TSTP Solution File: SYN719-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN719-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.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 : Thu Sep 29 23:57:04 EDT 2022

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Proof 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   74
% Syntax   : Number of formulae    :  120 (  32 unt;  36 typ;   0 def)
%            Number of atoms       :  476 (   0 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  677 ( 317   ~; 311   |;   0   &)
%                                         (  49 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :   32 (  32 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  21   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   30 (  30 usr;  15 con; 0-2 aty)
%            Number of variables   :  221 ( 201   !;   0   ?; 221   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p70_type,type,
    p70: ( $i * $i ) > $o ).

tff(f38_type,type,
    f38: ( $i * $i ) > $i ).

tff(f40_type,type,
    f40: ( $i * $i ) > $i ).

tff(c81_type,type,
    c81: $i ).

tff(f42_type,type,
    f42: ( $i * $i ) > $i ).

tff(c85_type,type,
    c85: $i ).

tff(f44_type,type,
    f44: ( $i * $i ) > $i ).

tff(f46_type,type,
    f46: ( $i * $i ) > $i ).

tff(c79_type,type,
    c79: $i ).

tff(c87_type,type,
    c87: $i ).

tff(f30_type,type,
    f30: ( $i * $i ) > $i ).

tff(f32_type,type,
    f32: ( $i * $i ) > $i ).

tff(f8_type,type,
    f8: ( $i * $i ) > $i ).

tff(c76_type,type,
    c76: $i ).

tff(c75_type,type,
    c75: $i ).

tff(c89_type,type,
    c89: $i ).

tff(c88_type,type,
    c88: $i ).

tff(p69_type,type,
    p69: ( $i * $i ) > $o ).

tff(f36_type,type,
    f36: ( $i * $i ) > $i ).

tff(c86_type,type,
    c86: $i ).

tff(p14_type,type,
    p14: ( $i * $i ) > $o ).

tff(f23_type,type,
    f23: ( $i * $i ) > $i ).

tff(f26_type,type,
    f26: ( $i * $i ) > $i ).

tff(c84_type,type,
    c84: $i ).

tff(p68_type,type,
    p68: ( $i * $i ) > $o ).

tff(f19_type,type,
    f19: ( $i * $i ) > $i ).

tff(f21_type,type,
    f21: ( $i * $i ) > $i ).

tff(c77_type,type,
    c77: $i ).

tff(c83_type,type,
    c83: $i ).

tff(p67_type,type,
    p67: ( $i * $i ) > $o ).

tff(c82_type,type,
    c82: $i ).

tff(f16_type,type,
    f16: ( $i * $i ) > $i ).

tff(c80_type,type,
    c80: $i ).

tff(p66_type,type,
    p66: ( $i * $i ) > $o ).

tff(f12_type,type,
    f12: ( $i * $i ) > $i ).

tff(c78_type,type,
    c78: $i ).

tff(1,plain,
    ^ [X13: $i] :
      refl(
        ( p14(X13,X13)
      <=> p14(X13,X13) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X13: $i] : p14(X13,X13)
  <=> ! [X13: $i] : p14(X13,X13) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X13: $i] : p14(X13,X13)
  <=> ! [X13: $i] : p14(X13,X13) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X13: $i] : p14(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_38) ).

tff(5,plain,
    ! [X13: $i] : p14(X13,X13),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X13: $i] : p14(X13,X13),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X13: $i] : p14(X13,X13),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X13: $i] : p14(X13,X13)
    | p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X20: $i] :
      refl(
        ( p14(f23(f26(c84,c85),X20),X20)
      <=> p14(f23(f26(c84,c85),X20),X20) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
  <=> ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
  <=> ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_45) ).

tff(14,plain,
    ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [X20: $i] : p14(f23(f26(c84,c85),X20),X20)
    | p14(f23(f26(c84,c85),c81),c81) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    p14(f23(f26(c84,c85),c81),c81),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      refl(
        ( ( ~ p14(X13,X15)
          | ~ p14(X13,X14)
          | p14(X14,X15) )
      <=> ( ~ p14(X13,X15)
          | ~ p14(X13,X14)
          | p14(X14,X15) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p14(X13,X15)
        | ~ p14(X13,X14)
        | p14(X14,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p14(X13,X15)
        | ~ p14(X13,X14)
        | p14(X14,X15) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p14(X13,X15)
        | ~ p14(X13,X14)
        | p14(X14,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p14(X13,X15)
        | ~ p14(X13,X14)
        | p14(X14,X15) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p14(X14,X15)
              | ~ p14(X13,X14) )
          <=> ( ~ p14(X13,X14)
              | p14(X14,X15) ) )),
          ( ( p14(X14,X15)
            | ~ p14(X13,X14)
            | ~ p14(X13,X15) )
        <=> ( ~ p14(X13,X14)
            | p14(X14,X15)
            | ~ p14(X13,X15) ) )),
        rewrite(
          ( ( ~ p14(X13,X14)
            | p14(X14,X15)
            | ~ p14(X13,X15) )
        <=> ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) ) )),
        ( ( p14(X14,X15)
          | ~ p14(X13,X14)
          | ~ p14(X13,X15) )
      <=> ( ~ p14(X13,X15)
          | ~ p14(X13,X14)
          | p14(X14,X15) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( p14(X14,X15)
        | ~ p14(X13,X14)
        | ~ p14(X13,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p14(X13,X15)
        | ~ p14(X13,X14)
        | p14(X14,X15) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,axiom,
    ! [X14: $i,X13: $i,X15: $i] :
      ( p14(X14,X15)
      | ~ p14(X13,X14)
      | ~ p14(X13,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_90) ).

tff(25,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p14(X13,X15)
      | ~ p14(X13,X14)
      | p14(X14,X15) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p14(X13,X15)
      | ~ p14(X13,X14)
      | p14(X14,X15) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p14(X13,X15)
      | ~ p14(X13,X14)
      | p14(X14,X15) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p14(X13,X15)
      | ~ p14(X13,X14)
      | p14(X14,X15) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81)) )
  <=> ( ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
    inference(monotonicity,[status(thm)],[30]) ).

tff(32,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p14(X13,X15)
            | ~ p14(X13,X14)
            | p14(X14,X15) )
      | ~ p14(f23(f26(c84,c85),c81),c81)
      | p14(c81,f23(f26(c84,c85),c81))
      | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ) ),
    inference(transitivity,[status(thm)],[31,29]) ).

tff(33,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p14(X13,X15)
          | ~ p14(X13,X14)
          | p14(X14,X15) )
    | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81))
    | ~ p14(f23(f26(c84,c85),c81),c81)
    | p14(c81,f23(f26(c84,c85),c81)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p14(X13,X15)
          | ~ p14(X13,X14)
          | p14(X14,X15) )
    | ~ p14(f23(f26(c84,c85),c81),c81)
    | p14(c81,f23(f26(c84,c85),c81))
    | ~ p14(f23(f26(c84,c85),c81),f23(f26(c84,c85),c81)) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    p14(c81,f23(f26(c84,c85),c81)),
    inference(unit_resolution,[status(thm)],[34,28,18,9]) ).

tff(36,plain,
    ^ [X222: $i,X224: $i,X221: $i,X223: $i] :
      refl(
        ( ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p66(f12(c78,c77),X221)
          | ~ p67(f16(c80,X224),c82)
          | p68(f19(f21(c83,c77),X221),X222) )
      <=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p66(f12(c78,c77),X221)
          | ~ p67(f16(c80,X224),c82)
          | p68(f19(f21(c83,c77),X221),X222) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p66(f12(c78,c77),X221)
        | ~ p67(f16(c80,X224),c82)
        | p68(f19(f21(c83,c77),X221),X222) )
  <=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p66(f12(c78,c77),X221)
        | ~ p67(f16(c80,X224),c82)
        | p68(f19(f21(c83,c77),X221),X222) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p66(f12(c78,c77),X221)
        | ~ p67(f16(c80,X224),c82)
        | p68(f19(f21(c83,c77),X221),X222) )
  <=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p66(f12(c78,c77),X221)
        | ~ p67(f16(c80,X224),c82)
        | p68(f19(f21(c83,c77),X221),X222) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ^ [X222: $i,X224: $i,X221: $i,X223: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  rewrite(
                    ( ( p68(f19(f21(c83,c77),X221),X222)
                      | ~ p67(f16(c80,X224),c82) )
                  <=> ( ~ p67(f16(c80,X224),c82)
                      | p68(f19(f21(c83,c77),X221),X222) ) )),
                  ( ( p68(f19(f21(c83,c77),X221),X222)
                    | ~ p67(f16(c80,X224),c82)
                    | ~ p66(f12(c78,c77),X221) )
                <=> ( ~ p67(f16(c80,X224),c82)
                    | p68(f19(f21(c83,c77),X221),X222)
                    | ~ p66(f12(c78,c77),X221) ) )),
                rewrite(
                  ( ( ~ p67(f16(c80,X224),c82)
                    | p68(f19(f21(c83,c77),X221),X222)
                    | ~ p66(f12(c78,c77),X221) )
                <=> ( ~ p66(f12(c78,c77),X221)
                    | ~ p67(f16(c80,X224),c82)
                    | p68(f19(f21(c83,c77),X221),X222) ) )),
                ( ( p68(f19(f21(c83,c77),X221),X222)
                  | ~ p67(f16(c80,X224),c82)
                  | ~ p66(f12(c78,c77),X221) )
              <=> ( ~ p66(f12(c78,c77),X221)
                  | ~ p67(f16(c80,X224),c82)
                  | p68(f19(f21(c83,c77),X221),X222) ) )),
              ( ( p68(f19(f21(c83,c77),X221),X222)
                | ~ p67(f16(c80,X224),c82)
                | ~ p66(f12(c78,c77),X221)
                | ~ p14(X222,f23(f26(c84,X223),X224)) )
            <=> ( ~ p66(f12(c78,c77),X221)
                | ~ p67(f16(c80,X224),c82)
                | p68(f19(f21(c83,c77),X221),X222)
                | ~ p14(X222,f23(f26(c84,X223),X224)) ) )),
            rewrite(
              ( ( ~ p66(f12(c78,c77),X221)
                | ~ p67(f16(c80,X224),c82)
                | p68(f19(f21(c83,c77),X221),X222)
                | ~ p14(X222,f23(f26(c84,X223),X224)) )
            <=> ( ~ p14(X222,f23(f26(c84,X223),X224))
                | ~ p66(f12(c78,c77),X221)
                | ~ p67(f16(c80,X224),c82)
                | p68(f19(f21(c83,c77),X221),X222) ) )),
            ( ( p68(f19(f21(c83,c77),X221),X222)
              | ~ p67(f16(c80,X224),c82)
              | ~ p66(f12(c78,c77),X221)
              | ~ p14(X222,f23(f26(c84,X223),X224)) )
          <=> ( ~ p14(X222,f23(f26(c84,X223),X224))
              | ~ p66(f12(c78,c77),X221)
              | ~ p67(f16(c80,X224),c82)
              | p68(f19(f21(c83,c77),X221),X222) ) )),
          ( ( p68(f19(f21(c83,c77),X221),X222)
            | ~ p67(f16(c80,X224),c82)
            | ~ p66(f12(c78,c77),X221)
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
        <=> ( ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222)
            | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) ) )),
        rewrite(
          ( ( ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222)
            | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
        <=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) ) )),
        ( ( p68(f19(f21(c83,c77),X221),X222)
          | ~ p67(f16(c80,X224),c82)
          | ~ p66(f12(c78,c77),X221)
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
      <=> ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p66(f12(c78,c77),X221)
          | ~ p67(f16(c80,X224),c82)
          | p68(f19(f21(c83,c77),X221),X222) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( p68(f19(f21(c83,c77),X221),X222)
        | ~ p67(f16(c80,X224),c82)
        | ~ p66(f12(c78,c77),X221)
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) )
  <=> ! [X222: $i,X224: $i,X221: $i,X223: $i] :
        ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
        | ~ p14(X222,f23(f26(c84,X223),X224))
        | ~ p66(f12(c78,c77),X221)
        | ~ p67(f16(c80,X224),c82)
        | p68(f19(f21(c83,c77),X221),X222) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,axiom,
    ! [X222: $i,X224: $i,X221: $i,X223: $i] :
      ( p68(f19(f21(c83,c77),X221),X222)
      | ~ p67(f16(c80,X224),c82)
      | ~ p66(f12(c78,c77),X221)
      | ~ p14(X222,f23(f26(c84,X223),X224))
      | ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p68_126) ).

tff(42,plain,
    ! [X222: $i,X224: $i,X221: $i,X223: $i] :
      ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(X222,f23(f26(c84,X223),X224))
      | ~ p66(f12(c78,c77),X221)
      | ~ p67(f16(c80,X224),c82)
      | p68(f19(f21(c83,c77),X221),X222) ),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ! [X222: $i,X224: $i,X221: $i,X223: $i] :
      ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(X222,f23(f26(c84,X223),X224))
      | ~ p66(f12(c78,c77),X221)
      | ~ p67(f16(c80,X224),c82)
      | p68(f19(f21(c83,c77),X221),X222) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ! [X222: $i,X224: $i,X221: $i,X223: $i] :
      ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(X222,f23(f26(c84,X223),X224))
      | ~ p66(f12(c78,c77),X221)
      | ~ p67(f16(c80,X224),c82)
      | p68(f19(f21(c83,c77),X221),X222) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [X222: $i,X224: $i,X221: $i,X223: $i] :
      ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(X222,f23(f26(c84,X223),X224))
      | ~ p66(f12(c78,c77),X221)
      | ~ p67(f16(c80,X224),c82)
      | p68(f19(f21(c83,c77),X221),X222) ),
    inference(modus_ponens,[status(thm)],[44,37]) ).

tff(46,plain,
    ( ~ p68(f19(f21(c83,c77),c79),c81)
  <=> ~ p68(f19(f21(c83,c77),c79),c81) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,axiom,
    ~ p68(f19(f21(c83,c77),c79),c81),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p68_46) ).

tff(48,plain,
    ~ p68(f19(f21(c83,c77),c79),c81),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    ( p67(f16(c80,c81),c82)
  <=> p67(f16(c80,c81),c82) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,axiom,
    p67(f16(c80,c81),c82),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p67_42) ).

tff(51,plain,
    p67(f16(c80,c81),c82),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    ( p66(f12(c78,c77),c79)
  <=> p66(f12(c78,c77),c79) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,axiom,
    p66(f12(c78,c77),c79),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p66_41) ).

tff(54,plain,
    p66(f12(c78,c77),c79),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    ( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | p68(f19(f21(c83,c77),c79),c81)
      | ~ p67(f16(c80,c81),c82)
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) )
  <=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | p68(f19(f21(c83,c77),c79),c81)
      | ~ p67(f16(c80,c81),c82)
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(56,plain,
    ( ( ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p67(f16(c80,c81),c82)
      | p68(f19(f21(c83,c77),c79),c81) )
  <=> ( p68(f19(f21(c83,c77),c79),c81)
      | ~ p67(f16(c80,c81),c82)
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(57,plain,
    ( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p67(f16(c80,c81),c82)
      | p68(f19(f21(c83,c77),c79),c81) )
  <=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | p68(f19(f21(c83,c77),c79),c81)
      | ~ p67(f16(c80,c81),c82)
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(monotonicity,[status(thm)],[56]) ).

tff(58,plain,
    ( ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p67(f16(c80,c81),c82)
      | p68(f19(f21(c83,c77),c79),c81) )
  <=> ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
            ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
            | ~ p14(X222,f23(f26(c84,X223),X224))
            | ~ p66(f12(c78,c77),X221)
            | ~ p67(f16(c80,X224),c82)
            | p68(f19(f21(c83,c77),X221),X222) )
      | p68(f19(f21(c83,c77),c79),c81)
      | ~ p67(f16(c80,c81),c82)
      | ~ p14(c81,f23(f26(c84,c85),c81))
      | ~ p66(f12(c78,c77),c79)
      | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(transitivity,[status(thm)],[57,55]) ).

tff(59,plain,
    ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
          ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p66(f12(c78,c77),X221)
          | ~ p67(f16(c80,X224),c82)
          | p68(f19(f21(c83,c77),X221),X222) )
    | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
    | ~ p14(c81,f23(f26(c84,c85),c81))
    | ~ p66(f12(c78,c77),c79)
    | ~ p67(f16(c80,c81),c82)
    | p68(f19(f21(c83,c77),c79),c81) ),
    inference(quant_inst,[status(thm)],]) ).

tff(60,plain,
    ( ~ ! [X222: $i,X224: $i,X221: $i,X223: $i] :
          ( ~ p69(f36(c86,f38(X223,f40(f42(f44(f46(c87,X221),X222),X223),X224))),f30(c88,f32(c89,f8(c75,c76))))
          | ~ p14(X222,f23(f26(c84,X223),X224))
          | ~ p66(f12(c78,c77),X221)
          | ~ p67(f16(c80,X224),c82)
          | p68(f19(f21(c83,c77),X221),X222) )
    | p68(f19(f21(c83,c77),c79),c81)
    | ~ p67(f16(c80,c81),c82)
    | ~ p14(c81,f23(f26(c84,c85),c81))
    | ~ p66(f12(c78,c77),c79)
    | ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    ~ p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))),
    inference(unit_resolution,[status(thm)],[60,54,51,48,45,35]) ).

tff(62,plain,
    ^ [X230: $i,X229: $i] :
      refl(
        ( ( p69(f36(c86,X229),X230)
          | ~ p70(X230,X229) )
      <=> ( p69(f36(c86,X229),X230)
          | ~ p70(X230,X229) ) )),
    inference(bind,[status(th)],]) ).

tff(63,plain,
    ( ! [X230: $i,X229: $i] :
        ( p69(f36(c86,X229),X230)
        | ~ p70(X230,X229) )
  <=> ! [X230: $i,X229: $i] :
        ( p69(f36(c86,X229),X230)
        | ~ p70(X230,X229) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,plain,
    ( ! [X230: $i,X229: $i] :
        ( p69(f36(c86,X229),X230)
        | ~ p70(X230,X229) )
  <=> ! [X230: $i,X229: $i] :
        ( p69(f36(c86,X229),X230)
        | ~ p70(X230,X229) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,axiom,
    ! [X230: $i,X229: $i] :
      ( p69(f36(c86,X229),X230)
      | ~ p70(X230,X229) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p69_52) ).

tff(66,plain,
    ! [X230: $i,X229: $i] :
      ( p69(f36(c86,X229),X230)
      | ~ p70(X230,X229) ),
    inference(modus_ponens,[status(thm)],[65,64]) ).

tff(67,plain,
    ! [X230: $i,X229: $i] :
      ( p69(f36(c86,X229),X230)
      | ~ p70(X230,X229) ),
    inference(skolemize,[status(sab)],[66]) ).

tff(68,plain,
    ! [X230: $i,X229: $i] :
      ( p69(f36(c86,X229),X230)
      | ~ p70(X230,X229) ),
    inference(modus_ponens,[status(thm)],[67,63]) ).

tff(69,plain,
    ( ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) )
  <=> ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ( p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
  <=> ( ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(71,plain,
    ( ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
  <=> ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(monotonicity,[status(thm)],[70]) ).

tff(72,plain,
    ( ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) )
  <=> ( ~ ! [X230: $i,X229: $i] :
            ( p69(f36(c86,X229),X230)
            | ~ p70(X230,X229) )
      | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
      | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ) ),
    inference(transitivity,[status(thm)],[71,69]) ).

tff(73,plain,
    ( ~ ! [X230: $i,X229: $i] :
          ( p69(f36(c86,X229),X230)
          | ~ p70(X230,X229) )
    | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76))))
    | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(74,plain,
    ( ~ ! [X230: $i,X229: $i] :
          ( p69(f36(c86,X229),X230)
          | ~ p70(X230,X229) )
    | ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81)))
    | p69(f36(c86,f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),f30(c88,f32(c89,f8(c75,c76)))) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    ~ p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))),
    inference(unit_resolution,[status(thm)],[74,68,61]) ).

tff(76,plain,
    ^ [X242: $i,X243: $i] :
      refl(
        ( p70(f30(c88,X242),f38(c85,X243))
      <=> p70(f30(c88,X242),f38(c85,X243)) )),
    inference(bind,[status(th)],]) ).

tff(77,plain,
    ( ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
  <=> ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)) ),
    inference(quant_intro,[status(thm)],[76]) ).

tff(78,plain,
    ( ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
  <=> ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,axiom,
    ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p70_43) ).

tff(80,plain,
    ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
    inference(modus_ponens,[status(thm)],[79,78]) ).

tff(81,plain,
    ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
    inference(skolemize,[status(sab)],[80]) ).

tff(82,plain,
    ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243)),
    inference(modus_ponens,[status(thm)],[81,77]) ).

tff(83,plain,
    ( ~ ! [X242: $i,X243: $i] : p70(f30(c88,X242),f38(c85,X243))
    | p70(f30(c88,f32(c89,f8(c75,c76))),f38(c85,f40(f42(f44(f46(c87,c79),c81),c85),c81))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(84,plain,
    $false,
    inference(unit_resolution,[status(thm)],[83,82,75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN719-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 06:53:10 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.20/0.55  % SZS status Unsatisfiable
% 0.20/0.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------