TSTP Solution File: COM023+4 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : COM023+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.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 02:10:30 EDT 2024

% Result   : Theorem 4.22s 1.16s
% Output   : CNFRefutation 4.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   68 (  18 unt;   0 def)
%            Number of atoms       :  651 (  65 equ)
%            Maximal formula atoms :   52 (   9 avg)
%            Number of connectives :  797 ( 214   ~; 230   |; 343   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  183 (   0 sgn  91   !;  71   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,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) )
     => ? [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(f18,conjecture,
    ( isConfluent0(xR)
    | ! [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) )
       => ? [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__) ).

fof(f19,negated_conjecture,
    ~ ( isConfluent0(xR)
      | ! [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) )
         => ? [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) ) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f25,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) )
     => ? [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,[],[f17]) ).

fof(f26,plain,
    ~ ( isConfluent0(xR)
      | ! [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) )
         => ? [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,[],[f19]) ).

fof(f49,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) )
      | ( ~ 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,[],[f25]) ).

fof(f50,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) )
      | ( ~ 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,[],[f49]) ).

fof(f51,plain,
    ( ~ isConfluent0(xR)
    & ? [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) )
        & 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,[],[f26]) ).

fof(f52,plain,
    ( ~ isConfluent0(xR)
    & ? [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) )
        & 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,[],[f51]) ).

fof(f61,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(f62,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(f63,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(f64,plain,
    ! [X0,X1,X2] :
      ( sP6(X2,X1)
      | ( ~ 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,[],[f50,f63,f62,f61]) ).

fof(f65,plain,
    ! [X5,X1] :
      ( ( ~ 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 )
      | ~ sP8(X5,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f66,plain,
    ( ~ isConfluent0(xR)
    & ? [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 )
            | sP8(X5,X1)
            | ~ aElement0(X5) )
        & 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(definition_folding,[],[f52,f65]) ).

fof(f104,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,[],[f63]) ).

fof(f105,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,[],[f104]) ).

fof(f106,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,[],[f62]) ).

fof(f107,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,[],[f106]) ).

fof(f108,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(f109,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(f110,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])],[f107,f109,f108]) ).

fof(f115,plain,
    ! [X5,X1] :
      ( ( ~ 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 )
      | ~ sP8(X5,X1) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f116,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 )
      | ~ sP8(X0,X1) ),
    inference(rectify,[],[f115]) ).

fof(f117,plain,
    ( ~ isConfluent0(xR)
    & ? [X0,X1,X2] :
        ( ! [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 )
            | sP8(X3,X1)
            | ~ aElement0(X3) )
        & sdtmndtasgtdt0(X0,xR,X2)
        & ( ( sdtmndtplgtdt0(X0,xR,X2)
            & ( ? [X5] :
                  ( sdtmndtplgtdt0(X5,xR,X2)
                  & aReductOfIn0(X5,X0,xR)
                  & aElement0(X5) )
              | aReductOfIn0(X2,X0,xR) ) )
          | X0 = X2 )
        & sdtmndtasgtdt0(X0,xR,X1)
        & ( ( sdtmndtplgtdt0(X0,xR,X1)
            & ( ? [X6] :
                  ( sdtmndtplgtdt0(X6,xR,X1)
                  & aReductOfIn0(X6,X0,xR)
                  & aElement0(X6) )
              | aReductOfIn0(X1,X0,xR) ) )
          | X0 = X1 )
        & aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) ) ),
    inference(rectify,[],[f66]) ).

fof(f118,plain,
    ( ? [X0,X1,X2] :
        ( ! [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 )
            | sP8(X3,X1)
            | ~ aElement0(X3) )
        & sdtmndtasgtdt0(X0,xR,X2)
        & ( ( sdtmndtplgtdt0(X0,xR,X2)
            & ( ? [X5] :
                  ( sdtmndtplgtdt0(X5,xR,X2)
                  & aReductOfIn0(X5,X0,xR)
                  & aElement0(X5) )
              | aReductOfIn0(X2,X0,xR) ) )
          | X0 = X2 )
        & sdtmndtasgtdt0(X0,xR,X1)
        & ( ( sdtmndtplgtdt0(X0,xR,X1)
            & ( ? [X6] :
                  ( sdtmndtplgtdt0(X6,xR,X1)
                  & aReductOfIn0(X6,X0,xR)
                  & aElement0(X6) )
              | aReductOfIn0(X1,X0,xR) ) )
          | X0 = X1 )
        & aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
   => ( ! [X3] :
          ( ( ~ sdtmndtasgtdt0(sK30,xR,X3)
            & ~ sdtmndtplgtdt0(sK30,xR,X3)
            & ! [X4] :
                ( ~ sdtmndtplgtdt0(X4,xR,X3)
                | ~ aReductOfIn0(X4,sK30,xR)
                | ~ aElement0(X4) )
            & ~ aReductOfIn0(X3,sK30,xR)
            & sK30 != X3 )
          | sP8(X3,sK29)
          | ~ aElement0(X3) )
      & sdtmndtasgtdt0(sK28,xR,sK30)
      & ( ( sdtmndtplgtdt0(sK28,xR,sK30)
          & ( ? [X5] :
                ( sdtmndtplgtdt0(X5,xR,sK30)
                & aReductOfIn0(X5,sK28,xR)
                & aElement0(X5) )
            | aReductOfIn0(sK30,sK28,xR) ) )
        | sK28 = sK30 )
      & sdtmndtasgtdt0(sK28,xR,sK29)
      & ( ( sdtmndtplgtdt0(sK28,xR,sK29)
          & ( ? [X6] :
                ( sdtmndtplgtdt0(X6,xR,sK29)
                & aReductOfIn0(X6,sK28,xR)
                & aElement0(X6) )
            | aReductOfIn0(sK29,sK28,xR) ) )
        | sK28 = sK29 )
      & aElement0(sK30)
      & aElement0(sK29)
      & aElement0(sK28) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ( ? [X5] :
        ( sdtmndtplgtdt0(X5,xR,sK30)
        & aReductOfIn0(X5,sK28,xR)
        & aElement0(X5) )
   => ( sdtmndtplgtdt0(sK31,xR,sK30)
      & aReductOfIn0(sK31,sK28,xR)
      & aElement0(sK31) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ( ? [X6] :
        ( sdtmndtplgtdt0(X6,xR,sK29)
        & aReductOfIn0(X6,sK28,xR)
        & aElement0(X6) )
   => ( sdtmndtplgtdt0(sK32,xR,sK29)
      & aReductOfIn0(sK32,sK28,xR)
      & aElement0(sK32) ) ),
    introduced(choice_axiom,[]) ).

fof(f121,plain,
    ( ~ isConfluent0(xR)
    & ! [X3] :
        ( ( ~ sdtmndtasgtdt0(sK30,xR,X3)
          & ~ sdtmndtplgtdt0(sK30,xR,X3)
          & ! [X4] :
              ( ~ sdtmndtplgtdt0(X4,xR,X3)
              | ~ aReductOfIn0(X4,sK30,xR)
              | ~ aElement0(X4) )
          & ~ aReductOfIn0(X3,sK30,xR)
          & sK30 != X3 )
        | sP8(X3,sK29)
        | ~ aElement0(X3) )
    & sdtmndtasgtdt0(sK28,xR,sK30)
    & ( ( sdtmndtplgtdt0(sK28,xR,sK30)
        & ( ( sdtmndtplgtdt0(sK31,xR,sK30)
            & aReductOfIn0(sK31,sK28,xR)
            & aElement0(sK31) )
          | aReductOfIn0(sK30,sK28,xR) ) )
      | sK28 = sK30 )
    & sdtmndtasgtdt0(sK28,xR,sK29)
    & ( ( sdtmndtplgtdt0(sK28,xR,sK29)
        & ( ( sdtmndtplgtdt0(sK32,xR,sK29)
            & aReductOfIn0(sK32,sK28,xR)
            & aElement0(sK32) )
          | aReductOfIn0(sK29,sK28,xR) ) )
      | sK28 = sK29 )
    & aElement0(sK30)
    & aElement0(sK29)
    & aElement0(sK28) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32])],[f117,f120,f119,f118]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( ~ sdtmndtasgtdt0(X1,xR,X0)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( aElement0(sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f206,plain,
    ! [X2,X0,X1] :
      ( sP6(X2,X1)
      | ~ sdtmndtasgtdt0(X0,xR,X2)
      | sP7(X1,X0)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f211,plain,
    ! [X0,X1] :
      ( ~ sdtmndtasgtdt0(X1,xR,X0)
      | ~ sP8(X0,X1) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f212,plain,
    aElement0(sK28),
    inference(cnf_transformation,[],[f121]) ).

fof(f213,plain,
    aElement0(sK29),
    inference(cnf_transformation,[],[f121]) ).

fof(f214,plain,
    aElement0(sK30),
    inference(cnf_transformation,[],[f121]) ).

fof(f219,plain,
    sdtmndtasgtdt0(sK28,xR,sK29),
    inference(cnf_transformation,[],[f121]) ).

fof(f224,plain,
    sdtmndtasgtdt0(sK28,xR,sK30),
    inference(cnf_transformation,[],[f121]) ).

fof(f229,plain,
    ! [X3] :
      ( ~ sdtmndtasgtdt0(sK30,xR,X3)
      | sP8(X3,sK29)
      | ~ aElement0(X3) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_112,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ sP7(X1,X0) ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_117,plain,
    ( ~ sP6(X0,X1)
    | sdtmndtasgtdt0(X0,xR,sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_122,plain,
    ( ~ sP6(X0,X1)
    | sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_124,plain,
    ( ~ sP6(X0,X1)
    | aElement0(sK25(X0,X1)) ),
    inference(cnf_transformation,[],[f190]) ).

cnf(c_129,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | sP7(X2,X0)
    | sP6(X1,X2) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_134,plain,
    ( ~ sdtmndtasgtdt0(X0,xR,X1)
    | ~ sP8(X1,X0) ),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_140,negated_conjecture,
    ( ~ sdtmndtasgtdt0(sK30,xR,X0)
    | ~ aElement0(X0)
    | sP8(X0,sK29) ),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_145,negated_conjecture,
    sdtmndtasgtdt0(sK28,xR,sK30),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_150,negated_conjecture,
    sdtmndtasgtdt0(sK28,xR,sK29),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_155,negated_conjecture,
    aElement0(sK30),
    inference(cnf_transformation,[],[f214]) ).

cnf(c_156,negated_conjecture,
    aElement0(sK29),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_157,negated_conjecture,
    aElement0(sK28),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_10921,negated_conjecture,
    aElement0(sK28),
    inference(demodulation,[status(thm)],[c_157]) ).

cnf(c_10922,negated_conjecture,
    aElement0(sK29),
    inference(demodulation,[status(thm)],[c_156]) ).

cnf(c_10923,negated_conjecture,
    aElement0(sK30),
    inference(demodulation,[status(thm)],[c_155]) ).

cnf(c_10928,negated_conjecture,
    sdtmndtasgtdt0(sK28,xR,sK29),
    inference(demodulation,[status(thm)],[c_150]) ).

cnf(c_10933,negated_conjecture,
    sdtmndtasgtdt0(sK28,xR,sK30),
    inference(demodulation,[status(thm)],[c_145]) ).

cnf(c_10937,negated_conjecture,
    ( ~ sdtmndtasgtdt0(sK30,xR,X0)
    | ~ aElement0(X0)
    | sP8(X0,sK29) ),
    inference(demodulation,[status(thm)],[c_140]) ).

cnf(c_12883,plain,
    ~ sP7(sK30,sK28),
    inference(superposition,[status(thm)],[c_10933,c_112]) ).

cnf(c_13054,plain,
    ( ~ sP8(sK25(X0,X1),X0)
    | ~ sP6(X0,X1) ),
    inference(superposition,[status(thm)],[c_117,c_134]) ).

cnf(c_13073,plain,
    ( ~ aElement0(sK25(X0,sK30))
    | ~ sP6(X0,sK30)
    | sP8(sK25(X0,sK30),sK29) ),
    inference(superposition,[status(thm)],[c_122,c_10937]) ).

cnf(c_13131,plain,
    ( ~ sP6(X0,sK30)
    | sP8(sK25(X0,sK30),sK29) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13073,c_124]) ).

cnf(c_13134,plain,
    ~ sP6(sK29,sK30),
    inference(superposition,[status(thm)],[c_13131,c_13054]) ).

cnf(c_14819,plain,
    ( ~ aElement0(X0)
    | ~ aElement0(sK29)
    | ~ aElement0(sK28)
    | sP7(X0,sK28)
    | sP6(sK29,X0) ),
    inference(superposition,[status(thm)],[c_10928,c_129]) ).

cnf(c_14824,plain,
    ( ~ aElement0(X0)
    | sP7(X0,sK28)
    | sP6(sK29,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_14819,c_10921,c_10922]) ).

cnf(c_15012,plain,
    ( ~ aElement0(sK30)
    | sP6(sK29,sK30) ),
    inference(superposition,[status(thm)],[c_14824,c_12883]) ).

cnf(c_15017,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_15012,c_13134,c_10923]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM023+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri May  3 00:13:21 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.21/0.47  Running first-order theorem proving
% 0.21/0.47  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
% 4.22/1.16  % SZS status Started for theBenchmark.p
% 4.22/1.16  % SZS status Theorem for theBenchmark.p
% 4.22/1.16  
% 4.22/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.22/1.16  
% 4.22/1.16  ------  iProver source info
% 4.22/1.16  
% 4.22/1.16  git: date: 2024-05-02 19:28:25 +0000
% 4.22/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.22/1.16  git: non_committed_changes: false
% 4.22/1.16  
% 4.22/1.16  ------ Parsing...
% 4.22/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.22/1.16  
% 4.22/1.16  ------ 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 
% 4.22/1.16  
% 4.22/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.22/1.16  
% 4.22/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.22/1.16  ------ Proving...
% 4.22/1.16  ------ Problem Properties 
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  clauses                                 101
% 4.22/1.16  conjectures                             18
% 4.22/1.16  EPR                                     47
% 4.22/1.16  Horn                                    55
% 4.22/1.16  unary                                   12
% 4.22/1.16  binary                                  22
% 4.22/1.16  lits                                    379
% 4.22/1.16  lits eq                                 25
% 4.22/1.16  fd_pure                                 0
% 4.22/1.16  fd_pseudo                               0
% 4.22/1.16  fd_cond                                 0
% 4.22/1.16  fd_pseudo_cond                          9
% 4.22/1.16  AC symbols                              0
% 4.22/1.16  
% 4.22/1.16  ------ Schedule dynamic 5 is on 
% 4.22/1.16  
% 4.22/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  ------ 
% 4.22/1.16  Current options:
% 4.22/1.16  ------ 
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  ------ Proving...
% 4.22/1.16  
% 4.22/1.16  
% 4.22/1.16  % SZS status Theorem for theBenchmark.p
% 4.22/1.16  
% 4.22/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.22/1.16  
% 4.22/1.17  
%------------------------------------------------------------------------------