgtdt0(xw,xR,xd)
    & ( ( sdtmndtplgtdt0(xw,xR,xd)
        & ( ( sdtmndtplgtdt0(sK34,xR,xd)
            & aReductOfIn0(sK34,xw,xR)
            & aElement0(sK34) )
          | aReductOfIn0(xd,xw,xR) ) )
      | xw = xd )
    & aElement0(xd) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f60,f134]) ).

fof(f136,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xb,xR,X0)
        & ~ sdtmndtplgtdt0(xb,xR,X0)
        & ! [X2] :
            ( ~ sdtmndtplgtdt0(X2,xR,X0)
            | ~ aReductOfIn0(X2,xb,xR)
            | ~ aElement0(X2) )
        & ~ aReductOfIn0(X0,xb,xR)
        & xb != X0 )
      | ~ sP8(X0) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f137,plain,
    ! [X0] :
      ( ( ~ sdtmndtasgtdt0(xb,xR,X0)
        & ~ sdtmndtplgtdt0(xb,xR,X0)
        & ! [X1] :
            ( ~ sdtmndtplgtdt0(X1,xR,X0)
            | ~ aReductOfIn0(X1,xb,xR)
            | ~ aElement0(X1) )
        & ~ aReductOfIn0(X0,xb,xR)
        & xb != X0 )
      | ~ sP8(X0) ),
    inference(rectify,[],[f136]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( aElement0(X2)
      | ~ aReductOfIn0(X2,X0,X1)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f148,plain,
    ! [X2,X3,X0,X1] :
      ( sdtmndtasgtdt0(X0,X1,X3)
      | ~ sdtmndtasgtdt0(X2,X1,X3)
      | ~ sdtmndtasgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f183,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f15]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( iLess0(X1,X0)
      | ~ aReductOfIn0(X1,X0,xR)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f201,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f17]) ).

fof(f202,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f17]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ~ sdtmndtasgtdt0(X1,xR,X0)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f114]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( aElement0(sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f225,plain,
    ! [X2,X0,X1] :
      ( sP6(X2,X1)
      | ~ iLess0(X0,xa)
      | ~ sdtmndtasgtdt0(X0,xR,X2)
      | sP7(X1,X0)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f234,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f128]) ).

fof(f235,plain,
    aReductOfIn0(xu,xa,xR),
    inference(cnf_transformation,[],[f128]) ).

fof(f240,plain,
    sdtmndtasgtdt0(xu,xR,xb),
    inference(cnf_transformation,[],[f128]) ).

fof(f248,plain,
    aElement0(xw),
    inference(cnf_transformation,[],[f133]) ).

fof(f253,plain,
    sdtmndtasgtdt0(xu,xR,xw),
    inference(cnf_transformation,[],[f133]) ).

fof(f259,plain,
    aElement0(xd),
    inference(cnf_transformation,[],[f135]) ).

fof(f264,plain,
    sdtmndtasgtdt0(xw,xR,xd),
    inference(cnf_transformation,[],[f135]) ).

fof(f271,plain,
    ! [X0] :
      ( ~ sdtmndtasgtdt0(xb,xR,X0)
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f276,plain,
    ! [X0] :
      ( ~ sdtmndtasgtdt0(xd,xR,X0)
      | sP8(X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_49,plain,
    ( ~ aReductOfIn0(X0,X1,X2)
    | ~ aElement0(X1)
    | ~ aRewritingSystem0(X2)
    | aElement0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_59,plain,
    ( ~ sdtmndtasgtdt0(X0,X1,X2)
    | ~ sdtmndtasgtdt0(X3,X1,X0)
    | ~ aElement0(X0)
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | ~ aRewritingSystem0(X1)
    | sdtmndtasgtdt0(X3,X1,X2) ),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_94,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_102,plain,
    ( ~ aReductOfIn0(X0,X1,xR)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | iLess0(X0,X1) ),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_113,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f202]) ).

cnf(c_114,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f201]) ).

cnf(c_115,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ sP7(X1,X0) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_120,plain,
    ( ~ sP6(X0,X1)
    | sdtmndtasgtdt0(X0,xR,sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_125,plain,
    ( ~ sP6(X0,X1)
    | sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_127,plain,
    ( ~ sP6(X0,X1)
    | aElement0(sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_132,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ iLess0(X0,xa)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | sP7(X2,X0)
    | sP6(X1,X2) ),
    inference(cnf_transformation,[],[f225]) ).

cnf(c_145,plain,
    sdtmndtasgtdt0(xu,xR,xb),
    inference(cnf_transformation,[],[f240]) ).

cnf(c_150,plain,
    aReductOfIn0(xu,xa,xR),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_151,plain,
    aElement0(xu),
    inference(cnf_transformation,[],[f234]) ).

cnf(c_164,plain,
    sdtmndtasgtdt0(xu,xR,xw),
    inference(cnf_transformation,[],[f253]) ).

cnf(c_169,plain,
    aElement0(xw),
    inference(cnf_transformation,[],[f248]) ).

cnf(c_172,plain,
    sdtmndtasgtdt0(xw,xR,xd),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_177,plain,
    aElement0(xd),
    inference(cnf_transformation,[],[f259]) ).

cnf(c_178,plain,
    ( ~ sdtmndtasgtdt0(xb,xR,X0)
    | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f271]) ).

cnf(c_183,negated_conjecture,
    ( ~ sdtmndtasgtdt0(xd,xR,X0)
    | ~ aElement0(X0)
    | sP8(X0) ),
    inference(cnf_transformation,[],[f276]) ).

cnf(c_2619,plain,
    ( X0 != xR
    | ~ aReductOfIn0(X1,X2,X0)
    | ~ aElement0(X2)
    | aElement0(X1) ),
    inference(resolution_lifted,[status(thm)],[c_49,c_94]) ).

cnf(c_2620,plain,
    ( ~ aReductOfIn0(X0,X1,xR)
    | ~ aElement0(X1)
    | aElement0(X0) ),
    inference(unflattening,[status(thm)],[c_2619]) ).

cnf(c_2670,plain,
    ( X0 != xR
    | ~ sdtmndtasgtdt0(X1,X0,X2)
    | ~ sdtmndtasgtdt0(X3,X0,X1)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aElement0(X3)
    | sdtmndtasgtdt0(X3,X0,X2) ),
    inference(resolution_lifted,[status(thm)],[c_59,c_94]) ).

cnf(c_2671,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ sdtmndtasgtdt0(X2,xR,X0)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | sdtmndtasgtdt0(X2,xR,X1) ),
    inference(unflattening,[status(thm)],[c_2670]) ).

cnf(c_2840,plain,
    ( ~ aReductOfIn0(X0,X1,xR)
    | ~ aElement0(X1)
    | iLess0(X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_102,c_2620]) ).

cnf(c_14274,plain,
    ( ~ sP8(sK25(xb,X0))
    | ~ sP6(xb,X0) ),
    inference(superposition,[status(thm)],[c_120,c_178]) ).

cnf(c_14323,plain,
    ( ~ aElement0(sK25(X0,xd))
    | ~ sP6(X0,xd)
    | sP8(sK25(X0,xd)) ),
    inference(superposition,[status(thm)],[c_125,c_183]) ).

cnf(c_14440,plain,
    ( ~ sP6(X0,xd)
    | sP8(sK25(X0,xd)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14323,c_127]) ).

cnf(c_14453,plain,
    ~ sP6(xb,xd),
    inference(superposition,[status(thm)],[c_14440,c_14274]) ).

cnf(c_14479,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,xw)
    | ~ aElement0(X0)
    | ~ aElement0(xw)
    | ~ aElement0(xd)
    | sdtmndtasgtdt0(X0,xR,xd) ),
    inference(superposition,[status(thm)],[c_172,c_2671]) ).

cnf(c_14482,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,xw)
    | ~ aElement0(X0)
    | sdtmndtasgtdt0(X0,xR,xd) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14479,c_177,c_169]) ).

cnf(c_14659,plain,
    ( ~ aElement0(xa)
    | iLess0(xu,xa) ),
    inference(superposition,[status(thm)],[c_150,c_2840]) ).

cnf(c_14666,plain,
    iLess0(xu,xa),
    inference(forward_subsumption_resolution,[status(thm)],[c_14659,c_114]) ).

cnf(c_18486,plain,
    ( ~ iLess0(xu,xa)
    | ~ aElement0(X0)
    | ~ aElement0(xb)
    | ~ aElement0(xu)
    | sP7(X0,xu)
    | sP6(xb,X0) ),
    inference(superposition,[status(thm)],[c_145,c_132]) ).

cnf(c_18540,plain,
    ( ~ aElement0(X0)
    | sP7(X0,xu)
    | sP6(xb,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18486,c_151,c_113,c_14666]) ).

cnf(c_27166,plain,
    ( ~ aElement0(xu)
    | sdtmndtasgtdt0(xu,xR,xd) ),
    inference(superposition,[status(thm)],[c_164,c_14482]) ).

cnf(c_27168,plain,
    sdtmndtasgtdt0(xu,xR,xd),
    inference(forward_subsumption_resolution,[status(thm)],[c_27166,c_151]) ).

cnf(c_27181,plain,
    ~ sP7(xd,xu),
    inference(superposition,[status(thm)],[c_27168,c_115]) ).

cnf(c_27311,plain,
    ( ~ aElement0(xd)
    | sP6(xb,xd) ),
    inference(superposition,[status(thm)],[c_18540,c_27181]) ).

cnf(c_27316,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_27311,c_14453,c_177]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COM020+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 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 Aug 29 13:31:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.31/1.65  % SZS status Started for theBenchmark.p
% 7.31/1.65  % SZS status Theorem for theBenchmark.p
% 7.31/1.65  
% 7.31/1.65  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.31/1.65  
% 7.31/1.65  ------  iProver source info
% 7.31/1.65  
% 7.31/1.65  git: date: 2023-05-31 18:12:56 +0000
% 7.31/1.65  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.31/1.65  git: non_committed_changes: false
% 7.31/1.65  git: last_make_outside_of_git: false
% 7.31/1.65  
% 7.31/1.65  ------ Parsing...
% 7.31/1.65  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.31/1.65  
% 7.31/1.65  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 7.31/1.65  
% 7.31/1.65  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.31/1.65  
% 7.31/1.65  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.31/1.65  ------ Proving...
% 7.31/1.65  ------ Problem Properties 
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  clauses                                 122
% 7.31/1.65  conjectures                             3
% 7.31/1.65  EPR                                     75
% 7.31/1.65  Horn                                    61
% 7.31/1.65  unary                                   21
% 7.31/1.65  binary                                  35
% 7.31/1.65  lits                                    381
% 7.31/1.65  lits eq                                 37
% 7.31/1.65  fd_pure                                 0
% 7.31/1.65  fd_pseudo                               0
% 7.31/1.65  fd_cond                                 0
% 7.31/1.65  fd_pseudo_cond                          9
% 7.31/1.65  AC symbols                              0
% 7.31/1.65  
% 7.31/1.65  ------ Schedule dynamic 5 is on 
% 7.31/1.65  
% 7.31/1.65  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  ------ 
% 7.31/1.65  Current options:
% 7.31/1.65  ------ 
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  ------ Proving...
% 7.31/1.65  
% 7.31/1.65  
% 7.31/1.65  % SZS status Theorem for theBenchmark.p
% 7.31/1.65  
% 7.31/1.65  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.31/1.65  
% 7.31/1.65  
%------------------------------------------------------------------------------