TSTP Solution File: KRS100+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS100+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 : Sat Sep 17 17:44:44 EDT 2022

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   59 (  12 unt;   8 typ;   0 def)
%            Number of atoms       :  913 (   0 equ)
%            Maximal formula atoms :   32 (  17 avg)
%            Number of connectives : 1624 ( 793   ~; 701   |;  83   &)
%                                         (  41 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   31 (  31 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   7   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :  214 ( 198   !;   9   ?; 214   :)

% Comments : 
%------------------------------------------------------------------------------
tff(cd_type,type,
    cd: $i > $o ).

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

tff(i2003_11_14_17_20_32704_type,type,
    i2003_11_14_17_20_32704: $i ).

tff(rr_type,type,
    rr: ( $i * $i ) > $o ).

tff(ce_type,type,
    ce: $i > $o ).

tff(cUnsatisfiable_type,type,
    cUnsatisfiable: $i > $o ).

tff(tptp_fun_Y_2_type,type,
    tptp_fun_Y_2: $i > $i ).

tff(tptp_fun_Y_1_type,type,
    tptp_fun_Y_1: $i > $i ).

tff(1,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ rr(X,tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) ) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ rr(X,tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) ) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $i] :
      refl(
        ( ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(6,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[5]) ).

tff(7,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(transitivity,[status(thm)],[6,4]) ).

tff(8,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ cUnsatisfiable(X)
              | ( ! [Y: $i] :
                    ( ~ cd(Y)
                    | ce(Y)
                    | ~ rr(X,Y) )
                & ! [Y: $i] :
                    ( cd(Y)
                    | ~ rr(X,Y) )
                & rr(X,tptp_fun_Y_0(X))
                & ~ ce(tptp_fun_Y_0(X)) ) )
          <=> ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) ) )),
          trans(
            monotonicity(
              rewrite(
                ( ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
              <=> ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) ) )),
              quant_intro(
                proof_bind(
                  ^ [Y: $i] :
                    trans(
                      monotonicity(
                        rewrite(
                          ( ( rr(X,Y)
                            & ~ ce(Y) )
                        <=> ~ ( ce(Y)
                              | ~ rr(X,Y) ) )),
                        ( ~ ( rr(X,Y)
                            & ~ ce(Y) )
                      <=> ~ ~ ( ce(Y)
                              | ~ rr(X,Y) ) )),
                      rewrite(
                        ( ~ ~ ( ce(Y)
                              | ~ rr(X,Y) )
                      <=> ( ce(Y)
                          | ~ rr(X,Y) ) )),
                      ( ~ ( rr(X,Y)
                          & ~ ce(Y) )
                    <=> ( ce(Y)
                        | ~ rr(X,Y) ) ))),
                ( ! [Y: $i] :
                    ~ ( rr(X,Y)
                      & ~ ce(Y) )
              <=> ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) )),
              ( ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ~ ( rr(X,Y)
                      & ~ ce(Y) ) )
            <=> ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )),
            rewrite(
              ( ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) )
            <=> ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )),
            ( ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ~ ( rr(X,Y)
                    & ~ ce(Y) ) )
          <=> ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )),
          ( ( ( ~ cUnsatisfiable(X)
              | ( ! [Y: $i] :
                    ( ~ cd(Y)
                    | ce(Y)
                    | ~ rr(X,Y) )
                & ! [Y: $i] :
                    ( cd(Y)
                    | ~ rr(X,Y) )
                & rr(X,tptp_fun_Y_0(X))
                & ~ ce(tptp_fun_Y_0(X)) ) )
            & ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ~ ( rr(X,Y)
                    & ~ ce(Y) ) ) )
        <=> ( ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
            & ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) )),
        rewrite(
          ( ( ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
            & ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) )
        <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                  | ~ ( ce(tptp_fun_Y_0(X))
                      | ~ ! [Y: $i] :
                            ( ~ cd(Y)
                            | ce(Y)
                            | ~ rr(X,Y) )
                      | ~ ! [Y: $i] :
                            ( cd(Y)
                            | ~ rr(X,Y) )
                      | ~ rr(X,tptp_fun_Y_0(X)) ) )
              | ~ ( cUnsatisfiable(X)
                  | ~ ( ~ cd(tptp_fun_Y_1(X))
                      | ce(tptp_fun_Y_1(X))
                      | ~ rr(X,tptp_fun_Y_1(X)) )
                  | ~ ( cd(tptp_fun_Y_2(X))
                      | ~ rr(X,tptp_fun_Y_2(X)) )
                  | ! [Y: $i] :
                      ( ce(Y)
                      | ~ rr(X,Y) ) ) ) )),
        ( ( ( ~ cUnsatisfiable(X)
            | ( ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(X,Y) )
              & ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(X,Y) )
              & rr(X,tptp_fun_Y_0(X))
              & ~ ce(tptp_fun_Y_0(X)) ) )
          & ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & ~ ce(Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) )
                    | ~ rr(X,tptp_fun_Y_0(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( ! [Y: $i] :
                ( ~ cd(Y)
                | ce(Y)
                | ~ rr(X,Y) )
            & ! [Y: $i] :
                ( cd(Y)
                | ~ rr(X,Y) )
            & rr(X,tptp_fun_Y_0(X))
            & ~ ce(tptp_fun_Y_0(X)) ) )
        & ( cUnsatisfiable(X)
          | ~ ( ~ cd(tptp_fun_Y_1(X))
              | ce(tptp_fun_Y_1(X))
              | ~ rr(X,tptp_fun_Y_1(X)) )
          | ~ ( cd(tptp_fun_Y_2(X))
              | ~ rr(X,tptp_fun_Y_2(X)) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & ~ ce(Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ce(tptp_fun_Y_0(X))
                  | ~ ! [Y: $i] :
                        ( ~ cd(Y)
                        | ce(Y)
                        | ~ rr(X,Y) )
                  | ~ ! [Y: $i] :
                        ( cd(Y)
                        | ~ rr(X,Y) )
                  | ~ rr(X,tptp_fun_Y_0(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ~ ( ~ cd(tptp_fun_Y_1(X))
                  | ce(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_1(X)) )
              | ~ ( cd(tptp_fun_Y_2(X))
                  | ~ rr(X,tptp_fun_Y_2(X)) )
              | ! [Y: $i] :
                  ( ce(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ( ~ cUnsatisfiable(X)
            | ( ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(X,Y) )
              & ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(X,Y) )
              & rr(X,tptp_fun_Y_0(X))
              & ~ ce(tptp_fun_Y_0(X)) ) )
          & ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & ~ ce(Y) ) ) )
      <=> ( ( ~ cUnsatisfiable(X)
            | ( ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(X,Y) )
              & ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(X,Y) )
              & rr(X,tptp_fun_Y_0(X))
              & ~ ce(tptp_fun_Y_0(X)) ) )
          & ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & ~ ce(Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( ! [Y: $i] :
                ( ~ cd(Y)
                | ce(Y)
                | ~ rr(X,Y) )
            & ! [Y: $i] :
                ( cd(Y)
                | ~ rr(X,Y) )
            & rr(X,tptp_fun_Y_0(X))
            & ~ ce(tptp_fun_Y_0(X)) ) )
        & ( cUnsatisfiable(X)
          | ~ ( ~ cd(tptp_fun_Y_1(X))
              | ce(tptp_fun_Y_1(X))
              | ~ rr(X,tptp_fun_Y_1(X)) )
          | ~ ( cd(tptp_fun_Y_2(X))
              | ~ rr(X,tptp_fun_Y_2(X)) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & ~ ce(Y) ) ) )
  <=> ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( ! [Y: $i] :
                ( ~ cd(Y)
                | ce(Y)
                | ~ rr(X,Y) )
            & ! [Y: $i] :
                ( cd(Y)
                | ~ rr(X,Y) )
            & rr(X,tptp_fun_Y_0(X))
            & ~ ce(tptp_fun_Y_0(X)) ) )
        & ( cUnsatisfiable(X)
          | ~ ( ~ cd(tptp_fun_Y_1(X))
              | ce(tptp_fun_Y_1(X))
              | ~ rr(X,tptp_fun_Y_1(X)) )
          | ~ ( cd(tptp_fun_Y_2(X))
              | ~ rr(X,tptp_fun_Y_2(X)) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & ~ ce(Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(X,Y) )
          & ! [Y: $i] :
              ( cd(Y)
              | ~ rr(X,Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & ~ ce(Y) ) ) )
  <=> ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(X,Y) )
          & ! [Y: $i] :
              ( cd(Y)
              | ~ rr(X,Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & ~ ce(Y) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cUnsatisfiable(X)
        <=> ( ! [Y: $i] :
                ( rr(X,Y)
               => ( ce(Y)
                  | ~ cd(Y) ) )
            & ! [Y: $i] :
                ( rr(X,Y)
               => cd(Y) )
            & ? [Y: $i] :
                ( rr(X,Y)
                & ~ ce(Y) ) ) )
      <=> ( cUnsatisfiable(X)
        <=> ( ! [Y: $i] :
                ( ~ cd(Y)
                | ce(Y)
                | ~ rr(X,Y) )
            & ! [Y: $i] :
                ( cd(Y)
                | ~ rr(X,Y) )
            & ? [Y: $i] :
                ( rr(X,Y)
                & ~ ce(Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ! [Y: $i] :
              ( rr(X,Y)
             => ( ce(Y)
                | ~ cd(Y) ) )
          & ! [Y: $i] :
              ( rr(X,Y)
             => cd(Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & ~ ce(Y) ) ) )
  <=> ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(X,Y) )
          & ! [Y: $i] :
              ( cd(Y)
              | ~ rr(X,Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & ~ ce(Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y: $i] :
            ( rr(X,Y)
           => ( ce(Y)
              | ~ cd(Y) ) )
        & ! [Y: $i] :
            ( rr(X,Y)
           => cd(Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & ~ ce(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(16,plain,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(X,Y) )
        & ! [Y: $i] :
            ( cd(Y)
            | ~ rr(X,Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & ~ ce(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(X,Y) )
        & ! [Y: $i] :
            ( cd(Y)
            | ~ rr(X,Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & ~ ce(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X: $i] :
      ( ( ~ cUnsatisfiable(X)
        | ( ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(X,Y) )
          & ! [Y: $i] :
              ( cd(Y)
              | ~ rr(X,Y) )
          & rr(X,tptp_fun_Y_0(X))
          & ~ ce(tptp_fun_Y_0(X)) ) )
      & ( cUnsatisfiable(X)
        | ~ ( ~ cd(tptp_fun_Y_1(X))
            | ce(tptp_fun_Y_1(X))
            | ~ rr(X,tptp_fun_Y_1(X)) )
        | ~ ( cd(tptp_fun_Y_2(X))
            | ~ rr(X,tptp_fun_Y_2(X)) )
        | ! [Y: $i] :
            ~ ( rr(X,Y)
              & ~ ce(Y) ) ) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X: $i] :
      ( ( ~ cUnsatisfiable(X)
        | ( ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(X,Y) )
          & ! [Y: $i] :
              ( cd(Y)
              | ~ rr(X,Y) )
          & rr(X,tptp_fun_Y_0(X))
          & ~ ce(tptp_fun_Y_0(X)) ) )
      & ( cUnsatisfiable(X)
        | ~ ( ~ cd(tptp_fun_Y_1(X))
            | ce(tptp_fun_Y_1(X))
            | ~ rr(X,tptp_fun_Y_1(X)) )
        | ~ ( cd(tptp_fun_Y_2(X))
            | ~ rr(X,tptp_fun_Y_2(X)) )
        | ! [Y: $i] :
            ~ ( rr(X,Y)
              & ~ ce(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cUnsatisfiable(X)
            | ~ ( ce(tptp_fun_Y_0(X))
                | ~ ! [Y: $i] :
                      ( ~ cd(Y)
                      | ce(Y)
                      | ~ rr(X,Y) )
                | ~ ! [Y: $i] :
                      ( cd(Y)
                      | ~ rr(X,Y) )
                | ~ rr(X,tptp_fun_Y_0(X)) ) )
        | ~ ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ( ce(Y)
                | ~ rr(X,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[19,9]) ).

tff(21,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cUnsatisfiable(X)
            | ~ ( ce(tptp_fun_Y_0(X))
                | ~ ! [Y: $i] :
                      ( ~ cd(Y)
                      | ce(Y)
                      | ~ rr(X,Y) )
                | ~ ! [Y: $i] :
                      ( cd(Y)
                      | ~ rr(X,Y) )
                | ~ rr(X,tptp_fun_Y_0(X)) ) )
        | ~ ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ( ce(Y)
                | ~ rr(X,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[20,7]) ).

tff(22,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cUnsatisfiable(X)
            | ~ ( ce(tptp_fun_Y_0(X))
                | ~ rr(X,tptp_fun_Y_0(X))
                | ~ ! [Y: $i] :
                      ( ~ cd(Y)
                      | ce(Y)
                      | ~ rr(X,Y) )
                | ~ ! [Y: $i] :
                      ( cd(Y)
                      | ~ rr(X,Y) ) ) )
        | ~ ( cUnsatisfiable(X)
            | ~ ( ~ cd(tptp_fun_Y_1(X))
                | ce(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_1(X)) )
            | ~ ( cd(tptp_fun_Y_2(X))
                | ~ rr(X,tptp_fun_Y_2(X)) )
            | ! [Y: $i] :
                ( ce(Y)
                | ~ rr(X,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[21,2]) ).

tff(23,plain,
    ( ~ ! [X: $i] :
          ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ce(tptp_fun_Y_0(X))
                    | ~ rr(X,tptp_fun_Y_0(X))
                    | ~ ! [Y: $i] :
                          ( ~ cd(Y)
                          | ce(Y)
                          | ~ rr(X,Y) )
                    | ~ ! [Y: $i] :
                          ( cd(Y)
                          | ~ rr(X,Y) ) ) )
            | ~ ( cUnsatisfiable(X)
                | ~ ( ~ cd(tptp_fun_Y_1(X))
                    | ce(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_1(X)) )
                | ~ ( cd(tptp_fun_Y_2(X))
                    | ~ rr(X,tptp_fun_Y_2(X)) )
                | ! [Y: $i] :
                    ( ce(Y)
                    | ~ rr(X,Y) ) ) )
    | ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
            | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
                | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
                | ~ ! [Y: $i] :
                      ( ~ cd(Y)
                      | ce(Y)
                      | ~ rr(i2003_11_14_17_20_32704,Y) )
                | ~ ! [Y: $i] :
                      ( cd(Y)
                      | ~ rr(i2003_11_14_17_20_32704,Y) ) ) )
        | ~ ( cUnsatisfiable(i2003_11_14_17_20_32704)
            | ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_32704))
                | ce(tptp_fun_Y_1(i2003_11_14_17_20_32704))
                | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_1(i2003_11_14_17_20_32704)) )
            | ~ ( cd(tptp_fun_Y_2(i2003_11_14_17_20_32704))
                | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_2(i2003_11_14_17_20_32704)) )
            | ! [Y: $i] :
                ( ce(Y)
                | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
          | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
              | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
              | ~ ! [Y: $i] :
                    ( ~ cd(Y)
                    | ce(Y)
                    | ~ rr(i2003_11_14_17_20_32704,Y) )
              | ~ ! [Y: $i] :
                    ( cd(Y)
                    | ~ rr(i2003_11_14_17_20_32704,Y) ) ) )
      | ~ ( cUnsatisfiable(i2003_11_14_17_20_32704)
          | ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_32704))
              | ce(tptp_fun_Y_1(i2003_11_14_17_20_32704))
              | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_1(i2003_11_14_17_20_32704)) )
          | ~ ( cd(tptp_fun_Y_2(i2003_11_14_17_20_32704))
              | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_2(i2003_11_14_17_20_32704)) )
          | ! [Y: $i] :
              ( ce(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[23,22]) ).

tff(25,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
        | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) )
            | ~ ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) ) ) )
    | ~ ( cUnsatisfiable(i2003_11_14_17_20_32704)
        | ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_32704))
            | ce(tptp_fun_Y_1(i2003_11_14_17_20_32704))
            | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_1(i2003_11_14_17_20_32704)) )
        | ~ ( cd(tptp_fun_Y_2(i2003_11_14_17_20_32704))
            | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_2(i2003_11_14_17_20_32704)) )
        | ! [Y: $i] :
            ( ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) ) )
    | ~ cUnsatisfiable(i2003_11_14_17_20_32704)
    | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) )
        | ~ ! [Y: $i] :
              ( cd(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(26,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
    | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) )
        | ~ ! [Y: $i] :
              ( cd(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[25,24]) ).

tff(27,plain,
    ( cUnsatisfiable(i2003_11_14_17_20_32704)
  <=> cUnsatisfiable(i2003_11_14_17_20_32704) ),
    inference(rewrite,[status(thm)],]) ).

tff(28,axiom,
    cUnsatisfiable(i2003_11_14_17_20_32704),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

tff(29,plain,
    cUnsatisfiable(i2003_11_14_17_20_32704),
    inference(modus_ponens,[status(thm)],[28,27]) ).

tff(30,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
        | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) )
            | ~ ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) ) ) )
    | ~ cUnsatisfiable(i2003_11_14_17_20_32704)
    | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) )
        | ~ ! [Y: $i] :
              ( cd(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ),
    inference(tautology,[status(thm)],]) ).

tff(31,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_32704)
        | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
            | ~ ! [Y: $i] :
                  ( ~ cd(Y)
                  | ce(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) )
            | ~ ! [Y: $i] :
                  ( cd(Y)
                  | ~ rr(i2003_11_14_17_20_32704,Y) ) ) )
    | ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
        | ~ ! [Y: $i] :
              ( ~ cd(Y)
              | ce(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) )
        | ~ ! [Y: $i] :
              ( cd(Y)
              | ~ rr(i2003_11_14_17_20_32704,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[30,29]) ).

tff(32,plain,
    ~ ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ~ ! [Y: $i] :
            ( cd(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) ) ),
    inference(unit_resolution,[status(thm)],[31,26]) ).

tff(33,plain,
    ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ! [Y: $i] :
        ( cd(Y)
        | ~ rr(i2003_11_14_17_20_32704,Y) ) ),
    inference(tautology,[status(thm)],]) ).

tff(34,plain,
    ! [Y: $i] :
      ( cd(Y)
      | ~ rr(i2003_11_14_17_20_32704,Y) ),
    inference(unit_resolution,[status(thm)],[33,32]) ).

tff(35,plain,
    ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(tautology,[status(thm)],]) ).

tff(36,plain,
    rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)),
    inference(unit_resolution,[status(thm)],[35,32]) ).

tff(37,plain,
    ( ( ~ ! [Y: $i] :
            ( cd(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) )
  <=> ( ~ ! [Y: $i] :
            ( cd(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)),
    inference(unit_resolution,[status(thm)],[39,36,34]) ).

tff(41,plain,
    ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ! [Y: $i] :
        ( ~ cd(Y)
        | ce(Y)
        | ~ rr(i2003_11_14_17_20_32704,Y) ) ),
    inference(tautology,[status(thm)],]) ).

tff(42,plain,
    ! [Y: $i] :
      ( ~ cd(Y)
      | ce(Y)
      | ~ rr(i2003_11_14_17_20_32704,Y) ),
    inference(unit_resolution,[status(thm)],[41,32]) ).

tff(43,plain,
    ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ ! [Y: $i] :
          ( cd(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ ce(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(tautology,[status(thm)],]) ).

tff(44,plain,
    ~ ce(tptp_fun_Y_0(i2003_11_14_17_20_32704)),
    inference(unit_resolution,[status(thm)],[43,32]) ).

tff(45,plain,
    ( ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) )
  <=> ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) )
  <=> ( ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ( ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) )
  <=> ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ) ),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    ( ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) )
  <=> ( ~ ! [Y: $i] :
            ( ~ cd(Y)
            | ce(Y)
            | ~ rr(i2003_11_14_17_20_32704,Y) )
      | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
      | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ) ),
    inference(transitivity,[status(thm)],[47,45]) ).

tff(49,plain,
    ( ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(50,plain,
    ( ~ ! [Y: $i] :
          ( ~ cd(Y)
          | ce(Y)
          | ~ rr(i2003_11_14_17_20_32704,Y) )
    | ce(tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ rr(i2003_11_14_17_20_32704,tptp_fun_Y_0(i2003_11_14_17_20_32704))
    | ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_32704)) ),
    inference(modus_ponens,[status(thm)],[49,48]) ).

tff(51,plain,
    $false,
    inference(unit_resolution,[status(thm)],[50,44,36,42,40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS100+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Sep  1 09:34:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.12/0.39  % SZS status Unsatisfiable
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------