TSTP Solution File: SYN593-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN593-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 23:56:33 EDT 2022

% Result   : Unsatisfiable 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   52 (  15 unt;  17 typ;   0 def)
%            Number of atoms       :  318 (   0 equ)
%            Maximal formula atoms :   24 (   9 avg)
%            Number of connectives :  367 ( 104   ~; 239   |;   0   &)
%                                         (  24 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    7 (   3 avg)
%            Number of FOOLs       :   20 (  20 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  11   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   84 (  76   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p12_type,type,
    p12: ( $i * $i ) > $o ).

tff(f13_type,type,
    f13: $i > $i ).

tff(c18_type,type,
    c18: $i ).

tff(p15_type,type,
    p15: ( $i * $i ) > $o ).

tff(f4_type,type,
    f4: ( $i * $i ) > $i ).

tff(f11_type,type,
    f11: $i > $i ).

tff(f6_type,type,
    f6: ( $i * $i ) > $i ).

tff(f7_type,type,
    f7: $i > $i ).

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

tff(f9_type,type,
    f9: $i > $i ).

tff(c17_type,type,
    c17: $i ).

tff(f10_type,type,
    f10: $i > $i ).

tff(p3_type,type,
    p3: ( $i * $i ) > $o ).

tff(c20_type,type,
    c20: $i ).

tff(c19_type,type,
    c19: $i ).

tff(c16_type,type,
    c16: $i ).

tff(c21_type,type,
    c21: $i ).

tff(1,plain,
    ^ [X6: $i,X7: $i,X5: $i,X8: $i] :
      refl(
        ( ( p3(X7,X8)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p12(f13(X5),f13(c18)) )
      <=> ( p3(X7,X8)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p12(f13(X5),f13(c18)) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p12(f13(X5),f13(c18)) )
  <=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p12(f13(X5),f13(c18)) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p12(f13(X5),f13(c18)) )
  <=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p12(f13(X5),f13(c18)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [X6: $i,X7: $i,X5: $i,X8: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              trans(
                monotonicity(
                  rewrite(
                    ( ( p3(X7,X8)
                      | p12(f13(X5),f13(c18))
                      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5) )
                  <=> ( p3(X7,X8)
                      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                      | p12(f13(X5),f13(c18)) ) )),
                  ( ( p3(X7,X8)
                    | p12(f13(X5),f13(c18))
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
                <=> ( p3(X7,X8)
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                    | p12(f13(X5),f13(c18))
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) ) )),
                rewrite(
                  ( ( p3(X7,X8)
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                    | p12(f13(X5),f13(c18))
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
                <=> ( p3(X7,X8)
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                    | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                    | p12(f13(X5),f13(c18)) ) )),
                ( ( p3(X7,X8)
                  | p12(f13(X5),f13(c18))
                  | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                  | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5) )
              <=> ( p3(X7,X8)
                  | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                  | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                  | p12(f13(X5),f13(c18)) ) )),
              ( ( p3(X7,X8)
                | p12(f13(X5),f13(c18))
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
            <=> ( p3(X7,X8)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                | p12(f13(X5),f13(c18))
                | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) ) )),
            rewrite(
              ( ( p3(X7,X8)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                | p12(f13(X5),f13(c18))
                | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
            <=> ( p3(X7,X8)
                | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
                | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
                | p12(f13(X5),f13(c18)) ) )),
            ( ( p3(X7,X8)
              | p12(f13(X5),f13(c18))
              | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
              | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
              | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5) )
          <=> ( p3(X7,X8)
              | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
              | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
              | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
              | p12(f13(X5),f13(c18)) ) )),
          ( ( p3(X7,X8)
            | p12(f13(X5),f13(c18))
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
        <=> ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18))
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) ) )),
        rewrite(
          ( ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18))
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
        <=> ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) ) )),
        ( ( p3(X7,X8)
          | p12(f13(X5),f13(c18))
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
      <=> ( p3(X7,X8)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p12(f13(X5),f13(c18)) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | p12(f13(X5),f13(c18))
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) )
  <=> ! [X6: $i,X7: $i,X5: $i,X8: $i] :
        ( p3(X7,X8)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
        | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
        | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
        | p12(f13(X5),f13(c18)) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [X6: $i,X7: $i,X5: $i,X8: $i] :
      ( p3(X7,X8)
      | p12(f13(X5),f13(c18))
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_27) ).

tff(7,plain,
    ! [X6: $i,X7: $i,X5: $i,X8: $i] :
      ( p3(X7,X8)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
      | p12(f13(X5),f13(c18)) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [X6: $i,X7: $i,X5: $i,X8: $i] :
      ( p3(X7,X8)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
      | p12(f13(X5),f13(c18)) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [X6: $i,X7: $i,X5: $i,X8: $i] :
      ( p3(X7,X8)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
      | p12(f13(X5),f13(c18)) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [X6: $i,X7: $i,X5: $i,X8: $i] :
      ( p3(X7,X8)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
      | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
      | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
      | p12(f13(X5),f13(c18)) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
  <=> ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_24) ).

tff(13,plain,
    ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
  <=> ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_23) ).

tff(16,plain,
    ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
  <=> p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,axiom,
    p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_19) ).

tff(19,plain,
    p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ( p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
  <=> p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_18) ).

tff(22,plain,
    p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ~ p12(f13(c20),f13(c18))
  <=> ~ p12(f13(c20),f13(c18)) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,axiom,
    ~ p12(f13(c20),f13(c18)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p12_6) ).

tff(25,plain,
    ~ p12(f13(c20),f13(c18)),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ( ~ p3(c21,c19)
  <=> ~ p3(c21,c19) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,axiom,
    ~ p3(c21,c19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p3_5) ).

tff(28,plain,
    ~ p3(c21,c19),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | p12(f13(c20),f13(c18))
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) )
  <=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | p12(f13(c20),f13(c18))
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ( ( p3(c21,c19)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | p12(f13(c20),f13(c18)) )
  <=> ( p3(c21,c19)
      | p12(f13(c20),f13(c18))
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | p12(f13(c20),f13(c18)) )
  <=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | p12(f13(c20),f13(c18))
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
    inference(monotonicity,[status(thm)],[30]) ).

tff(32,plain,
    ( ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | p12(f13(c20),f13(c18)) )
  <=> ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
            ( p3(X7,X8)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
            | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
            | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
            | p12(f13(X5),f13(c18)) )
      | p3(c21,c19)
      | p12(f13(c20),f13(c18))
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
      | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
      | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ) ),
    inference(transitivity,[status(thm)],[31,29]) ).

tff(33,plain,
    ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
          ( p3(X7,X8)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p12(f13(X5),f13(c18)) )
    | p3(c21,c19)
    | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20)
    | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
    | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
    | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
    | p12(f13(c20),f13(c18)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X6: $i,X7: $i,X5: $i,X8: $i] :
          ( p3(X7,X8)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X8),X5)
          | ~ p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),X7),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X7)),X5)
          | p15(f4(f6(f10(X6),f6(f7(f8(f9(c17))),c18)),f11(X8)),X5)
          | p12(f13(X5),f13(c18)) )
    | p3(c21,c19)
    | p12(f13(c20),f13(c18))
    | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c21)),c20)
    | p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),f11(c19)),c20)
    | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c21),c20)
    | ~ p15(f4(f6(f10(c16),f6(f7(f8(f9(c17))),c18)),c19),c20) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    $false,
    inference(unit_resolution,[status(thm)],[34,28,25,22,19,16,13,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN593-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Sep  5 05:53:50 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33  Usage: tptp [options] [-file:]file
% 0.13/0.33    -h, -?       prints this message.
% 0.13/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.33    -m, -model   generate model.
% 0.13/0.33    -p, -proof   generate proof.
% 0.13/0.33    -c, -core    generate unsat core of named formulas.
% 0.13/0.33    -st, -statistics display statistics.
% 0.13/0.33    -t:timeout   set timeout (in second).
% 0.13/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33    -<param>:<value> configuration parameter and value.
% 0.13/0.33    -o:<output-file> file to place output in.
% 0.19/0.38  % SZS status Unsatisfiable
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------