TSTP Solution File: SYN710-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN710-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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 23:57:01 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Proof 0.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   75 (  14 unt;  16 typ;   0 def)
%            Number of atoms       :  254 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  325 ( 142   ~; 155   |;   0   &)
%                                         (  28 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of FOOLs       :   12 (  12 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   8 con; 0-2 aty)
%            Number of variables   :  166 ( 150   !;   0   ?; 166   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p33_type,type,
    p33: ( $i * $i ) > $o ).

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

tff(c50_type,type,
    c50: $i ).

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

tff(c49_type,type,
    c49: $i ).

tff(c48_type,type,
    c48: $i ).

tff(f18_type,type,
    f18: ( $i * $i ) > $i ).

tff(f20_type,type,
    f20: ( $i * $i ) > $i ).

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

tff(c43_type,type,
    c43: $i ).

tff(c47_type,type,
    c47: $i ).

tff(f22_type,type,
    f22: ( $i * $i ) > $i ).

tff(c52_type,type,
    c52: $i ).

tff(c51_type,type,
    c51: $i ).

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

tff(c46_type,type,
    c46: $i ).

tff(1,plain,
    ^ [X80: $i,X79: $i] :
      refl(
        ( ( p33(f11(c46,X79),X80)
          | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
      <=> ( p33(f11(c46,X79),X80)
          | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
  <=> ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
  <=> ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_72) ).

tff(5,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | p33(f18(c51,f20(f22(c52,X79),X80)),X79) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ p33(f11(c46,c50),f9(c47,c43))
  <=> ~ p33(f11(c46,c50),f9(c47,c43)) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    ~ p33(f11(c46,c50),f9(c47,c43)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p33_25) ).

tff(10,plain,
    ~ p33(f11(c46,c50),f9(c47,c43)),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ( ( ~ ! [X80: $i,X79: $i] :
            ( p33(f11(c46,X79),X80)
            | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
      | p33(f11(c46,c50),f9(c47,c43))
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) )
  <=> ( ~ ! [X80: $i,X79: $i] :
            ( p33(f11(c46,X79),X80)
            | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
      | p33(f11(c46,c50),f9(c47,c43))
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    ( ~ ! [X80: $i,X79: $i] :
          ( p33(f11(c46,X79),X80)
          | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
    | p33(f11(c46,c50),f9(c47,c43))
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ),
    inference(quant_inst,[status(thm)],]) ).

tff(13,plain,
    ( ~ ! [X80: $i,X79: $i] :
          ( p33(f11(c46,X79),X80)
          | p33(f18(c51,f20(f22(c52,X79),X80)),X79) )
    | p33(f11(c46,c50),f9(c47,c43))
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50) ),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50),
    inference(unit_resolution,[status(thm)],[13,10,7]) ).

tff(15,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      refl(
        ( ( ~ p33(f18(c51,X13),X15)
          | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
      <=> ( ~ p33(f18(c51,X13),X15)
          | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) )),
    inference(bind,[status(th)],]) ).

tff(16,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p33(f18(c51,X13),X15)
        | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p33(f18(c51,X13),X15)
        | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
    inference(quant_intro,[status(thm)],[15]) ).

tff(17,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p33(f18(c51,X13),X15)
        | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p33(f18(c51,X13),X15)
        | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      rewrite(
        ( ( p33(f18(c51,X13),f13(f16(c48,X14),X15))
          | ~ p33(f18(c51,X13),X15) )
      <=> ( ~ p33(f18(c51,X13),X15)
          | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( p33(f18(c51,X13),f13(f16(c48,X14),X15))
        | ~ p33(f18(c51,X13),X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p33(f18(c51,X13),X15)
        | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,axiom,
    ! [X14: $i,X13: $i,X15: $i] :
      ( p33(f18(c51,X13),f13(f16(c48,X14),X15))
      | ~ p33(f18(c51,X13),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_75) ).

tff(21,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p33(f18(c51,X13),X15)
      | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p33(f18(c51,X13),X15)
      | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
    inference(modus_ponens,[status(thm)],[21,17]) ).

tff(23,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p33(f18(c51,X13),X15)
      | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
    inference(skolemize,[status(sab)],[22]) ).

tff(24,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p33(f18(c51,X13),X15)
      | p33(f18(c51,X13),f13(f16(c48,X14),X15)) ),
    inference(modus_ponens,[status(thm)],[23,16]) ).

tff(25,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p33(f18(c51,X13),X15)
            | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p33(f18(c51,X13),X15)
            | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p33(f18(c51,X13),X15)
          | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p33(f18(c51,X13),X15)
          | p33(f18(c51,X13),f13(f16(c48,X14),X15)) )
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),c50)
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)),
    inference(unit_resolution,[status(thm)],[27,24,14]) ).

tff(29,plain,
    ^ [X80: $i,X79: $i] :
      refl(
        ( ( p33(f11(c46,X79),X80)
          | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
      <=> ( p33(f11(c46,X79),X80)
          | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
  <=> ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
  <=> ! [X80: $i,X79: $i] :
        ( p33(f11(c46,X79),X80)
        | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_73) ).

tff(33,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [X80: $i,X79: $i] :
      ( p33(f11(c46,X79),X80)
      | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ( ~ ! [X80: $i,X79: $i] :
            ( p33(f11(c46,X79),X80)
            | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
      | p33(f11(c46,c50),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
  <=> ( ~ ! [X80: $i,X79: $i] :
            ( p33(f11(c46,X79),X80)
            | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
      | p33(f11(c46,c50),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    ( ~ ! [X80: $i,X79: $i] :
          ( p33(f11(c46,X79),X80)
          | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
    | p33(f11(c46,c50),f9(c47,c43))
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X80: $i,X79: $i] :
          ( p33(f11(c46,X79),X80)
          | ~ p33(f18(c51,f20(f22(c52,X79),X80)),X80) )
    | p33(f11(c46,c50),f9(c47,c43))
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)),
    inference(unit_resolution,[status(thm)],[38,10,35]) ).

tff(40,plain,
    ^ [X80: $i,X81: $i,X79: $i] :
      refl(
        ( ( ~ p33(f18(c51,X81),X79)
          | ~ p33(f11(c46,X79),X80)
          | p33(f18(c51,X81),X80) )
      <=> ( ~ p33(f18(c51,X81),X79)
          | ~ p33(f11(c46,X79),X80)
          | p33(f18(c51,X81),X80) ) )),
    inference(bind,[status(th)],]) ).

tff(41,plain,
    ( ! [X80: $i,X81: $i,X79: $i] :
        ( ~ p33(f18(c51,X81),X79)
        | ~ p33(f11(c46,X79),X80)
        | p33(f18(c51,X81),X80) )
  <=> ! [X80: $i,X81: $i,X79: $i] :
        ( ~ p33(f18(c51,X81),X79)
        | ~ p33(f11(c46,X79),X80)
        | p33(f18(c51,X81),X80) ) ),
    inference(quant_intro,[status(thm)],[40]) ).

tff(42,plain,
    ( ! [X80: $i,X81: $i,X79: $i] :
        ( ~ p33(f18(c51,X81),X79)
        | ~ p33(f11(c46,X79),X80)
        | p33(f18(c51,X81),X80) )
  <=> ! [X80: $i,X81: $i,X79: $i] :
        ( ~ p33(f18(c51,X81),X79)
        | ~ p33(f11(c46,X79),X80)
        | p33(f18(c51,X81),X80) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ^ [X80: $i,X81: $i,X79: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p33(f18(c51,X81),X80)
              | ~ p33(f11(c46,X79),X80) )
          <=> ( ~ p33(f11(c46,X79),X80)
              | p33(f18(c51,X81),X80) ) )),
          ( ( p33(f18(c51,X81),X80)
            | ~ p33(f11(c46,X79),X80)
            | ~ p33(f18(c51,X81),X79) )
        <=> ( ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80)
            | ~ p33(f18(c51,X81),X79) ) )),
        rewrite(
          ( ( ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80)
            | ~ p33(f18(c51,X81),X79) )
        <=> ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) ) )),
        ( ( p33(f18(c51,X81),X80)
          | ~ p33(f11(c46,X79),X80)
          | ~ p33(f18(c51,X81),X79) )
      <=> ( ~ p33(f18(c51,X81),X79)
          | ~ p33(f11(c46,X79),X80)
          | p33(f18(c51,X81),X80) ) )),
    inference(bind,[status(th)],]) ).

tff(44,plain,
    ( ! [X80: $i,X81: $i,X79: $i] :
        ( p33(f18(c51,X81),X80)
        | ~ p33(f11(c46,X79),X80)
        | ~ p33(f18(c51,X81),X79) )
  <=> ! [X80: $i,X81: $i,X79: $i] :
        ( ~ p33(f18(c51,X81),X79)
        | ~ p33(f11(c46,X79),X80)
        | p33(f18(c51,X81),X80) ) ),
    inference(quant_intro,[status(thm)],[43]) ).

tff(45,axiom,
    ! [X80: $i,X81: $i,X79: $i] :
      ( p33(f18(c51,X81),X80)
      | ~ p33(f11(c46,X79),X80)
      | ~ p33(f18(c51,X81),X79) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_80) ).

tff(46,plain,
    ! [X80: $i,X81: $i,X79: $i] :
      ( ~ p33(f18(c51,X81),X79)
      | ~ p33(f11(c46,X79),X80)
      | p33(f18(c51,X81),X80) ),
    inference(modus_ponens,[status(thm)],[45,44]) ).

tff(47,plain,
    ! [X80: $i,X81: $i,X79: $i] :
      ( ~ p33(f18(c51,X81),X79)
      | ~ p33(f11(c46,X79),X80)
      | p33(f18(c51,X81),X80) ),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ! [X80: $i,X81: $i,X79: $i] :
      ( ~ p33(f18(c51,X81),X79)
      | ~ p33(f11(c46,X79),X80)
      | p33(f18(c51,X81),X80) ),
    inference(skolemize,[status(sab)],[47]) ).

tff(49,plain,
    ! [X80: $i,X81: $i,X79: $i] :
      ( ~ p33(f18(c51,X81),X79)
      | ~ p33(f11(c46,X79),X80)
      | p33(f18(c51,X81),X80) ),
    inference(modus_ponens,[status(thm)],[48,41]) ).

tff(50,plain,
    ( p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
  <=> p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,axiom,
    p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_50) ).

tff(52,plain,
    p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43)),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ( ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) )
  <=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
  <=> ( p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ( ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
  <=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
    inference(monotonicity,[status(thm)],[54]) ).

tff(56,plain,
    ( ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) )
  <=> ( ~ ! [X80: $i,X81: $i,X79: $i] :
            ( ~ p33(f18(c51,X81),X79)
            | ~ p33(f11(c46,X79),X80)
            | p33(f18(c51,X81),X80) )
      | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
      | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
      | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ) ),
    inference(transitivity,[status(thm)],[55,53]) ).

tff(57,plain,
    ( ~ ! [X80: $i,X81: $i,X79: $i] :
          ( ~ p33(f18(c51,X81),X79)
          | ~ p33(f11(c46,X79),X80)
          | p33(f18(c51,X81),X80) )
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50))
    | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(58,plain,
    ( ~ ! [X80: $i,X81: $i,X79: $i] :
          ( ~ p33(f18(c51,X81),X79)
          | ~ p33(f11(c46,X79),X80)
          | p33(f18(c51,X81),X80) )
    | p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f9(c47,c43))
    | ~ p33(f11(c46,f13(f16(c48,c49),c50)),f9(c47,c43))
    | ~ p33(f18(c51,f20(f22(c52,c50),f9(c47,c43))),f13(f16(c48,c49),c50)) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    $false,
    inference(unit_resolution,[status(thm)],[58,52,49,39,28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN710-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n019.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 : Mon Sep  5 06:44:20 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.20/0.54  % SZS status Unsatisfiable
% 0.20/0.54  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------