TSTP Solution File: KRS115+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KRS115+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n011.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 17:44:49 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   97
% Syntax   : Number of formulae    :  219 (  50 unt;  16 typ;   0 def)
%            Number of atoms       : 1666 ( 127 equ)
%            Maximal formula atoms :   28 (   8 avg)
%            Number of connectives : 2589 (1229   ~; 978   |; 210   &)
%                                         ( 139 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :  103 ( 103 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  15   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  639 ( 565   !;  35   ?; 639   :)

% Comments : 
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
    ra_Px1: ( $i * $i ) > $o ).

tff(tptp_fun_Y0_4_type,type,
    tptp_fun_Y0_4: $i > $i ).

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

tff(i2003_11_14_17_21_30578_type,type,
    i2003_11_14_17_21_30578: $i ).

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

tff(rf2_type,type,
    rf2: ( $i * $i ) > $o ).

tff(cowlThing_type,type,
    cowlThing: $i > $o ).

tff(cowlNothing_type,type,
    cowlNothing: $i > $o ).

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

tff(cp1_type,type,
    cp1: $i > $o ).

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

tff(rf1_type,type,
    rf1: ( $i * $i ) > $o ).

tff(cp2_type,type,
    cp2: $i > $o ).

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

tff(cp2xcomp_type,type,
    cp2xcomp: $i > $o ).

tff(tptp_fun_Y_3_type,type,
    tptp_fun_Y_3: $i > $i ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ~ ( cowlNothing(X)
            | ~ cowlThing(X) )
      <=> ~ ( cowlNothing(X)
            | ~ cowlThing(X) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] :
        ~ ( cowlNothing(X)
          | ~ cowlThing(X) )
  <=> ! [X: $i] :
        ~ ( cowlNothing(X)
          | ~ cowlThing(X) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cowlThing(X)
          & ~ cowlNothing(X) )
      <=> ~ ( cowlNothing(X)
            | ~ cowlThing(X) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [X: $i] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
  <=> ! [X: $i] :
        ~ ( cowlNothing(X)
          | ~ cowlThing(X) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ! [X: $i] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
  <=> ! [X: $i] :
        ( cowlThing(X)
        & ~ cowlNothing(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ! [X: $i] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).

tff(7,plain,
    ! [X: $i] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [X: $i] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ),
    inference(skolemize,[status(sab)],[7]) ).

tff(9,plain,
    ! [X: $i] :
      ~ ( cowlNothing(X)
        | ~ cowlThing(X) ),
    inference(modus_ponens,[status(thm)],[8,4]) ).

tff(10,plain,
    ! [X: $i] :
      ~ ( cowlNothing(X)
        | ~ cowlThing(X) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ ! [X: $i] :
          ~ ( cowlNothing(X)
            | ~ cowlThing(X) )
    | ~ ( cowlNothing(i2003_11_14_17_21_30578)
        | ~ cowlThing(i2003_11_14_17_21_30578) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    ~ ( cowlNothing(i2003_11_14_17_21_30578)
      | ~ cowlThing(i2003_11_14_17_21_30578) ),
    inference(unit_resolution,[status(thm)],[11,10]) ).

tff(13,plain,
    ( cowlNothing(i2003_11_14_17_21_30578)
    | ~ cowlThing(i2003_11_14_17_21_30578)
    | cowlThing(i2003_11_14_17_21_30578) ),
    inference(tautology,[status(thm)],]) ).

tff(14,plain,
    cowlThing(i2003_11_14_17_21_30578),
    inference(unit_resolution,[status(thm)],[13,12]) ).

tff(15,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(18,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[17]) ).

tff(19,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) ) ),
    inference(transitivity,[status(thm)],[18,16]) ).

tff(20,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ~ ( rf2(X,Y0)
                  & rf2(X,Y1) )
              | ( Y0 = Y1 ) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(21,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf2(X,Y0)
                & rf2(X,Y1) )
            | ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(X,Y1)
            | ~ rf2(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[20]) ).

tff(22,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf2(X,Y0)
                & rf2(X,Y1) )
            | ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf2(X,Y0)
                & rf2(X,Y1) )
            | ( Y0 = Y1 ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          quant_intro(
            proof_bind(
              ^ [Y0: $i,Y1: $i] :
                rewrite(
                  ( ( ( rf2(X,Y0)
                      & rf2(X,Y1) )
                   => ( Y0 = Y1 ) )
                <=> ( ~ ( rf2(X,Y0)
                        & rf2(X,Y1) )
                    | ( Y0 = Y1 ) ) ))),
            ( ! [Y0: $i,Y1: $i] :
                ( ( rf2(X,Y0)
                  & rf2(X,Y1) )
               => ( Y0 = Y1 ) )
          <=> ! [Y0: $i,Y1: $i] :
                ( ~ ( rf2(X,Y0)
                    & rf2(X,Y1) )
                | ( Y0 = Y1 ) ) )),
          ( ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ( rf2(X,Y0)
                  & rf2(X,Y1) )
               => ( Y0 = Y1 ) ) )
        <=> ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ~ ( rf2(X,Y0)
                    & rf2(X,Y1) )
                | ( Y0 = Y1 ) ) ) )),
        rewrite(
          ( ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ~ ( rf2(X,Y0)
                    & rf2(X,Y1) )
                | ( Y0 = Y1 ) ) )
        <=> ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ~ ( rf2(X,Y0)
                    & rf2(X,Y1) )
                | ( Y0 = Y1 ) ) ) )),
        ( ( cowlThing(X)
         => ! [Y0: $i,Y1: $i] :
              ( ( rf2(X,Y0)
                & rf2(X,Y1) )
             => ( Y0 = Y1 ) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ~ ( rf2(X,Y0)
                  & rf2(X,Y1) )
              | ( Y0 = Y1 ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(24,plain,
    ( ! [X: $i] :
        ( cowlThing(X)
       => ! [Y0: $i,Y1: $i] :
            ( ( rf2(X,Y0)
              & rf2(X,Y1) )
           => ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf2(X,Y0)
                & rf2(X,Y1) )
            | ( Y0 = Y1 ) ) ) ),
    inference(quant_intro,[status(thm)],[23]) ).

tff(25,axiom,
    ! [X: $i] :
      ( cowlThing(X)
     => ! [Y0: $i,Y1: $i] :
          ( ( rf2(X,Y0)
            & rf2(X,Y1) )
         => ( Y0 = Y1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).

tff(26,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf2(X,Y0)
              & rf2(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf2(X,Y0)
              & rf2(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(modus_ponens,[status(thm)],[26,22]) ).

tff(28,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf2(X,Y0)
              & rf2(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(skolemize,[status(sab)],[27]) ).

tff(29,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(X,Y1)
          | ~ rf2(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[28,21]) ).

tff(30,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(X,Y1)
          | ~ rf2(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[29,19]) ).

tff(31,plain,
    ( ( ~ ! [X: $i] :
            ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ( Y0 = Y1 )
                | ~ rf2(X,Y1)
                | ~ rf2(X,Y0) ) )
      | ~ cowlThing(i2003_11_14_17_21_30578)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(i2003_11_14_17_21_30578,Y1)
          | ~ rf2(i2003_11_14_17_21_30578,Y0) ) )
  <=> ( ~ ! [X: $i] :
            ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ( Y0 = Y1 )
                | ~ rf2(X,Y1)
                | ~ rf2(X,Y0) ) )
      | ~ cowlThing(i2003_11_14_17_21_30578)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(i2003_11_14_17_21_30578,Y1)
          | ~ rf2(i2003_11_14_17_21_30578,Y0) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ~ ! [X: $i] :
          ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) )
    | ~ cowlThing(i2003_11_14_17_21_30578)
    | ! [Y0: $i,Y1: $i] :
        ( ( Y0 = Y1 )
        | ~ rf2(i2003_11_14_17_21_30578,Y1)
        | ~ rf2(i2003_11_14_17_21_30578,Y0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [X: $i] :
          ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf2(X,Y1)
              | ~ rf2(X,Y0) ) )
    | ~ cowlThing(i2003_11_14_17_21_30578)
    | ! [Y0: $i,Y1: $i] :
        ( ( Y0 = Y1 )
        | ~ rf2(i2003_11_14_17_21_30578,Y1)
        | ~ rf2(i2003_11_14_17_21_30578,Y0) ) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [Y0: $i,Y1: $i] :
      ( ( Y0 = Y1 )
      | ~ rf2(i2003_11_14_17_21_30578,Y1)
      | ~ rf2(i2003_11_14_17_21_30578,Y0) ),
    inference(unit_resolution,[status(thm)],[33,30,14]) ).

tff(35,plain,
    ^ [X: $i] :
      refl(
        ( ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(36,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[35]) ).

tff(37,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(38,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[37]) ).

tff(39,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(transitivity,[status(thm)],[38,36]) ).

tff(40,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ cUnsatisfiable(X)
              | ( rf2(X,tptp_fun_Y_0(X))
                & cp2(tptp_fun_Y_0(X))
                & rf1(X,tptp_fun_Y_1(X))
                & cp1(tptp_fun_Y_1(X))
                & rr(X,tptp_fun_Y_2(X))
                & cowlThing(tptp_fun_Y_2(X)) ) )
          <=> ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) ) )),
          trans(
            monotonicity(
              quant_intro(
                proof_bind(
                  ^ [Y: $i] :
                    trans(
                      monotonicity(
                        rewrite(
                          ( ( rf2(X,Y)
                            & cp2(Y) )
                        <=> ~ ( ~ cp2(Y)
                              | ~ rf2(X,Y) ) )),
                        ( ~ ( rf2(X,Y)
                            & cp2(Y) )
                      <=> ~ ~ ( ~ cp2(Y)
                              | ~ rf2(X,Y) ) )),
                      rewrite(
                        ( ~ ~ ( ~ cp2(Y)
                              | ~ rf2(X,Y) )
                      <=> ( ~ cp2(Y)
                          | ~ rf2(X,Y) ) )),
                      ( ~ ( rf2(X,Y)
                          & cp2(Y) )
                    <=> ( ~ cp2(Y)
                        | ~ rf2(X,Y) ) ))),
                ( ! [Y: $i] :
                    ~ ( rf2(X,Y)
                      & cp2(Y) )
              <=> ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) ) )),
              quant_intro(
                proof_bind(
                  ^ [Y: $i] :
                    trans(
                      monotonicity(
                        rewrite(
                          ( ( rf1(X,Y)
                            & cp1(Y) )
                        <=> ~ ( ~ cp1(Y)
                              | ~ rf1(X,Y) ) )),
                        ( ~ ( rf1(X,Y)
                            & cp1(Y) )
                      <=> ~ ~ ( ~ cp1(Y)
                              | ~ rf1(X,Y) ) )),
                      rewrite(
                        ( ~ ~ ( ~ cp1(Y)
                              | ~ rf1(X,Y) )
                      <=> ( ~ cp1(Y)
                          | ~ rf1(X,Y) ) )),
                      ( ~ ( rf1(X,Y)
                          & cp1(Y) )
                    <=> ( ~ cp1(Y)
                        | ~ rf1(X,Y) ) ))),
                ( ! [Y: $i] :
                    ~ ( rf1(X,Y)
                      & cp1(Y) )
              <=> ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) ) )),
              quant_intro(
                proof_bind(
                  ^ [Y: $i] :
                    trans(
                      monotonicity(
                        rewrite(
                          ( ( rr(X,Y)
                            & cowlThing(Y) )
                        <=> ~ ( ~ cowlThing(Y)
                              | ~ rr(X,Y) ) )),
                        ( ~ ( rr(X,Y)
                            & cowlThing(Y) )
                      <=> ~ ~ ( ~ cowlThing(Y)
                              | ~ rr(X,Y) ) )),
                      rewrite(
                        ( ~ ~ ( ~ cowlThing(Y)
                              | ~ rr(X,Y) )
                      <=> ( ~ cowlThing(Y)
                          | ~ rr(X,Y) ) )),
                      ( ~ ( rr(X,Y)
                          & cowlThing(Y) )
                    <=> ( ~ cowlThing(Y)
                        | ~ rr(X,Y) ) ))),
                ( ! [Y: $i] :
                    ~ ( rr(X,Y)
                      & cowlThing(Y) )
              <=> ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) )),
              ( ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ~ ( rf2(X,Y)
                      & cp2(Y) )
                | ! [Y: $i] :
                    ~ ( rf1(X,Y)
                      & cp1(Y) )
                | ! [Y: $i] :
                    ~ ( rr(X,Y)
                      & cowlThing(Y) ) )
            <=> ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) )),
            rewrite(
              ( ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) )
            <=> ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) )),
            ( ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ~ ( rf2(X,Y)
                    & cp2(Y) )
              | ! [Y: $i] :
                  ~ ( rf1(X,Y)
                    & cp1(Y) )
              | ! [Y: $i] :
                  ~ ( rr(X,Y)
                    & cowlThing(Y) ) )
          <=> ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) )),
          ( ( ( ~ cUnsatisfiable(X)
              | ( rf2(X,tptp_fun_Y_0(X))
                & cp2(tptp_fun_Y_0(X))
                & rf1(X,tptp_fun_Y_1(X))
                & cp1(tptp_fun_Y_1(X))
                & rr(X,tptp_fun_Y_2(X))
                & cowlThing(tptp_fun_Y_2(X)) ) )
            & ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ~ ( rf2(X,Y)
                    & cp2(Y) )
              | ! [Y: $i] :
                  ~ ( rf1(X,Y)
                    & cp1(Y) )
              | ! [Y: $i] :
                  ~ ( rr(X,Y)
                    & cowlThing(Y) ) ) )
        <=> ( ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            & ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) ) )),
        rewrite(
          ( ( ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            & ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) )
        <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                  | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                      | ~ cp2(tptp_fun_Y_0(X))
                      | ~ rf1(X,tptp_fun_Y_1(X))
                      | ~ cp1(tptp_fun_Y_1(X))
                      | ~ rr(X,tptp_fun_Y_2(X))
                      | ~ cowlThing(tptp_fun_Y_2(X)) ) )
              | ~ ( cUnsatisfiable(X)
                  | ! [Y: $i] :
                      ( ~ cp2(Y)
                      | ~ rf2(X,Y) )
                  | ! [Y: $i] :
                      ( ~ cp1(Y)
                      | ~ rf1(X,Y) )
                  | ! [Y: $i] :
                      ( ~ cowlThing(Y)
                      | ~ rr(X,Y) ) ) ) )),
        ( ( ( ~ cUnsatisfiable(X)
            | ( rf2(X,tptp_fun_Y_0(X))
              & cp2(tptp_fun_Y_0(X))
              & rf1(X,tptp_fun_Y_1(X))
              & cp1(tptp_fun_Y_1(X))
              & rr(X,tptp_fun_Y_2(X))
              & cowlThing(tptp_fun_Y_2(X)) ) )
          & ( cUnsatisfiable(X)
            | ! [Y: $i] :
                ~ ( rf2(X,Y)
                  & cp2(Y) )
            | ! [Y: $i] :
                ~ ( rf1(X,Y)
                  & cp1(Y) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & cowlThing(Y) ) ) )
      <=> ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(41,plain,
    ( ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( rf2(X,tptp_fun_Y_0(X))
            & cp2(tptp_fun_Y_0(X))
            & rf1(X,tptp_fun_Y_1(X))
            & cp1(tptp_fun_Y_1(X))
            & rr(X,tptp_fun_Y_2(X))
            & cowlThing(tptp_fun_Y_2(X)) ) )
        & ( cUnsatisfiable(X)
          | ! [Y: $i] :
              ~ ( rf2(X,Y)
                & cp2(Y) )
          | ! [Y: $i] :
              ~ ( rf1(X,Y)
                & cp1(Y) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & cowlThing(Y) ) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cUnsatisfiable(X)
              | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                  | ~ cp2(tptp_fun_Y_0(X))
                  | ~ rf1(X,tptp_fun_Y_1(X))
                  | ~ cp1(tptp_fun_Y_1(X))
                  | ~ rr(X,tptp_fun_Y_2(X))
                  | ~ cowlThing(tptp_fun_Y_2(X)) ) )
          | ~ ( cUnsatisfiable(X)
              | ! [Y: $i] :
                  ( ~ cp2(Y)
                  | ~ rf2(X,Y) )
              | ! [Y: $i] :
                  ( ~ cp1(Y)
                  | ~ rf1(X,Y) )
              | ! [Y: $i] :
                  ( ~ cowlThing(Y)
                  | ~ rr(X,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[40]) ).

tff(42,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ( ~ cUnsatisfiable(X)
            | ( rf2(X,tptp_fun_Y_0(X))
              & cp2(tptp_fun_Y_0(X))
              & rf1(X,tptp_fun_Y_1(X))
              & cp1(tptp_fun_Y_1(X))
              & rr(X,tptp_fun_Y_2(X))
              & cowlThing(tptp_fun_Y_2(X)) ) )
          & ( cUnsatisfiable(X)
            | ! [Y: $i] :
                ~ ( rf2(X,Y)
                  & cp2(Y) )
            | ! [Y: $i] :
                ~ ( rf1(X,Y)
                  & cp1(Y) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & cowlThing(Y) ) ) )
      <=> ( ( ~ cUnsatisfiable(X)
            | ( rf2(X,tptp_fun_Y_0(X))
              & cp2(tptp_fun_Y_0(X))
              & rf1(X,tptp_fun_Y_1(X))
              & cp1(tptp_fun_Y_1(X))
              & rr(X,tptp_fun_Y_2(X))
              & cowlThing(tptp_fun_Y_2(X)) ) )
          & ( cUnsatisfiable(X)
            | ! [Y: $i] :
                ~ ( rf2(X,Y)
                  & cp2(Y) )
            | ! [Y: $i] :
                ~ ( rf1(X,Y)
                  & cp1(Y) )
            | ! [Y: $i] :
                ~ ( rr(X,Y)
                  & cowlThing(Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(43,plain,
    ( ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( rf2(X,tptp_fun_Y_0(X))
            & cp2(tptp_fun_Y_0(X))
            & rf1(X,tptp_fun_Y_1(X))
            & cp1(tptp_fun_Y_1(X))
            & rr(X,tptp_fun_Y_2(X))
            & cowlThing(tptp_fun_Y_2(X)) ) )
        & ( cUnsatisfiable(X)
          | ! [Y: $i] :
              ~ ( rf2(X,Y)
                & cp2(Y) )
          | ! [Y: $i] :
              ~ ( rf1(X,Y)
                & cp1(Y) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & cowlThing(Y) ) ) )
  <=> ! [X: $i] :
        ( ( ~ cUnsatisfiable(X)
          | ( rf2(X,tptp_fun_Y_0(X))
            & cp2(tptp_fun_Y_0(X))
            & rf1(X,tptp_fun_Y_1(X))
            & cp1(tptp_fun_Y_1(X))
            & rr(X,tptp_fun_Y_2(X))
            & cowlThing(tptp_fun_Y_2(X)) ) )
        & ( cUnsatisfiable(X)
          | ! [Y: $i] :
              ~ ( rf2(X,Y)
                & cp2(Y) )
          | ! [Y: $i] :
              ~ ( rf1(X,Y)
                & cp1(Y) )
          | ! [Y: $i] :
              ~ ( rr(X,Y)
                & cowlThing(Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,plain,
    ( ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ? [Y: $i] :
              ( rf2(X,Y)
              & cp2(Y) )
          & ? [Y: $i] :
              ( rf1(X,Y)
              & cp1(Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & cowlThing(Y) ) ) )
  <=> ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ? [Y: $i] :
              ( rf2(X,Y)
              & cp2(Y) )
          & ? [Y: $i] :
              ( rf1(X,Y)
              & cp1(Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & cowlThing(Y) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cUnsatisfiable(X)
        <=> ( ? [Y: $i] :
                ( rf2(X,Y)
                & cp2(Y) )
            & ? [Y: $i] :
                ( rf1(X,Y)
                & cp1(Y) )
            & ? [Y: $i] :
                ( rr(X,Y)
                & cowlThing(Y) ) ) )
      <=> ( cUnsatisfiable(X)
        <=> ( ? [Y: $i] :
                ( rf2(X,Y)
                & cp2(Y) )
            & ? [Y: $i] :
                ( rf1(X,Y)
                & cp1(Y) )
            & ? [Y: $i] :
                ( rr(X,Y)
                & cowlThing(Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(46,plain,
    ( ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ? [Y: $i] :
              ( rf2(X,Y)
              & cp2(Y) )
          & ? [Y: $i] :
              ( rf1(X,Y)
              & cp1(Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & cowlThing(Y) ) ) )
  <=> ! [X: $i] :
        ( cUnsatisfiable(X)
      <=> ( ? [Y: $i] :
              ( rf2(X,Y)
              & cp2(Y) )
          & ? [Y: $i] :
              ( rf1(X,Y)
              & cp1(Y) )
          & ? [Y: $i] :
              ( rr(X,Y)
              & cowlThing(Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[45]) ).

tff(47,axiom,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y: $i] :
            ( rf2(X,Y)
            & cp2(Y) )
        & ? [Y: $i] :
            ( rf1(X,Y)
            & cp1(Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & cowlThing(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).

tff(48,plain,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y: $i] :
            ( rf2(X,Y)
            & cp2(Y) )
        & ? [Y: $i] :
            ( rf1(X,Y)
            & cp1(Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & cowlThing(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ! [X: $i] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y: $i] :
            ( rf2(X,Y)
            & cp2(Y) )
        & ? [Y: $i] :
            ( rf1(X,Y)
            & cp1(Y) )
        & ? [Y: $i] :
            ( rr(X,Y)
            & cowlThing(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[48,44]) ).

tff(50,plain,
    ! [X: $i] :
      ( ( ~ cUnsatisfiable(X)
        | ( rf2(X,tptp_fun_Y_0(X))
          & cp2(tptp_fun_Y_0(X))
          & rf1(X,tptp_fun_Y_1(X))
          & cp1(tptp_fun_Y_1(X))
          & rr(X,tptp_fun_Y_2(X))
          & cowlThing(tptp_fun_Y_2(X)) ) )
      & ( cUnsatisfiable(X)
        | ! [Y: $i] :
            ~ ( rf2(X,Y)
              & cp2(Y) )
        | ! [Y: $i] :
            ~ ( rf1(X,Y)
              & cp1(Y) )
        | ! [Y: $i] :
            ~ ( rr(X,Y)
              & cowlThing(Y) ) ) ),
    inference(skolemize,[status(sab)],[49]) ).

tff(51,plain,
    ! [X: $i] :
      ( ( ~ cUnsatisfiable(X)
        | ( rf2(X,tptp_fun_Y_0(X))
          & cp2(tptp_fun_Y_0(X))
          & rf1(X,tptp_fun_Y_1(X))
          & cp1(tptp_fun_Y_1(X))
          & rr(X,tptp_fun_Y_2(X))
          & cowlThing(tptp_fun_Y_2(X)) ) )
      & ( cUnsatisfiable(X)
        | ! [Y: $i] :
            ~ ( rf2(X,Y)
              & cp2(Y) )
        | ! [Y: $i] :
            ~ ( rf1(X,Y)
              & cp1(Y) )
        | ! [Y: $i] :
            ~ ( rr(X,Y)
              & cowlThing(Y) ) ) ),
    inference(modus_ponens,[status(thm)],[50,43]) ).

tff(52,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cUnsatisfiable(X)
            | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                | ~ cp2(tptp_fun_Y_0(X))
                | ~ rf1(X,tptp_fun_Y_1(X))
                | ~ cp1(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_2(X))
                | ~ cowlThing(tptp_fun_Y_2(X)) ) )
        | ~ ( cUnsatisfiable(X)
            | ! [Y: $i] :
                ( ~ cp2(Y)
                | ~ rf2(X,Y) )
            | ! [Y: $i] :
                ( ~ cp1(Y)
                | ~ rf1(X,Y) )
            | ! [Y: $i] :
                ( ~ cowlThing(Y)
                | ~ rr(X,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[51,41]) ).

tff(53,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cUnsatisfiable(X)
            | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                | ~ cp2(tptp_fun_Y_0(X))
                | ~ rf1(X,tptp_fun_Y_1(X))
                | ~ cp1(tptp_fun_Y_1(X))
                | ~ rr(X,tptp_fun_Y_2(X))
                | ~ cowlThing(tptp_fun_Y_2(X)) ) )
        | ~ ( cUnsatisfiable(X)
            | ! [Y: $i] :
                ( ~ cp2(Y)
                | ~ rf2(X,Y) )
            | ! [Y: $i] :
                ( ~ cp1(Y)
                | ~ rf1(X,Y) )
            | ! [Y: $i] :
                ( ~ cowlThing(Y)
                | ~ rr(X,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[52,39]) ).

tff(54,plain,
    ( ~ ! [X: $i] :
          ~ ( ~ ( ~ cUnsatisfiable(X)
                | ~ ( ~ rf2(X,tptp_fun_Y_0(X))
                    | ~ cp2(tptp_fun_Y_0(X))
                    | ~ rf1(X,tptp_fun_Y_1(X))
                    | ~ cp1(tptp_fun_Y_1(X))
                    | ~ rr(X,tptp_fun_Y_2(X))
                    | ~ cowlThing(tptp_fun_Y_2(X)) ) )
            | ~ ( cUnsatisfiable(X)
                | ! [Y: $i] :
                    ( ~ cp2(Y)
                    | ~ rf2(X,Y) )
                | ! [Y: $i] :
                    ( ~ cp1(Y)
                    | ~ rf1(X,Y) )
                | ! [Y: $i] :
                    ( ~ cowlThing(Y)
                    | ~ rr(X,Y) ) ) )
    | ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
            | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
                | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
                | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
                | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
                | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
                | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) )
        | ~ ( cUnsatisfiable(i2003_11_14_17_21_30578)
            | ! [Y: $i] :
                ( ~ cp2(Y)
                | ~ rf2(i2003_11_14_17_21_30578,Y) )
            | ! [Y: $i] :
                ( ~ cp1(Y)
                | ~ rf1(i2003_11_14_17_21_30578,Y) )
            | ! [Y: $i] :
                ( ~ cowlThing(Y)
                | ~ rr(i2003_11_14_17_21_30578,Y) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(55,plain,
    ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
          | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
              | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
              | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
              | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
              | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
              | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) )
      | ~ ( cUnsatisfiable(i2003_11_14_17_21_30578)
          | ! [Y: $i] :
              ( ~ cp2(Y)
              | ~ rf2(i2003_11_14_17_21_30578,Y) )
          | ! [Y: $i] :
              ( ~ cp1(Y)
              | ~ rf1(i2003_11_14_17_21_30578,Y) )
          | ! [Y: $i] :
              ( ~ cowlThing(Y)
              | ~ rr(i2003_11_14_17_21_30578,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[54,53]) ).

tff(56,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
        | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
            | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) )
    | ~ ( cUnsatisfiable(i2003_11_14_17_21_30578)
        | ! [Y: $i] :
            ( ~ cp2(Y)
            | ~ rf2(i2003_11_14_17_21_30578,Y) )
        | ! [Y: $i] :
            ( ~ cp1(Y)
            | ~ rf1(i2003_11_14_17_21_30578,Y) )
        | ! [Y: $i] :
            ( ~ cowlThing(Y)
            | ~ rr(i2003_11_14_17_21_30578,Y) ) )
    | ~ cUnsatisfiable(i2003_11_14_17_21_30578)
    | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
        | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(tautology,[status(thm)],]) ).

tff(57,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
    | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
        | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(unit_resolution,[status(thm)],[56,55]) ).

tff(58,plain,
    ( cUnsatisfiable(i2003_11_14_17_21_30578)
  <=> cUnsatisfiable(i2003_11_14_17_21_30578) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,axiom,
    cUnsatisfiable(i2003_11_14_17_21_30578),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).

tff(60,plain,
    cUnsatisfiable(i2003_11_14_17_21_30578),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
        | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
            | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) )
    | ~ cUnsatisfiable(i2003_11_14_17_21_30578)
    | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
        | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(tautology,[status(thm)],]) ).

tff(62,plain,
    ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_30578)
        | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
            | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) )
    | ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
        | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(unit_resolution,[status(thm)],[61,60]) ).

tff(63,plain,
    ~ ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(unit_resolution,[status(thm)],[62,57]) ).

tff(64,plain,
    ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(tautology,[status(thm)],]) ).

tff(65,plain,
    rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[64,63]) ).

tff(66,plain,
    ^ [X: $i,Y: $i] :
      refl(
        ( ( ~ rr(X,Y)
          | rf2(X,Y) )
      <=> ( ~ rr(X,Y)
          | rf2(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(67,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf2(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf2(X,Y) ) ),
    inference(quant_intro,[status(thm)],[66]) ).

tff(68,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf2(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf2(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ^ [X: $i,Y: $i] :
      rewrite(
        ( ( rr(X,Y)
         => rf2(X,Y) )
      <=> ( ~ rr(X,Y)
          | rf2(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(70,plain,
    ( ! [X: $i,Y: $i] :
        ( rr(X,Y)
       => rf2(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf2(X,Y) ) ),
    inference(quant_intro,[status(thm)],[69]) ).

tff(71,axiom,
    ! [X: $i,Y: $i] :
      ( rr(X,Y)
     => rf2(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).

tff(72,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf2(X,Y) ),
    inference(modus_ponens,[status(thm)],[71,70]) ).

tff(73,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf2(X,Y) ),
    inference(modus_ponens,[status(thm)],[72,68]) ).

tff(74,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf2(X,Y) ),
    inference(skolemize,[status(sab)],[73]) ).

tff(75,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf2(X,Y) ),
    inference(modus_ponens,[status(thm)],[74,67]) ).

tff(76,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ rr(X,Y)
            | rf2(X,Y) )
      | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ rr(X,Y)
            | rf2(X,Y) )
      | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(77,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ rr(X,Y)
          | rf2(X,Y) )
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(78,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ rr(X,Y)
          | rf2(X,Y) )
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(modus_ponens,[status(thm)],[77,76]) ).

tff(79,plain,
    rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[78,75,65]) ).

tff(80,plain,
    ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578)) ),
    inference(tautology,[status(thm)],]) ).

tff(81,plain,
    rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[80,63]) ).

tff(82,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(83,plain,
    ( ( ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(monotonicity,[status(thm)],[83]) ).

tff(85,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf2(i2003_11_14_17_21_30578,Y1)
            | ~ rf2(i2003_11_14_17_21_30578,Y0) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
      | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(transitivity,[status(thm)],[84,82]) ).

tff(86,plain,
    ( ~ ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(i2003_11_14_17_21_30578,Y1)
          | ~ rf2(i2003_11_14_17_21_30578,Y0) )
    | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
    | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(87,plain,
    ( ~ ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf2(i2003_11_14_17_21_30578,Y1)
          | ~ rf2(i2003_11_14_17_21_30578,Y0) )
    | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578) )
    | ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(modus_ponens,[status(thm)],[86,85]) ).

tff(88,plain,
    tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_0(i2003_11_14_17_21_30578),
    inference(unit_resolution,[status(thm)],[87,81,79,34]) ).

tff(89,plain,
    tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578),
    inference(symmetry,[status(thm)],[88]) ).

tff(90,plain,
    ( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578)))
  <=> ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))) ),
    inference(monotonicity,[status(thm)],[89]) ).

tff(91,plain,
    ( ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578)))
  <=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))) ),
    inference(symmetry,[status(thm)],[90]) ).

tff(92,plain,
    ^ [X: $i] :
      refl(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(93,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[92]) ).

tff(94,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(95,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[94]) ).

tff(96,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) ) ),
    inference(transitivity,[status(thm)],[95,93]) ).

tff(97,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ~ ( rf1(X,Y0)
                  & rf1(X,Y1) )
              | ( Y0 = Y1 ) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(98,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf1(X,Y0)
                & rf1(X,Y1) )
            | ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(X,Y1)
            | ~ rf1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[97]) ).

tff(99,plain,
    ( ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf1(X,Y0)
                & rf1(X,Y1) )
            | ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf1(X,Y0)
                & rf1(X,Y1) )
            | ( Y0 = Y1 ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(100,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          quant_intro(
            proof_bind(
              ^ [Y0: $i,Y1: $i] :
                rewrite(
                  ( ( ( rf1(X,Y0)
                      & rf1(X,Y1) )
                   => ( Y0 = Y1 ) )
                <=> ( ~ ( rf1(X,Y0)
                        & rf1(X,Y1) )
                    | ( Y0 = Y1 ) ) ))),
            ( ! [Y0: $i,Y1: $i] :
                ( ( rf1(X,Y0)
                  & rf1(X,Y1) )
               => ( Y0 = Y1 ) )
          <=> ! [Y0: $i,Y1: $i] :
                ( ~ ( rf1(X,Y0)
                    & rf1(X,Y1) )
                | ( Y0 = Y1 ) ) )),
          ( ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ( rf1(X,Y0)
                  & rf1(X,Y1) )
               => ( Y0 = Y1 ) ) )
        <=> ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ~ ( rf1(X,Y0)
                    & rf1(X,Y1) )
                | ( Y0 = Y1 ) ) ) )),
        rewrite(
          ( ( cowlThing(X)
           => ! [Y0: $i,Y1: $i] :
                ( ~ ( rf1(X,Y0)
                    & rf1(X,Y1) )
                | ( Y0 = Y1 ) ) )
        <=> ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ~ ( rf1(X,Y0)
                    & rf1(X,Y1) )
                | ( Y0 = Y1 ) ) ) )),
        ( ( cowlThing(X)
         => ! [Y0: $i,Y1: $i] :
              ( ( rf1(X,Y0)
                & rf1(X,Y1) )
             => ( Y0 = Y1 ) ) )
      <=> ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ~ ( rf1(X,Y0)
                  & rf1(X,Y1) )
              | ( Y0 = Y1 ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(101,plain,
    ( ! [X: $i] :
        ( cowlThing(X)
       => ! [Y0: $i,Y1: $i] :
            ( ( rf1(X,Y0)
              & rf1(X,Y1) )
           => ( Y0 = Y1 ) ) )
  <=> ! [X: $i] :
        ( ~ cowlThing(X)
        | ! [Y0: $i,Y1: $i] :
            ( ~ ( rf1(X,Y0)
                & rf1(X,Y1) )
            | ( Y0 = Y1 ) ) ) ),
    inference(quant_intro,[status(thm)],[100]) ).

tff(102,axiom,
    ! [X: $i] :
      ( cowlThing(X)
     => ! [Y0: $i,Y1: $i] :
          ( ( rf1(X,Y0)
            & rf1(X,Y1) )
         => ( Y0 = Y1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).

tff(103,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf1(X,Y0)
              & rf1(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(modus_ponens,[status(thm)],[102,101]) ).

tff(104,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf1(X,Y0)
              & rf1(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(modus_ponens,[status(thm)],[103,99]) ).

tff(105,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ~ ( rf1(X,Y0)
              & rf1(X,Y1) )
          | ( Y0 = Y1 ) ) ),
    inference(skolemize,[status(sab)],[104]) ).

tff(106,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(X,Y1)
          | ~ rf1(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[105,98]) ).

tff(107,plain,
    ! [X: $i] :
      ( ~ cowlThing(X)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(X,Y1)
          | ~ rf1(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[106,96]) ).

tff(108,plain,
    ( ( ~ ! [X: $i] :
            ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ( Y0 = Y1 )
                | ~ rf1(X,Y1)
                | ~ rf1(X,Y0) ) )
      | ~ cowlThing(i2003_11_14_17_21_30578)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(i2003_11_14_17_21_30578,Y1)
          | ~ rf1(i2003_11_14_17_21_30578,Y0) ) )
  <=> ( ~ ! [X: $i] :
            ( ~ cowlThing(X)
            | ! [Y0: $i,Y1: $i] :
                ( ( Y0 = Y1 )
                | ~ rf1(X,Y1)
                | ~ rf1(X,Y0) ) )
      | ~ cowlThing(i2003_11_14_17_21_30578)
      | ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(i2003_11_14_17_21_30578,Y1)
          | ~ rf1(i2003_11_14_17_21_30578,Y0) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,plain,
    ( ~ ! [X: $i] :
          ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) )
    | ~ cowlThing(i2003_11_14_17_21_30578)
    | ! [Y0: $i,Y1: $i] :
        ( ( Y0 = Y1 )
        | ~ rf1(i2003_11_14_17_21_30578,Y1)
        | ~ rf1(i2003_11_14_17_21_30578,Y0) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(110,plain,
    ( ~ ! [X: $i] :
          ( ~ cowlThing(X)
          | ! [Y0: $i,Y1: $i] :
              ( ( Y0 = Y1 )
              | ~ rf1(X,Y1)
              | ~ rf1(X,Y0) ) )
    | ~ cowlThing(i2003_11_14_17_21_30578)
    | ! [Y0: $i,Y1: $i] :
        ( ( Y0 = Y1 )
        | ~ rf1(i2003_11_14_17_21_30578,Y1)
        | ~ rf1(i2003_11_14_17_21_30578,Y0) ) ),
    inference(modus_ponens,[status(thm)],[109,108]) ).

tff(111,plain,
    ! [Y0: $i,Y1: $i] :
      ( ( Y0 = Y1 )
      | ~ rf1(i2003_11_14_17_21_30578,Y1)
      | ~ rf1(i2003_11_14_17_21_30578,Y0) ),
    inference(unit_resolution,[status(thm)],[110,107,14]) ).

tff(112,plain,
    ^ [X: $i,Y: $i] :
      refl(
        ( ( ~ rr(X,Y)
          | rf1(X,Y) )
      <=> ( ~ rr(X,Y)
          | rf1(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(113,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf1(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf1(X,Y) ) ),
    inference(quant_intro,[status(thm)],[112]) ).

tff(114,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf1(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf1(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(115,plain,
    ^ [X: $i,Y: $i] :
      rewrite(
        ( ( rr(X,Y)
         => rf1(X,Y) )
      <=> ( ~ rr(X,Y)
          | rf1(X,Y) ) )),
    inference(bind,[status(th)],]) ).

tff(116,plain,
    ( ! [X: $i,Y: $i] :
        ( rr(X,Y)
       => rf1(X,Y) )
  <=> ! [X: $i,Y: $i] :
        ( ~ rr(X,Y)
        | rf1(X,Y) ) ),
    inference(quant_intro,[status(thm)],[115]) ).

tff(117,axiom,
    ! [X: $i,Y: $i] :
      ( rr(X,Y)
     => rf1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).

tff(118,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf1(X,Y) ),
    inference(modus_ponens,[status(thm)],[117,116]) ).

tff(119,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf1(X,Y) ),
    inference(modus_ponens,[status(thm)],[118,114]) ).

tff(120,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf1(X,Y) ),
    inference(skolemize,[status(sab)],[119]) ).

tff(121,plain,
    ! [X: $i,Y: $i] :
      ( ~ rr(X,Y)
      | rf1(X,Y) ),
    inference(modus_ponens,[status(thm)],[120,113]) ).

tff(122,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ rr(X,Y)
            | rf1(X,Y) )
      | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ rr(X,Y)
            | rf1(X,Y) )
      | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(123,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ rr(X,Y)
          | rf1(X,Y) )
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(124,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ rr(X,Y)
          | rf1(X,Y) )
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(modus_ponens,[status(thm)],[123,122]) ).

tff(125,plain,
    rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[124,121,65]) ).

tff(126,plain,
    ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578)) ),
    inference(tautology,[status(thm)],]) ).

tff(127,plain,
    rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[126,63]) ).

tff(128,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(129,plain,
    ( ( ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(130,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) ) ),
    inference(monotonicity,[status(thm)],[129]) ).

tff(131,plain,
    ( ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [Y0: $i,Y1: $i] :
            ( ( Y0 = Y1 )
            | ~ rf1(i2003_11_14_17_21_30578,Y1)
            | ~ rf1(i2003_11_14_17_21_30578,Y0) )
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
      | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) ) ),
    inference(transitivity,[status(thm)],[130,128]) ).

tff(132,plain,
    ( ~ ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(i2003_11_14_17_21_30578,Y1)
          | ~ rf1(i2003_11_14_17_21_30578,Y0) )
    | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) )
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(133,plain,
    ( ~ ! [Y0: $i,Y1: $i] :
          ( ( Y0 = Y1 )
          | ~ rf1(i2003_11_14_17_21_30578,Y1)
          | ~ rf1(i2003_11_14_17_21_30578,Y0) )
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ( tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578) ) ),
    inference(modus_ponens,[status(thm)],[132,131]) ).

tff(134,plain,
    tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578),
    inference(unit_resolution,[status(thm)],[133,127,125,111]) ).

tff(135,plain,
    tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578),
    inference(symmetry,[status(thm)],[134]) ).

tff(136,plain,
    tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)) = tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578)),
    inference(monotonicity,[status(thm)],[135]) ).

tff(137,plain,
    ( ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))
  <=> ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))) ),
    inference(monotonicity,[status(thm)],[135,136]) ).

tff(138,plain,
    ^ [X: $i] :
      refl(
        ( ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
      <=> ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(139,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[138]) ).

tff(140,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
      <=> ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(141,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[140]) ).

tff(142,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
    inference(transitivity,[status(thm)],[141,139]) ).

tff(143,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) )
          <=> ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
          ( ( ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
            & ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
        <=> ( ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
            & ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
        rewrite(
          ( ( ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
            & ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
        <=> ~ ( ~ ( ~ cp2xcomp(X)
                  | ra_Px1(X,tptp_fun_Y0_4(X)) )
              | ~ ( cp2xcomp(X)
                  | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
        ( ( ( ~ cp2xcomp(X)
            | ra_Px1(X,tptp_fun_Y0_4(X)) )
          & ( cp2xcomp(X)
            | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
      <=> ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(144,plain,
    ( ! [X: $i] :
        ( ( ~ cp2xcomp(X)
          | ra_Px1(X,tptp_fun_Y0_4(X)) )
        & ( cp2xcomp(X)
          | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2xcomp(X)
              | ra_Px1(X,tptp_fun_Y0_4(X)) )
          | ~ ( cp2xcomp(X)
              | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
    inference(quant_intro,[status(thm)],[143]) ).

tff(145,plain,
    ( ! [X: $i] :
        ( cp2xcomp(X)
      <=> ? [Y0: $i] : ra_Px1(X,Y0) )
  <=> ! [X: $i] :
        ( cp2xcomp(X)
      <=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(146,axiom,
    ! [X: $i] :
      ( cp2xcomp(X)
    <=> ? [Y0: $i] : ra_Px1(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).

tff(147,plain,
    ! [X: $i] :
      ( cp2xcomp(X)
    <=> ? [Y0: $i] : ra_Px1(X,Y0) ),
    inference(modus_ponens,[status(thm)],[146,145]) ).

tff(148,plain,
    ! [X: $i] :
      ( ( ~ cp2xcomp(X)
        | ra_Px1(X,tptp_fun_Y0_4(X)) )
      & ( cp2xcomp(X)
        | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
    inference(skolemize,[status(sab)],[147]) ).

tff(149,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cp2xcomp(X)
            | ra_Px1(X,tptp_fun_Y0_4(X)) )
        | ~ ( cp2xcomp(X)
            | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[148,144]) ).

tff(150,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cp2xcomp(X)
            | ra_Px1(X,tptp_fun_Y0_4(X)) )
        | ~ ( cp2xcomp(X)
            | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
    inference(modus_ponens,[status(thm)],[149,142]) ).

tff(151,plain,
    ( ~ ! [X: $i] :
          ~ ( ~ ( ~ cp2xcomp(X)
                | ra_Px1(X,tptp_fun_Y0_4(X)) )
            | ~ ( cp2xcomp(X)
                | ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
    | ~ ( ~ ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) )
        | ~ ( cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
            | ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),Y0) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(152,plain,
    ~ ( ~ ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
          | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) )
      | ~ ( cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
          | ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),Y0) ) ),
    inference(unit_resolution,[status(thm)],[151,150]) ).

tff(153,plain,
    ( ~ ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) )
    | ~ ( cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),Y0) )
    | ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) ),
    inference(tautology,[status(thm)],]) ).

tff(154,plain,
    ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) ),
    inference(unit_resolution,[status(thm)],[153,152]) ).

tff(155,plain,
    ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)) ),
    inference(tautology,[status(thm)],]) ).

tff(156,plain,
    cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[155,63]) ).

tff(157,plain,
    ^ [X: $i] :
      refl(
        ( ( cp2xcomp(X)
          | ~ cp1(X) )
      <=> ( cp2xcomp(X)
          | ~ cp1(X) ) )),
    inference(bind,[status(th)],]) ).

tff(158,plain,
    ( ! [X: $i] :
        ( cp2xcomp(X)
        | ~ cp1(X) )
  <=> ! [X: $i] :
        ( cp2xcomp(X)
        | ~ cp1(X) ) ),
    inference(quant_intro,[status(thm)],[157]) ).

tff(159,plain,
    ( ! [X: $i] :
        ( cp2xcomp(X)
        | ~ cp1(X) )
  <=> ! [X: $i] :
        ( cp2xcomp(X)
        | ~ cp1(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(160,plain,
    ^ [X: $i] :
      rewrite(
        ( ( cp1(X)
         => cp2xcomp(X) )
      <=> ( cp2xcomp(X)
          | ~ cp1(X) ) )),
    inference(bind,[status(th)],]) ).

tff(161,plain,
    ( ! [X: $i] :
        ( cp1(X)
       => cp2xcomp(X) )
  <=> ! [X: $i] :
        ( cp2xcomp(X)
        | ~ cp1(X) ) ),
    inference(quant_intro,[status(thm)],[160]) ).

tff(162,axiom,
    ! [X: $i] :
      ( cp1(X)
     => cp2xcomp(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).

tff(163,plain,
    ! [X: $i] :
      ( cp2xcomp(X)
      | ~ cp1(X) ),
    inference(modus_ponens,[status(thm)],[162,161]) ).

tff(164,plain,
    ! [X: $i] :
      ( cp2xcomp(X)
      | ~ cp1(X) ),
    inference(modus_ponens,[status(thm)],[163,159]) ).

tff(165,plain,
    ! [X: $i] :
      ( cp2xcomp(X)
      | ~ cp1(X) ),
    inference(skolemize,[status(sab)],[164]) ).

tff(166,plain,
    ! [X: $i] :
      ( cp2xcomp(X)
      | ~ cp1(X) ),
    inference(modus_ponens,[status(thm)],[165,158]) ).

tff(167,plain,
    ( ( ~ ! [X: $i] :
            ( cp2xcomp(X)
            | ~ cp1(X) )
      | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)) )
  <=> ( ~ ! [X: $i] :
            ( cp2xcomp(X)
            | ~ cp1(X) )
      | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
      | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(168,plain,
    ( ~ ! [X: $i] :
          ( cp2xcomp(X)
          | ~ cp1(X) )
    | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(169,plain,
    ( ~ ! [X: $i] :
          ( cp2xcomp(X)
          | ~ cp1(X) )
    | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)) ),
    inference(modus_ponens,[status(thm)],[168,167]) ).

tff(170,plain,
    cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[169,166,156]) ).

tff(171,plain,
    ( ~ ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) )
    | ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) ),
    inference(tautology,[status(thm)],]) ).

tff(172,plain,
    ( ~ ( ~ cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))
        | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) )
    | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) ),
    inference(unit_resolution,[status(thm)],[171,170]) ).

tff(173,plain,
    ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))),
    inference(unit_resolution,[status(thm)],[172,154]) ).

tff(174,plain,
    ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))),
    inference(modus_ponens,[status(thm)],[173,137]) ).

tff(175,plain,
    ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))),
    inference(modus_ponens,[status(thm)],[174,91]) ).

tff(176,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) )
      <=> ~ ( ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) )
            | ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
    inference(bind,[status(th)],]) ).

tff(177,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) )
          | ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
    inference(quant_intro,[status(thm)],[176]) ).

tff(178,plain,
    ^ [X: $i] :
      refl(
        ( ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) )
      <=> ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(179,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
    inference(quant_intro,[status(thm)],[178]) ).

tff(180,plain,
    ^ [X: $i] :
      rewrite(
        ( ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) )
      <=> ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(181,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
    inference(quant_intro,[status(thm)],[180]) ).

tff(182,plain,
    ( ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
    inference(transitivity,[status(thm)],[181,179]) ).

tff(183,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          <=> ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
          ( ( ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
            & ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
        <=> ( ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
            & ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
        rewrite(
          ( ( ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
            & ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) )
        <=> ~ ( ~ ( ~ cp2(X)
                  | ! [Y: $i] : ~ ra_Px1(X,Y) )
              | ~ ( cp2(X)
                  | ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
        ( ( ( ~ cp2(X)
            | ! [Y: $i] : ~ ra_Px1(X,Y) )
          & ( cp2(X)
            | ra_Px1(X,tptp_fun_Y_3(X)) ) )
      <=> ~ ( ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) )
            | ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(184,plain,
    ( ! [X: $i] :
        ( ( ~ cp2(X)
          | ! [Y: $i] : ~ ra_Px1(X,Y) )
        & ( cp2(X)
          | ra_Px1(X,tptp_fun_Y_3(X)) ) )
  <=> ! [X: $i] :
        ~ ( ~ ( ~ cp2(X)
              | ! [Y: $i] : ~ ra_Px1(X,Y) )
          | ~ ( cp2(X)
              | ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
    inference(quant_intro,[status(thm)],[183]) ).

tff(185,plain,
    ( ! [X: $i] :
        ( cp2(X)
      <=> ~ ? [Y: $i] : ra_Px1(X,Y) )
  <=> ! [X: $i] :
        ( cp2(X)
      <=> ~ ? [Y: $i] : ra_Px1(X,Y) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(186,axiom,
    ! [X: $i] :
      ( cp2(X)
    <=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).

tff(187,plain,
    ! [X: $i] :
      ( cp2(X)
    <=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
    inference(modus_ponens,[status(thm)],[186,185]) ).

tff(188,plain,
    ! [X: $i] :
      ( ( ~ cp2(X)
        | ! [Y: $i] : ~ ra_Px1(X,Y) )
      & ( cp2(X)
        | ra_Px1(X,tptp_fun_Y_3(X)) ) ),
    inference(skolemize,[status(sab)],[187]) ).

tff(189,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cp2(X)
            | ! [Y: $i] : ~ ra_Px1(X,Y) )
        | ~ ( cp2(X)
            | ra_Px1(X,tptp_fun_Y_3(X)) ) ),
    inference(modus_ponens,[status(thm)],[188,184]) ).

tff(190,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ cp2(X)
            | ! [Y: $i] : ~ ra_Px1(X,Y) )
        | ~ ( cp2(X)
            | ra_Px1(X,tptp_fun_Y_3(X)) ) ),
    inference(modus_ponens,[status(thm)],[189,182]) ).

tff(191,plain,
    ! [X: $i] :
      ~ ( ~ ( cp2(X)
            | ra_Px1(X,tptp_fun_Y_3(X)) )
        | ~ ( ~ cp2(X)
            | ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
    inference(modus_ponens,[status(thm)],[190,177]) ).

tff(192,plain,
    ( ~ ! [X: $i] :
          ~ ( ~ ( cp2(X)
                | ra_Px1(X,tptp_fun_Y_3(X)) )
            | ~ ( ~ cp2(X)
                | ! [Y: $i] : ~ ra_Px1(X,Y) ) )
    | ~ ( ~ ( cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))) )
        | ~ ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
            | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(193,plain,
    ~ ( ~ ( cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
          | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))) )
      | ~ ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
          | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ) ),
    inference(unit_resolution,[status(thm)],[192,191]) ).

tff(194,plain,
    ( ~ ( cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))) )
    | ~ ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) )
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ),
    inference(tautology,[status(thm)],]) ).

tff(195,plain,
    ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ),
    inference(unit_resolution,[status(thm)],[194,193]) ).

tff(196,plain,
    ( ~ rf2(i2003_11_14_17_21_30578,tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ~ rf1(i2003_11_14_17_21_30578,tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))
    | ~ rr(i2003_11_14_17_21_30578,tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | ~ cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))
    | cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578)) ),
    inference(tautology,[status(thm)],]) ).

tff(197,plain,
    cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578)),
    inference(unit_resolution,[status(thm)],[196,63]) ).

tff(198,plain,
    ( ~ ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) )
    | ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
    | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ),
    inference(tautology,[status(thm)],]) ).

tff(199,plain,
    ( ~ ( ~ cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))
        | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) )
    | ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y) ),
    inference(unit_resolution,[status(thm)],[198,197]) ).

tff(200,plain,
    ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y),
    inference(unit_resolution,[status(thm)],[199,195]) ).

tff(201,plain,
    ( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),Y)
    | ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(202,plain,
    ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578),tptp_fun_Y0_4(tptp_fun_Y_2(i2003_11_14_17_21_30578))),
    inference(unit_resolution,[status(thm)],[201,200]) ).

tff(203,plain,
    $false,
    inference(unit_resolution,[status(thm)],[202,175]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KRS115+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Sep  1 09:32:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.44  % SZS status Unsatisfiable
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------