TSTP Solution File: SYN717-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN717-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n005.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 23:57:03 EDT 2022

% Result   : Unsatisfiable 0.20s 0.51s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   97 (  27 unt;  19 typ;   0 def)
%            Number of atoms       :  436 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  653 ( 321   ~; 287   |;   0   &)
%                                         (  45 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   26 (  26 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  11   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :  272 ( 246   !;   0   ?; 272   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p24_type,type,
    p24: ( $i * $i ) > $o ).

tff(f25_type,type,
    f25: ( $i * $i ) > $i ).

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

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

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

tff(p22_type,type,
    p22: ( $i * $i ) > $o ).

tff(p23_type,type,
    p23: ( $i * $i ) > $o ).

tff(p20_type,type,
    p20: ( $i * $i ) > $o ).

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

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

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

tff(p60_type,type,
    p60: ( $i * $i ) > $o ).

tff(p59_type,type,
    p59: ( $i * $i ) > $o ).

tff(c72_type,type,
    c72: $i ).

tff(f29_type,type,
    f29: ( $i * $i ) > $i ).

tff(f31_type,type,
    f31: ( $i * $i ) > $i ).

tff(f33_type,type,
    f33: ( $i * $i ) > $i ).

tff(c74_type,type,
    c74: $i ).

tff(c73_type,type,
    c73: $i ).

tff(1,plain,
    ^ [X55: $i] :
      refl(
        ( p22(X55,X55)
      <=> p22(X55,X55) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X55: $i] : p22(X55,X55)
  <=> ! [X55: $i] : p22(X55,X55) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X55: $i] : p22(X55,X55)
  <=> ! [X55: $i] : p22(X55,X55) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X55: $i] : p22(X55,X55),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22_28) ).

tff(5,plain,
    ! [X55: $i] : p22(X55,X55),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X55: $i] : p22(X55,X55),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X55: $i] : p22(X55,X55),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X55: $i] : p22(X55,X55)
    | p22(c75,c75) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p22(c75,c75),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X68: $i,X70: $i,X69: $i,X71: $i] :
      refl(
        ( ( ~ p23(X69,X71)
          | ~ p22(X68,X70)
          | p24(f25(X68,X69),f25(X70,X71)) )
      <=> ( ~ p23(X69,X71)
          | ~ p22(X68,X70)
          | p24(f25(X68,X69),f25(X70,X71)) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( ~ p23(X69,X71)
        | ~ p22(X68,X70)
        | p24(f25(X68,X69),f25(X70,X71)) )
  <=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( ~ p23(X69,X71)
        | ~ p22(X68,X70)
        | p24(f25(X68,X69),f25(X70,X71)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( ~ p23(X69,X71)
        | ~ p22(X68,X70)
        | p24(f25(X68,X69),f25(X70,X71)) )
  <=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( ~ p23(X69,X71)
        | ~ p22(X68,X70)
        | p24(f25(X68,X69),f25(X70,X71)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X68: $i,X70: $i,X69: $i,X71: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p24(f25(X68,X69),f25(X70,X71))
              | ~ p22(X68,X70) )
          <=> ( ~ p22(X68,X70)
              | p24(f25(X68,X69),f25(X70,X71)) ) )),
          ( ( p24(f25(X68,X69),f25(X70,X71))
            | ~ p22(X68,X70)
            | ~ p23(X69,X71) )
        <=> ( ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71))
            | ~ p23(X69,X71) ) )),
        rewrite(
          ( ( ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71))
            | ~ p23(X69,X71) )
        <=> ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) ) )),
        ( ( p24(f25(X68,X69),f25(X70,X71))
          | ~ p22(X68,X70)
          | ~ p23(X69,X71) )
      <=> ( ~ p23(X69,X71)
          | ~ p22(X68,X70)
          | p24(f25(X68,X69),f25(X70,X71)) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( p24(f25(X68,X69),f25(X70,X71))
        | ~ p22(X68,X70)
        | ~ p23(X69,X71) )
  <=> ! [X68: $i,X70: $i,X69: $i,X71: $i] :
        ( ~ p23(X69,X71)
        | ~ p22(X68,X70)
        | p24(f25(X68,X69),f25(X70,X71)) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X68: $i,X70: $i,X69: $i,X71: $i] :
      ( p24(f25(X68,X69),f25(X70,X71))
      | ~ p22(X68,X70)
      | ~ p23(X69,X71) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_94) ).

tff(16,plain,
    ! [X68: $i,X70: $i,X69: $i,X71: $i] :
      ( ~ p23(X69,X71)
      | ~ p22(X68,X70)
      | p24(f25(X68,X69),f25(X70,X71)) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X68: $i,X70: $i,X69: $i,X71: $i] :
      ( ~ p23(X69,X71)
      | ~ p22(X68,X70)
      | p24(f25(X68,X69),f25(X70,X71)) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X68: $i,X70: $i,X69: $i,X71: $i] :
      ( ~ p23(X69,X71)
      | ~ p22(X68,X70)
      | p24(f25(X68,X69),f25(X70,X71)) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X68: $i,X70: $i,X69: $i,X71: $i] :
      ( ~ p23(X69,X71)
      | ~ p22(X68,X70)
      | p24(f25(X68,X69),f25(X70,X71)) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( p23(c79,c77)
  <=> p23(c79,c77) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    p23(c79,c77),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23_36) ).

tff(22,plain,
    p23(c79,c77),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | p24(f25(c75,c79),f25(c75,c77))
      | ~ p22(c75,c75) )
  <=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | p24(f25(c75,c79),f25(c75,c77))
      | ~ p22(c75,c75) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ( ~ p23(c79,c77)
      | ~ p22(c75,c75)
      | p24(f25(c75,c79),f25(c75,c77)) )
  <=> ( ~ p23(c79,c77)
      | p24(f25(c75,c79),f25(c75,c77))
      | ~ p22(c75,c75) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | ~ p22(c75,c75)
      | p24(f25(c75,c79),f25(c75,c77)) )
  <=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | p24(f25(c75,c79),f25(c75,c77))
      | ~ p22(c75,c75) ) ),
    inference(monotonicity,[status(thm)],[24]) ).

tff(26,plain,
    ( ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | ~ p22(c75,c75)
      | p24(f25(c75,c79),f25(c75,c77)) )
  <=> ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
            ( ~ p23(X69,X71)
            | ~ p22(X68,X70)
            | p24(f25(X68,X69),f25(X70,X71)) )
      | ~ p23(c79,c77)
      | p24(f25(c75,c79),f25(c75,c77))
      | ~ p22(c75,c75) ) ),
    inference(transitivity,[status(thm)],[25,23]) ).

tff(27,plain,
    ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
          ( ~ p23(X69,X71)
          | ~ p22(X68,X70)
          | p24(f25(X68,X69),f25(X70,X71)) )
    | ~ p23(c79,c77)
    | ~ p22(c75,c75)
    | p24(f25(c75,c79),f25(c75,c77)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    ( ~ ! [X68: $i,X70: $i,X69: $i,X71: $i] :
          ( ~ p23(X69,X71)
          | ~ p22(X68,X70)
          | p24(f25(X68,X69),f25(X70,X71)) )
    | ~ p23(c79,c77)
    | p24(f25(c75,c79),f25(c75,c77))
    | ~ p22(c75,c75) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    p24(f25(c75,c79),f25(c75,c77)),
    inference(unit_resolution,[status(thm)],[28,22,19,9]) ).

tff(30,plain,
    ^ [X48: $i] :
      refl(
        ( p20(X48,X48)
      <=> p20(X48,X48) )),
    inference(bind,[status(th)],]) ).

tff(31,plain,
    ( ! [X48: $i] : p20(X48,X48)
  <=> ! [X48: $i] : p20(X48,X48) ),
    inference(quant_intro,[status(thm)],[30]) ).

tff(32,plain,
    ( ! [X48: $i] : p20(X48,X48)
  <=> ! [X48: $i] : p20(X48,X48) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,axiom,
    ! [X48: $i] : p20(X48,X48),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20_29) ).

tff(34,plain,
    ! [X48: $i] : p20(X48,X48),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ! [X48: $i] : p20(X48,X48),
    inference(skolemize,[status(sab)],[34]) ).

tff(36,plain,
    ! [X48: $i] : p20(X48,X48),
    inference(modus_ponens,[status(thm)],[35,31]) ).

tff(37,plain,
    ( ~ ! [X48: $i] : p20(X48,X48)
    | p20(f21(c76,c78),f21(c76,c78)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    p20(f21(c76,c78),f21(c76,c78)),
    inference(unit_resolution,[status(thm)],[37,36]) ).

tff(39,plain,
    ^ [X212: $i,X210: $i,X211: $i,X209: $i] :
      refl(
        ( ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p60(f25(c75,X209),f21(c76,X212)) )
      <=> ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p60(f25(c75,X209),f21(c76,X212)) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p60(f25(c75,X209),f21(c76,X212)) )
  <=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p60(f25(c75,X209),f21(c76,X212)) )
  <=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ^ [X212: $i,X210: $i,X211: $i,X209: $i] :
      rewrite(
        ( ( ~ p60(f25(c75,X209),f21(c76,X212))
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) )
      <=> ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p60(f25(c75,X209),f21(c76,X212)) ) )),
    inference(bind,[status(th)],]) ).

tff(43,plain,
    ( ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p60(f25(c75,X209),f21(c76,X212))
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) )
  <=> ! [X212: $i,X210: $i,X211: $i,X209: $i] :
        ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
        | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
        | ~ p60(f25(c75,X209),f21(c76,X212)) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,axiom,
    ! [X212: $i,X210: $i,X211: $i,X209: $i] :
      ( ~ p60(f25(c75,X209),f21(c76,X212))
      | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
      | ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p60_107) ).

tff(45,plain,
    ! [X212: $i,X210: $i,X211: $i,X209: $i] :
      ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
      | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
      | ~ p60(f25(c75,X209),f21(c76,X212)) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [X212: $i,X210: $i,X211: $i,X209: $i] :
      ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
      | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
      | ~ p60(f25(c75,X209),f21(c76,X212)) ),
    inference(modus_ponens,[status(thm)],[45,41]) ).

tff(47,plain,
    ! [X212: $i,X210: $i,X211: $i,X209: $i] :
      ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
      | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
      | ~ p60(f25(c75,X209),f21(c76,X212)) ),
    inference(skolemize,[status(sab)],[46]) ).

tff(48,plain,
    ! [X212: $i,X210: $i,X211: $i,X209: $i] :
      ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
      | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
      | ~ p60(f25(c75,X209),f21(c76,X212)) ),
    inference(modus_ponens,[status(thm)],[47,40]) ).

tff(49,plain,
    ( p59(f29(c73,f31(f33(c74,c77),c78)),c72)
  <=> p59(f29(c73,f31(f33(c74,c77),c78)),c72) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,axiom,
    p59(f29(c73,f31(f33(c74,c77),c78)),c72),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p59_44) ).

tff(51,plain,
    p59(f29(c73,f31(f33(c74,c77),c78)),c72),
    inference(modus_ponens,[status(thm)],[50,49]) ).

tff(52,plain,
    ( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ( ( ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,plain,
    ( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
    inference(monotonicity,[status(thm)],[53]) ).

tff(55,plain,
    ( ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
            ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
            | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
            | ~ p60(f25(c75,X209),f21(c76,X212)) )
      | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
      | ~ p60(f25(c75,c77),f21(c76,c78)) ) ),
    inference(transitivity,[status(thm)],[54,52]) ).

tff(56,plain,
    ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
          ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p60(f25(c75,X209),f21(c76,X212)) )
    | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
    | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
    | ~ p60(f25(c75,c77),f21(c76,c78)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(57,plain,
    ( ~ ! [X212: $i,X210: $i,X211: $i,X209: $i] :
          ( ~ p59(f29(c73,f31(f33(c74,X209),X210)),c72)
          | ~ p59(f29(c73,f31(f33(c74,X211),X212)),c72)
          | ~ p60(f25(c75,X209),f21(c76,X212)) )
    | ~ p59(f29(c73,f31(f33(c74,c77),c78)),c72)
    | ~ p60(f25(c75,c77),f21(c76,c78)) ),
    inference(modus_ponens,[status(thm)],[56,55]) ).

tff(58,plain,
    ~ p60(f25(c75,c77),f21(c76,c78)),
    inference(unit_resolution,[status(thm)],[57,51,48]) ).

tff(59,plain,
    ^ [X188: $i,X189: $i,X186: $i,X187: $i] :
      refl(
        ( ( ~ p20(X188,X187)
          | ~ p60(X189,X188)
          | ~ p24(X189,X186)
          | p60(X186,X187) )
      <=> ( ~ p20(X188,X187)
          | ~ p60(X189,X188)
          | ~ p24(X189,X186)
          | p60(X186,X187) ) )),
    inference(bind,[status(th)],]) ).

tff(60,plain,
    ( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( ~ p20(X188,X187)
        | ~ p60(X189,X188)
        | ~ p24(X189,X186)
        | p60(X186,X187) )
  <=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( ~ p20(X188,X187)
        | ~ p60(X189,X188)
        | ~ p24(X189,X186)
        | p60(X186,X187) ) ),
    inference(quant_intro,[status(thm)],[59]) ).

tff(61,plain,
    ( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( ~ p20(X188,X187)
        | ~ p60(X189,X188)
        | ~ p24(X189,X186)
        | p60(X186,X187) )
  <=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( ~ p20(X188,X187)
        | ~ p60(X189,X188)
        | ~ p24(X189,X186)
        | p60(X186,X187) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ^ [X188: $i,X189: $i,X186: $i,X187: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p60(X186,X187)
                  | ~ p24(X189,X186) )
              <=> ( ~ p24(X189,X186)
                  | p60(X186,X187) ) )),
              ( ( p60(X186,X187)
                | ~ p24(X189,X186)
                | ~ p60(X189,X188) )
            <=> ( ~ p24(X189,X186)
                | p60(X186,X187)
                | ~ p60(X189,X188) ) )),
            rewrite(
              ( ( ~ p24(X189,X186)
                | p60(X186,X187)
                | ~ p60(X189,X188) )
            <=> ( ~ p60(X189,X188)
                | ~ p24(X189,X186)
                | p60(X186,X187) ) )),
            ( ( p60(X186,X187)
              | ~ p24(X189,X186)
              | ~ p60(X189,X188) )
          <=> ( ~ p60(X189,X188)
              | ~ p24(X189,X186)
              | p60(X186,X187) ) )),
          ( ( p60(X186,X187)
            | ~ p24(X189,X186)
            | ~ p60(X189,X188)
            | ~ p20(X188,X187) )
        <=> ( ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187)
            | ~ p20(X188,X187) ) )),
        rewrite(
          ( ( ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187)
            | ~ p20(X188,X187) )
        <=> ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) ) )),
        ( ( p60(X186,X187)
          | ~ p24(X189,X186)
          | ~ p60(X189,X188)
          | ~ p20(X188,X187) )
      <=> ( ~ p20(X188,X187)
          | ~ p60(X189,X188)
          | ~ p24(X189,X186)
          | p60(X186,X187) ) )),
    inference(bind,[status(th)],]) ).

tff(63,plain,
    ( ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( p60(X186,X187)
        | ~ p24(X189,X186)
        | ~ p60(X189,X188)
        | ~ p20(X188,X187) )
  <=> ! [X188: $i,X189: $i,X186: $i,X187: $i] :
        ( ~ p20(X188,X187)
        | ~ p60(X189,X188)
        | ~ p24(X189,X186)
        | p60(X186,X187) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,axiom,
    ! [X188: $i,X189: $i,X186: $i,X187: $i] :
      ( p60(X186,X187)
      | ~ p24(X189,X186)
      | ~ p60(X189,X188)
      | ~ p20(X188,X187) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p60_84) ).

tff(65,plain,
    ! [X188: $i,X189: $i,X186: $i,X187: $i] :
      ( ~ p20(X188,X187)
      | ~ p60(X189,X188)
      | ~ p24(X189,X186)
      | p60(X186,X187) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    ! [X188: $i,X189: $i,X186: $i,X187: $i] :
      ( ~ p20(X188,X187)
      | ~ p60(X189,X188)
      | ~ p24(X189,X186)
      | p60(X186,X187) ),
    inference(modus_ponens,[status(thm)],[65,61]) ).

tff(67,plain,
    ! [X188: $i,X189: $i,X186: $i,X187: $i] :
      ( ~ p20(X188,X187)
      | ~ p60(X189,X188)
      | ~ p24(X189,X186)
      | p60(X186,X187) ),
    inference(skolemize,[status(sab)],[66]) ).

tff(68,plain,
    ! [X188: $i,X189: $i,X186: $i,X187: $i] :
      ( ~ p20(X188,X187)
      | ~ p60(X189,X188)
      | ~ p24(X189,X186)
      | p60(X186,X187) ),
    inference(modus_ponens,[status(thm)],[67,60]) ).

tff(69,plain,
    ( p60(f25(c75,c79),f21(c76,c78))
  <=> p60(f25(c75,c79),f21(c76,c78)) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,axiom,
    p60(f25(c75,c79),f21(c76,c78)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p60_42) ).

tff(71,plain,
    p60(f25(c75,c79),f21(c76,c78)),
    inference(modus_ponens,[status(thm)],[70,69]) ).

tff(72,plain,
    ( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | p60(f25(c75,c77),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | ~ p20(f21(c76,c78),f21(c76,c78)) )
  <=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | p60(f25(c75,c77),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,plain,
    ( ( ~ p20(f21(c76,c78),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( p60(f25(c75,c77),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(74,plain,
    ( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | ~ p20(f21(c76,c78),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | p60(f25(c75,c77),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
    inference(monotonicity,[status(thm)],[73]) ).

tff(75,plain,
    ( ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | ~ p20(f21(c76,c78),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | p60(f25(c75,c77),f21(c76,c78)) )
  <=> ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
            ( ~ p20(X188,X187)
            | ~ p60(X189,X188)
            | ~ p24(X189,X186)
            | p60(X186,X187) )
      | p60(f25(c75,c77),f21(c76,c78))
      | ~ p60(f25(c75,c79),f21(c76,c78))
      | ~ p24(f25(c75,c79),f25(c75,c77))
      | ~ p20(f21(c76,c78),f21(c76,c78)) ) ),
    inference(transitivity,[status(thm)],[74,72]) ).

tff(76,plain,
    ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
          ( ~ p20(X188,X187)
          | ~ p60(X189,X188)
          | ~ p24(X189,X186)
          | p60(X186,X187) )
    | ~ p20(f21(c76,c78),f21(c76,c78))
    | ~ p60(f25(c75,c79),f21(c76,c78))
    | ~ p24(f25(c75,c79),f25(c75,c77))
    | p60(f25(c75,c77),f21(c76,c78)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(77,plain,
    ( ~ ! [X188: $i,X189: $i,X186: $i,X187: $i] :
          ( ~ p20(X188,X187)
          | ~ p60(X189,X188)
          | ~ p24(X189,X186)
          | p60(X186,X187) )
    | p60(f25(c75,c77),f21(c76,c78))
    | ~ p60(f25(c75,c79),f21(c76,c78))
    | ~ p24(f25(c75,c79),f25(c75,c77))
    | ~ p20(f21(c76,c78),f21(c76,c78)) ),
    inference(modus_ponens,[status(thm)],[76,75]) ).

tff(78,plain,
    $false,
    inference(unit_resolution,[status(thm)],[77,71,68,58,38,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SYN717-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n005.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 06:43:18 EDT 2022
% 0.13/0.33  % 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.
% 0.20/0.51  % SZS status Unsatisfiable
% 0.20/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------