TSTP Solution File: ARI619_3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI619_3 : TPTP v8.1.0. Released v5.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 : Tue Sep  6 17:02:19 EDT 2022

% Result   : Theorem 0.11s 0.29s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   77 (  18 unt;   2 typ;   0 def)
%            Number of atoms       :  942 ( 356 equ)
%            Maximal formula atoms :   36 (  12 avg)
%            Number of connectives : 1839 ( 992   ~; 697   |;  91   &)
%                                         (  57 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   20 (  20 fml;   0 var)
%            Number arithmetic     : 1522 ( 152 atm; 299 fun; 915 num; 156 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (   1 usr;   8 con; 0-2 aty)
%            Number of variables   :  156 ( 132   !;  18   ?; 156   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pow2_type,type,
    pow2: $real > $o ).

tff(tptp_fun_Y_0_type,type,
    tptp_fun_Y_0: $real > $real ).

tff(1,plain,
    ^ [X: $real] :
      refl(
        ( ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      <=> ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $real] :
      rewrite(
        ( ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      <=> ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[4,2]) ).

tff(6,plain,
    ^ [X: $real] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( $greatereq(X,2)
                  & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
                  & pow2(tptp_fun_Y_0(X)) )
              <=> ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )),
              ( ( ( X = 1 )
                | ~ pow2(X)
                | ( $greatereq(X,2)
                  & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
                  & pow2(tptp_fun_Y_0(X)) ) )
            <=> ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) ) )),
            rewrite(
              ( ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            <=> ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) ) )),
            ( ( ( X = 1 )
              | ~ pow2(X)
              | ( $greatereq(X,2)
                & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
                & pow2(tptp_fun_Y_0(X)) ) )
          <=> ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) ) )),
          rewrite(
            ( ( pow2(X)
              | ( ( X != 1 )
                & ( ~ $greatereq(X,2)
                  | ! [Y: $real] :
                      ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                        & pow2(Y) ) ) ) )
          <=> ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )),
          ( ( ( ( X = 1 )
              | ~ pow2(X)
              | ( $greatereq(X,2)
                & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
                & pow2(tptp_fun_Y_0(X)) ) )
            & ( pow2(X)
              | ( ( X != 1 )
                & ( ~ $greatereq(X,2)
                  | ! [Y: $real] :
                      ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                        & pow2(Y) ) ) ) ) )
        <=> ( ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
            & ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
        rewrite(
          ( ( ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
            & ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
        <=> ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
        ( ( ( ( X = 1 )
            | ~ pow2(X)
            | ( $greatereq(X,2)
              & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
              & pow2(tptp_fun_Y_0(X)) ) )
          & ( pow2(X)
            | ( ( X != 1 )
              & ( ~ $greatereq(X,2)
                | ! [Y: $real] :
                    ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                      & pow2(Y) ) ) ) ) )
      <=> ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [X: $real] :
        ( ( ( X = 1 )
          | ~ pow2(X)
          | ( $greatereq(X,2)
            & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
            & pow2(tptp_fun_Y_0(X)) ) )
        & ( pow2(X)
          | ( ( X != 1 )
            & ( ~ $greatereq(X,2)
              | ! [Y: $real] :
                  ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                    & pow2(Y) ) ) ) ) )
  <=> ! [X: $real] :
        ~ ( ~ ( ( X = 1 )
              | ~ pow2(X)
              | ~ ( ~ $greatereq(X,2)
                  | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(X)) ) )
          | ~ ( pow2(X)
              | ~ ( ( X = 1 )
                  | ~ ( ~ $greatereq(X,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ^ [X: $real] :
      rewrite(
        ( ( ( ~ pow2(X)
            | ( X = 1 )
            | ( $greatereq(X,2)
              & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
              & pow2(tptp_fun_Y_0(X)) ) )
          & ( pow2(X)
            | ( ( X != 1 )
              & ( ~ $greatereq(X,2)
                | ! [Y: $real] :
                    ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                      & pow2(Y) ) ) ) ) )
      <=> ( ( ( X = 1 )
            | ~ pow2(X)
            | ( $greatereq(X,2)
              & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
              & pow2(tptp_fun_Y_0(X)) ) )
          & ( pow2(X)
            | ( ( X != 1 )
              & ( ~ $greatereq(X,2)
                | ! [Y: $real] :
                    ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                      & pow2(Y) ) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [X: $real] :
        ( ( ~ pow2(X)
          | ( X = 1 )
          | ( $greatereq(X,2)
            & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
            & pow2(tptp_fun_Y_0(X)) ) )
        & ( pow2(X)
          | ( ( X != 1 )
            & ( ~ $greatereq(X,2)
              | ! [Y: $real] :
                  ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                    & pow2(Y) ) ) ) ) )
  <=> ! [X: $real] :
        ( ( ( X = 1 )
          | ~ pow2(X)
          | ( $greatereq(X,2)
            & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
            & pow2(tptp_fun_Y_0(X)) ) )
        & ( pow2(X)
          | ( ( X != 1 )
            & ( ~ $greatereq(X,2)
              | ! [Y: $real] :
                  ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                    & pow2(Y) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ^ [X: $real] :
      rewrite(
        ( ( pow2(X)
        <=> ( ( X = 1 )
            | ( $greatereq(X,2)
              & ? [Y: $real] :
                  ( ( $sum($product(2,Y),$product(-1,X)) = 0 )
                  & pow2(Y) ) ) ) )
      <=> ( pow2(X)
        <=> ( ( X = 1 )
            | ( $greatereq(X,2)
              & ? [Y: $real] :
                  ( ( $sum(X,$product(-2,Y)) = 0 )
                  & pow2(Y) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $greatereq(X,2)
            & ? [Y: $real] :
                ( ( $sum($product(2,Y),$product(-1,X)) = 0 )
                & pow2(Y) ) ) ) )
  <=> ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $greatereq(X,2)
            & ? [Y: $real] :
                ( ( $sum(X,$product(-2,Y)) = 0 )
                & pow2(Y) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ^ [X: $real] :
      rewrite(
        ( ( pow2(X)
        <=> ( ( X = 1 )
            | ( $lesseq(2,X)
              & ? [Y: $real] :
                  ( ( $product(2,Y) = X )
                  & pow2(Y) ) ) ) )
      <=> ( pow2(X)
        <=> ( ( X = 1 )
            | ( $greatereq(X,2)
              & ? [Y: $real] :
                  ( ( $sum($product(2,Y),$product(-1,X)) = 0 )
                  & pow2(Y) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(13,plain,
    ( ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $lesseq(2,X)
            & ? [Y: $real] :
                ( ( $product(2,Y) = X )
                & pow2(Y) ) ) ) )
  <=> ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $greatereq(X,2)
            & ? [Y: $real] :
                ( ( $sum($product(2,Y),$product(-1,X)) = 0 )
                & pow2(Y) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[12]) ).

tff(14,plain,
    ( ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $lesseq(2,X)
            & ? [Y: $real] :
                ( ( $product(2,Y) = X )
                & pow2(Y) ) ) ) )
  <=> ! [X: $real] :
        ( pow2(X)
      <=> ( ( X = 1 )
          | ( $lesseq(2,X)
            & ? [Y: $real] :
                ( ( $product(2,Y) = X )
                & pow2(Y) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( ~ ( ! [X: $real] :
            ( pow2(X)
          <=> ( ( X = 1 )
              | ( $lesseq(2,X)
                & ? [Y: $real] :
                    ( ( $product(2,Y) = X )
                    & pow2(Y) ) ) ) )
       => ~ pow2(5) )
  <=> ~ ( ~ pow2(5)
        | ~ ! [X: $real] :
              ( pow2(X)
            <=> ( ( X = 1 )
                | ( $lesseq(2,X)
                  & ? [Y: $real] :
                      ( ( $product(2,Y) = X )
                      & pow2(Y) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    ~ ( ! [X: $real] :
          ( pow2(X)
        <=> ( ( X = 1 )
            | ( $lesseq(2,X)
              & ? [Y: $real] :
                  ( ( $product(2,Y) = X )
                  & pow2(Y) ) ) ) )
     => ~ pow2(5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_pow_of_2_5) ).

tff(17,plain,
    ~ ( ~ pow2(5)
      | ~ ! [X: $real] :
            ( pow2(X)
          <=> ( ( X = 1 )
              | ( $lesseq(2,X)
                & ? [Y: $real] :
                    ( ( $product(2,Y) = X )
                    & pow2(Y) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [X: $real] :
      ( pow2(X)
    <=> ( ( X = 1 )
        | ( $lesseq(2,X)
          & ? [Y: $real] :
              ( ( $product(2,Y) = X )
              & pow2(Y) ) ) ) ),
    inference(or_elim,[status(thm)],[17]) ).

tff(19,plain,
    ! [X: $real] :
      ( pow2(X)
    <=> ( ( X = 1 )
        | ( $lesseq(2,X)
          & ? [Y: $real] :
              ( ( $product(2,Y) = X )
              & pow2(Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[18,14]) ).

tff(20,plain,
    ! [X: $real] :
      ( pow2(X)
    <=> ( ( X = 1 )
        | ( $greatereq(X,2)
          & ? [Y: $real] :
              ( ( $sum($product(2,Y),$product(-1,X)) = 0 )
              & pow2(Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[19,13]) ).

tff(21,plain,
    ! [X: $real] :
      ( pow2(X)
    <=> ( ( X = 1 )
        | ( $greatereq(X,2)
          & ? [Y: $real] :
              ( ( $sum(X,$product(-2,Y)) = 0 )
              & pow2(Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[20,11]) ).

tff(22,plain,
    ! [X: $real] :
      ( ( ~ pow2(X)
        | ( X = 1 )
        | ( $greatereq(X,2)
          & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
          & pow2(tptp_fun_Y_0(X)) ) )
      & ( pow2(X)
        | ( ( X != 1 )
          & ( ~ $greatereq(X,2)
            | ! [Y: $real] :
                ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                  & pow2(Y) ) ) ) ) ),
    inference(skolemize,[status(sab)],[21]) ).

tff(23,plain,
    ! [X: $real] :
      ( ( ( X = 1 )
        | ~ pow2(X)
        | ( $greatereq(X,2)
          & ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
          & pow2(tptp_fun_Y_0(X)) ) )
      & ( pow2(X)
        | ( ( X != 1 )
          & ( ~ $greatereq(X,2)
            | ! [Y: $real] :
                ~ ( ( $sum(X,$product(-2,Y)) = 0 )
                  & pow2(Y) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[22,9]) ).

tff(24,plain,
    ! [X: $real] :
      ~ ( ~ ( ( X = 1 )
            | ~ pow2(X)
            | ~ ( ~ $greatereq(X,2)
                | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                | ~ pow2(tptp_fun_Y_0(X)) ) )
        | ~ ( pow2(X)
            | ~ ( ( X = 1 )
                | ~ ( ~ $greatereq(X,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[23,7]) ).

tff(25,plain,
    ! [X: $real] :
      ~ ( ~ ( ( X = 1 )
            | ~ pow2(X)
            | ~ ( ~ $greatereq(X,2)
                | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                | ~ pow2(tptp_fun_Y_0(X)) ) )
        | ~ ( pow2(X)
            | ~ ( ( X = 1 )
                | ~ ( ~ $greatereq(X,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[24,5]) ).

tff(26,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5/2)
              | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                  | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
          | ~ ( pow2(5/2)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/4 ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5/2)
              | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                  | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
          | ~ ( pow2(5/2)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/4 ) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ( ~ ( ~ ( ( 5/2 = 1 )
            | ~ pow2(5/2)
            | ~ ( ~ $greatereq(5/2,2)
                | ( $sum(5/2,$product(-2,tptp_fun_Y_0(5/2))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5/2)) ) )
        | ~ ( pow2(5/2)
            | ~ ( ( 5/2 = 1 )
                | ~ ( ~ $greatereq(5/2,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5/2,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ~ ( ~ ( ~ pow2(5/2)
            | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
        | ~ ( pow2(5/2)
            | ! [Y: $real] :
                ( ~ pow2(Y)
                | ( Y != 5/4 ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5/2 = 1 )
              | ~ pow2(5/2)
              | ~ ( ~ $greatereq(5/2,2)
                  | ( $sum(5/2,$product(-2,tptp_fun_Y_0(5/2))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5/2)) ) )
          | ~ ( pow2(5/2)
              | ~ ( ( 5/2 = 1 )
                  | ~ ( ~ $greatereq(5/2,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5/2,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5/2)
              | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                  | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
          | ~ ( pow2(5/2)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/4 ) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[27]) ).

tff(29,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5/2 = 1 )
              | ~ pow2(5/2)
              | ~ ( ~ $greatereq(5/2,2)
                  | ( $sum(5/2,$product(-2,tptp_fun_Y_0(5/2))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5/2)) ) )
          | ~ ( pow2(5/2)
              | ~ ( ( 5/2 = 1 )
                  | ~ ( ~ $greatereq(5/2,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5/2,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5/2)
              | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                  | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
          | ~ ( pow2(5/2)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/4 ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[28,26]) ).

tff(30,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ ( ~ ( ( 5/2 = 1 )
            | ~ pow2(5/2)
            | ~ ( ~ $greatereq(5/2,2)
                | ( $sum(5/2,$product(-2,tptp_fun_Y_0(5/2))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5/2)) ) )
        | ~ ( pow2(5/2)
            | ~ ( ( 5/2 = 1 )
                | ~ ( ~ $greatereq(5/2,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5/2,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(31,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ ( ~ ( ~ pow2(5/2)
            | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
                | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
        | ~ ( pow2(5/2)
            | ! [Y: $real] :
                ( ~ pow2(Y)
                | ( Y != 5/4 ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ~ ( ~ ( ~ pow2(5/2)
          | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
              | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
      | ~ ( pow2(5/2)
          | ! [Y: $real] :
              ( ~ pow2(Y)
              | ( Y != 5/4 ) ) ) ),
    inference(unit_resolution,[status(thm)],[31,25]) ).

tff(33,plain,
    ( ~ ( ~ pow2(5/2)
        | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
            | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
    | ~ ( pow2(5/2)
        | ! [Y: $real] :
            ( ~ pow2(Y)
            | ( Y != 5/4 ) ) )
    | ~ pow2(5/2)
    | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
        | ( tptp_fun_Y_0(5/2) != 5/4 ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(34,plain,
    ( ~ pow2(5/2)
    | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
        | ( tptp_fun_Y_0(5/2) != 5/4 ) ) ),
    inference(unit_resolution,[status(thm)],[33,32]) ).

tff(35,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5)
              | ~ ( ~ pow2(tptp_fun_Y_0(5))
                  | ( tptp_fun_Y_0(5) != 5/2 ) ) )
          | ~ ( pow2(5)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/2 ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5)
              | ~ ( ~ pow2(tptp_fun_Y_0(5))
                  | ( tptp_fun_Y_0(5) != 5/2 ) ) )
          | ~ ( pow2(5)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/2 ) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ~ ( ~ ( ( 5 = 1 )
            | ~ pow2(5)
            | ~ ( ~ $greatereq(5,2)
                | ( $sum(5,$product(-2,tptp_fun_Y_0(5))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5)) ) )
        | ~ ( pow2(5)
            | ~ ( ( 5 = 1 )
                | ~ ( ~ $greatereq(5,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ~ ( ~ ( ~ pow2(5)
            | ~ ( ~ pow2(tptp_fun_Y_0(5))
                | ( tptp_fun_Y_0(5) != 5/2 ) ) )
        | ~ ( pow2(5)
            | ! [Y: $real] :
                ( ~ pow2(Y)
                | ( Y != 5/2 ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5 = 1 )
              | ~ pow2(5)
              | ~ ( ~ $greatereq(5,2)
                  | ( $sum(5,$product(-2,tptp_fun_Y_0(5))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5)) ) )
          | ~ ( pow2(5)
              | ~ ( ( 5 = 1 )
                  | ~ ( ~ $greatereq(5,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5)
              | ~ ( ~ pow2(tptp_fun_Y_0(5))
                  | ( tptp_fun_Y_0(5) != 5/2 ) ) )
          | ~ ( pow2(5)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/2 ) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[36]) ).

tff(38,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5 = 1 )
              | ~ pow2(5)
              | ~ ( ~ $greatereq(5,2)
                  | ( $sum(5,$product(-2,tptp_fun_Y_0(5))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5)) ) )
          | ~ ( pow2(5)
              | ~ ( ( 5 = 1 )
                  | ~ ( ~ $greatereq(5,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ~ pow2(5)
              | ~ ( ~ pow2(tptp_fun_Y_0(5))
                  | ( tptp_fun_Y_0(5) != 5/2 ) ) )
          | ~ ( pow2(5)
              | ! [Y: $real] :
                  ( ~ pow2(Y)
                  | ( Y != 5/2 ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[37,35]) ).

tff(39,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ ( ~ ( ( 5 = 1 )
            | ~ pow2(5)
            | ~ ( ~ $greatereq(5,2)
                | ( $sum(5,$product(-2,tptp_fun_Y_0(5))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5)) ) )
        | ~ ( pow2(5)
            | ~ ( ( 5 = 1 )
                | ~ ( ~ $greatereq(5,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(40,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ ( ~ ( ~ pow2(5)
            | ~ ( ~ pow2(tptp_fun_Y_0(5))
                | ( tptp_fun_Y_0(5) != 5/2 ) ) )
        | ~ ( pow2(5)
            | ! [Y: $real] :
                ( ~ pow2(Y)
                | ( Y != 5/2 ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ~ ( ~ ( ~ pow2(5)
          | ~ ( ~ pow2(tptp_fun_Y_0(5))
              | ( tptp_fun_Y_0(5) != 5/2 ) ) )
      | ~ ( pow2(5)
          | ! [Y: $real] :
              ( ~ pow2(Y)
              | ( Y != 5/2 ) ) ) ),
    inference(unit_resolution,[status(thm)],[40,25]) ).

tff(42,plain,
    ( ~ ( ~ pow2(5)
        | ~ ( ~ pow2(tptp_fun_Y_0(5))
            | ( tptp_fun_Y_0(5) != 5/2 ) ) )
    | ~ ( pow2(5)
        | ! [Y: $real] :
            ( ~ pow2(Y)
            | ( Y != 5/2 ) ) )
    | ~ pow2(5)
    | ~ ( ~ pow2(tptp_fun_Y_0(5))
        | ( tptp_fun_Y_0(5) != 5/2 ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(43,plain,
    ( ~ pow2(5)
    | ~ ( ~ pow2(tptp_fun_Y_0(5))
        | ( tptp_fun_Y_0(5) != 5/2 ) ) ),
    inference(unit_resolution,[status(thm)],[42,41]) ).

tff(44,plain,
    ( pow2(5)
  <=> pow2(5) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    pow2(5),
    inference(or_elim,[status(thm)],[17]) ).

tff(46,plain,
    pow2(5),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ( ~ ( ~ pow2(5)
        | ~ ( ~ pow2(tptp_fun_Y_0(5))
            | ( tptp_fun_Y_0(5) != 5/2 ) ) )
    | ~ pow2(5)
    | ~ ( ~ pow2(tptp_fun_Y_0(5))
        | ( tptp_fun_Y_0(5) != 5/2 ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(48,plain,
    ( ~ ( ~ pow2(5)
        | ~ ( ~ pow2(tptp_fun_Y_0(5))
            | ( tptp_fun_Y_0(5) != 5/2 ) ) )
    | ~ ( ~ pow2(tptp_fun_Y_0(5))
        | ( tptp_fun_Y_0(5) != 5/2 ) ) ),
    inference(unit_resolution,[status(thm)],[47,46]) ).

tff(49,plain,
    ~ ( ~ pow2(tptp_fun_Y_0(5))
      | ( tptp_fun_Y_0(5) != 5/2 ) ),
    inference(unit_resolution,[status(thm)],[48,43]) ).

tff(50,plain,
    ( ~ pow2(tptp_fun_Y_0(5))
    | ( tptp_fun_Y_0(5) != 5/2 )
    | ( tptp_fun_Y_0(5) = 5/2 ) ),
    inference(tautology,[status(thm)],]) ).

tff(51,plain,
    tptp_fun_Y_0(5) = 5/2,
    inference(unit_resolution,[status(thm)],[50,49]) ).

tff(52,plain,
    5/2 = tptp_fun_Y_0(5),
    inference(symmetry,[status(thm)],[51]) ).

tff(53,plain,
    ( pow2(5/2)
  <=> pow2(tptp_fun_Y_0(5)) ),
    inference(monotonicity,[status(thm)],[52]) ).

tff(54,plain,
    ( pow2(tptp_fun_Y_0(5))
  <=> pow2(5/2) ),
    inference(symmetry,[status(thm)],[53]) ).

tff(55,plain,
    ( ~ pow2(tptp_fun_Y_0(5))
    | ( tptp_fun_Y_0(5) != 5/2 )
    | pow2(tptp_fun_Y_0(5)) ),
    inference(tautology,[status(thm)],]) ).

tff(56,plain,
    pow2(tptp_fun_Y_0(5)),
    inference(unit_resolution,[status(thm)],[55,49]) ).

tff(57,plain,
    pow2(5/2),
    inference(modus_ponens,[status(thm)],[56,54]) ).

tff(58,plain,
    ( ~ ( ~ pow2(5/2)
        | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
            | ( tptp_fun_Y_0(5/2) != 5/4 ) ) )
    | ~ pow2(5/2)
    | ~ ( ~ pow2(tptp_fun_Y_0(5/2))
        | ( tptp_fun_Y_0(5/2) != 5/4 ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(59,plain,
    ~ ( ~ pow2(tptp_fun_Y_0(5/2))
      | ( tptp_fun_Y_0(5/2) != 5/4 ) ),
    inference(unit_resolution,[status(thm)],[58,57,34]) ).

tff(60,plain,
    ( ~ pow2(tptp_fun_Y_0(5/2))
    | ( tptp_fun_Y_0(5/2) != 5/4 )
    | ( tptp_fun_Y_0(5/2) = 5/4 ) ),
    inference(tautology,[status(thm)],]) ).

tff(61,plain,
    tptp_fun_Y_0(5/2) = 5/4,
    inference(unit_resolution,[status(thm)],[60,59]) ).

tff(62,plain,
    5/4 = tptp_fun_Y_0(5/2),
    inference(symmetry,[status(thm)],[61]) ).

tff(63,plain,
    ( pow2(5/4)
  <=> pow2(tptp_fun_Y_0(5/2)) ),
    inference(monotonicity,[status(thm)],[62]) ).

tff(64,plain,
    ( pow2(tptp_fun_Y_0(5/2))
  <=> pow2(5/4) ),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    ( ~ pow2(tptp_fun_Y_0(5/2))
    | ( tptp_fun_Y_0(5/2) != 5/4 )
    | pow2(tptp_fun_Y_0(5/2)) ),
    inference(tautology,[status(thm)],]) ).

tff(66,plain,
    pow2(tptp_fun_Y_0(5/2)),
    inference(unit_resolution,[status(thm)],[65,59]) ).

tff(67,plain,
    pow2(5/4),
    inference(modus_ponens,[status(thm)],[66,64]) ).

tff(68,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ pow2(5/4) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ pow2(5/4) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ( ~ ( ~ ( ( 5/4 = 1 )
            | ~ pow2(5/4)
            | ~ ( ~ $greatereq(5/4,2)
                | ( $sum(5/4,$product(-2,tptp_fun_Y_0(5/4))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5/4)) ) )
        | ~ ( pow2(5/4)
            | ~ ( ( 5/4 = 1 )
                | ~ ( ~ $greatereq(5/4,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5/4,$product(-2,Y)) != 0 ) ) ) ) ) )
  <=> ~ pow2(5/4) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5/4 = 1 )
              | ~ pow2(5/4)
              | ~ ( ~ $greatereq(5/4,2)
                  | ( $sum(5/4,$product(-2,tptp_fun_Y_0(5/4))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5/4)) ) )
          | ~ ( pow2(5/4)
              | ~ ( ( 5/4 = 1 )
                  | ~ ( ~ $greatereq(5/4,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5/4,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ pow2(5/4) ) ),
    inference(monotonicity,[status(thm)],[69]) ).

tff(71,plain,
    ( ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ ( ~ ( ( 5/4 = 1 )
              | ~ pow2(5/4)
              | ~ ( ~ $greatereq(5/4,2)
                  | ( $sum(5/4,$product(-2,tptp_fun_Y_0(5/4))) != 0 )
                  | ~ pow2(tptp_fun_Y_0(5/4)) ) )
          | ~ ( pow2(5/4)
              | ~ ( ( 5/4 = 1 )
                  | ~ ( ~ $greatereq(5/4,2)
                      | ! [Y: $real] :
                          ( ~ pow2(Y)
                          | ( $sum(5/4,$product(-2,Y)) != 0 ) ) ) ) ) ) )
  <=> ( ~ ! [X: $real] :
            ~ ( ~ ( ( X = 1 )
                  | ~ pow2(X)
                  | ~ ( ~ $greatereq(X,2)
                      | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                      | ~ pow2(tptp_fun_Y_0(X)) ) )
              | ~ ( pow2(X)
                  | ~ ( ( X = 1 )
                      | ~ ( ~ $greatereq(X,2)
                          | ! [Y: $real] :
                              ( ~ pow2(Y)
                              | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
      | ~ pow2(5/4) ) ),
    inference(transitivity,[status(thm)],[70,68]) ).

tff(72,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ ( ~ ( ( 5/4 = 1 )
            | ~ pow2(5/4)
            | ~ ( ~ $greatereq(5/4,2)
                | ( $sum(5/4,$product(-2,tptp_fun_Y_0(5/4))) != 0 )
                | ~ pow2(tptp_fun_Y_0(5/4)) ) )
        | ~ ( pow2(5/4)
            | ~ ( ( 5/4 = 1 )
                | ~ ( ~ $greatereq(5/4,2)
                    | ! [Y: $real] :
                        ( ~ pow2(Y)
                        | ( $sum(5/4,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [X: $real] :
          ~ ( ~ ( ( X = 1 )
                | ~ pow2(X)
                | ~ ( ~ $greatereq(X,2)
                    | ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
                    | ~ pow2(tptp_fun_Y_0(X)) ) )
            | ~ ( pow2(X)
                | ~ ( ( X = 1 )
                    | ~ ( ~ $greatereq(X,2)
                        | ! [Y: $real] :
                            ( ~ pow2(Y)
                            | ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
    | ~ pow2(5/4) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ~ pow2(5/4),
    inference(unit_resolution,[status(thm)],[73,25]) ).

tff(75,plain,
    $false,
    inference(unit_resolution,[status(thm)],[74,67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : ARI619_3 : TPTP v8.1.0. Released v5.1.0.
% 0.00/0.08  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.27  % Computer : n002.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Tue Aug 30 01:08:28 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.07/0.27  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.27  Usage: tptp [options] [-file:]file
% 0.07/0.27    -h, -?       prints this message.
% 0.07/0.27    -smt2        print SMT-LIB2 benchmark.
% 0.07/0.27    -m, -model   generate model.
% 0.07/0.27    -p, -proof   generate proof.
% 0.07/0.27    -c, -core    generate unsat core of named formulas.
% 0.07/0.27    -st, -statistics display statistics.
% 0.07/0.27    -t:timeout   set timeout (in second).
% 0.07/0.27    -smt2status  display status in smt2 format instead of SZS.
% 0.07/0.27    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.27    -<param>:<value> configuration parameter and value.
% 0.07/0.27    -o:<output-file> file to place output in.
% 0.11/0.29  % SZS status Theorem
% 0.11/0.29  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------