TSTP Solution File: SYN659-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN659-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 23:56:49 EDT 2022

% Result   : Unsatisfiable 1.72s 1.33s
% Output   : Proof 1.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   75
% Syntax   : Number of formulae    :  148 (  43 unt;  16 typ;   0 def)
%            Number of atoms       :  773 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives : 1110 ( 518   ~; 514   |;   0   &)
%                                         (  78 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   49 (  49 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   9   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :  419 ( 382   !;   0   ?; 419   :)

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

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

tff(c33_type,type,
    c33: $i ).

tff(c32_type,type,
    c32: $i ).

tff(f15_type,type,
    f15: ( $i * $i ) > $i ).

tff(c41_type,type,
    c41: $i ).

tff(c40_type,type,
    c40: $i ).

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

tff(c28_type,type,
    c28: $i ).

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

tff(c29_type,type,
    c29: $i ).

tff(p7_type,type,
    p7: ( $i * $i ) > $o ).

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

tff(f17_type,type,
    f17: $i > $i ).

tff(c39_type,type,
    c39: $i ).

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

tff(1,plain,
    ^ [X87: $i] :
      refl(
        ( p7(X87,X87)
      <=> p7(X87,X87) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X87: $i] : p7(X87,X87)
  <=> ! [X87: $i] : p7(X87,X87) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X87: $i] : p7(X87,X87)
  <=> ! [X87: $i] : p7(X87,X87) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X87: $i] : p7(X87,X87),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_3) ).

tff(5,plain,
    ! [X87: $i] : p7(X87,X87),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X87: $i] : p7(X87,X87),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X87: $i] : p7(X87,X87),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X87: $i] : p7(X87,X87)
    | p7(f8(c28),f8(c28)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p7(f8(c28),f8(c28)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X87: $i,X88: $i,X89: $i] :
      refl(
        ( ( ~ p7(X87,X89)
          | ~ p7(X87,X88)
          | p7(X88,X89) )
      <=> ( ~ p7(X87,X89)
          | ~ p7(X87,X88)
          | p7(X88,X89) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X87: $i,X88: $i,X89: $i] :
        ( ~ p7(X87,X89)
        | ~ p7(X87,X88)
        | p7(X88,X89) )
  <=> ! [X87: $i,X88: $i,X89: $i] :
        ( ~ p7(X87,X89)
        | ~ p7(X87,X88)
        | p7(X88,X89) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X87: $i,X88: $i,X89: $i] :
        ( ~ p7(X87,X89)
        | ~ p7(X87,X88)
        | p7(X88,X89) )
  <=> ! [X87: $i,X88: $i,X89: $i] :
        ( ~ p7(X87,X89)
        | ~ p7(X87,X88)
        | p7(X88,X89) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X87: $i,X88: $i,X89: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p7(X88,X89)
              | ~ p7(X87,X88) )
          <=> ( ~ p7(X87,X88)
              | p7(X88,X89) ) )),
          ( ( p7(X88,X89)
            | ~ p7(X87,X88)
            | ~ p7(X87,X89) )
        <=> ( ~ p7(X87,X88)
            | p7(X88,X89)
            | ~ p7(X87,X89) ) )),
        rewrite(
          ( ( ~ p7(X87,X88)
            | p7(X88,X89)
            | ~ p7(X87,X89) )
        <=> ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) ) )),
        ( ( p7(X88,X89)
          | ~ p7(X87,X88)
          | ~ p7(X87,X89) )
      <=> ( ~ p7(X87,X89)
          | ~ p7(X87,X88)
          | p7(X88,X89) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X87: $i,X88: $i,X89: $i] :
        ( p7(X88,X89)
        | ~ p7(X87,X88)
        | ~ p7(X87,X89) )
  <=> ! [X87: $i,X88: $i,X89: $i] :
        ( ~ p7(X87,X89)
        | ~ p7(X87,X88)
        | p7(X88,X89) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X87: $i,X88: $i,X89: $i] :
      ( p7(X88,X89)
      | ~ p7(X87,X88)
      | ~ p7(X87,X89) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_31) ).

tff(16,plain,
    ! [X87: $i,X88: $i,X89: $i] :
      ( ~ p7(X87,X89)
      | ~ p7(X87,X88)
      | p7(X88,X89) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X87: $i,X88: $i,X89: $i] :
      ( ~ p7(X87,X89)
      | ~ p7(X87,X88)
      | p7(X88,X89) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X87: $i,X88: $i,X89: $i] :
      ( ~ p7(X87,X89)
      | ~ p7(X87,X88)
      | p7(X88,X89) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X87: $i,X88: $i,X89: $i] :
      ( ~ p7(X87,X89)
      | ~ p7(X87,X88)
      | p7(X88,X89) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( p7(f8(c28),c29)
  <=> p7(f8(c28),c29) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    p7(f8(c28),c29),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_13) ).

tff(22,plain,
    p7(f8(c28),c29),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),c29)
      | ~ p7(f8(c28),f8(c28))
      | p7(c29,f8(c28)) )
  <=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),c29)
      | ~ p7(f8(c28),f8(c28))
      | p7(c29,f8(c28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ( ~ p7(f8(c28),f8(c28))
      | ~ p7(f8(c28),c29)
      | p7(c29,f8(c28)) )
  <=> ( ~ p7(f8(c28),c29)
      | ~ p7(f8(c28),f8(c28))
      | p7(c29,f8(c28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),f8(c28))
      | ~ p7(f8(c28),c29)
      | p7(c29,f8(c28)) )
  <=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),c29)
      | ~ p7(f8(c28),f8(c28))
      | p7(c29,f8(c28)) ) ),
    inference(monotonicity,[status(thm)],[24]) ).

tff(26,plain,
    ( ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),f8(c28))
      | ~ p7(f8(c28),c29)
      | p7(c29,f8(c28)) )
  <=> ( ~ ! [X87: $i,X88: $i,X89: $i] :
            ( ~ p7(X87,X89)
            | ~ p7(X87,X88)
            | p7(X88,X89) )
      | ~ p7(f8(c28),c29)
      | ~ p7(f8(c28),f8(c28))
      | p7(c29,f8(c28)) ) ),
    inference(transitivity,[status(thm)],[25,23]) ).

tff(27,plain,
    ( ~ ! [X87: $i,X88: $i,X89: $i] :
          ( ~ p7(X87,X89)
          | ~ p7(X87,X88)
          | p7(X88,X89) )
    | ~ p7(f8(c28),f8(c28))
    | ~ p7(f8(c28),c29)
    | p7(c29,f8(c28)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(28,plain,
    ( ~ ! [X87: $i,X88: $i,X89: $i] :
          ( ~ p7(X87,X89)
          | ~ p7(X87,X88)
          | p7(X88,X89) )
    | ~ p7(f8(c28),c29)
    | ~ p7(f8(c28),f8(c28))
    | p7(c29,f8(c28)) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    p7(c29,f8(c28)),
    inference(unit_resolution,[status(thm)],[28,22,19,9]) ).

tff(30,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      refl(
        ( ( ~ p12(X13,X15)
          | ~ p12(X13,X14)
          | p12(X14,X15) )
      <=> ( ~ p12(X13,X15)
          | ~ p12(X13,X14)
          | p12(X14,X15) ) )),
    inference(bind,[status(th)],]) ).

tff(31,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p12(X13,X15)
        | ~ p12(X13,X14)
        | p12(X14,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p12(X13,X15)
        | ~ p12(X13,X14)
        | p12(X14,X15) ) ),
    inference(quant_intro,[status(thm)],[30]) ).

tff(32,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p12(X13,X15)
        | ~ p12(X13,X14)
        | p12(X14,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p12(X13,X15)
        | ~ p12(X13,X14)
        | p12(X14,X15) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ^ [X14: $i,X13: $i,X15: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p12(X14,X15)
              | ~ p12(X13,X14) )
          <=> ( ~ p12(X13,X14)
              | p12(X14,X15) ) )),
          ( ( p12(X14,X15)
            | ~ p12(X13,X14)
            | ~ p12(X13,X15) )
        <=> ( ~ p12(X13,X14)
            | p12(X14,X15)
            | ~ p12(X13,X15) ) )),
        rewrite(
          ( ( ~ p12(X13,X14)
            | p12(X14,X15)
            | ~ p12(X13,X15) )
        <=> ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) ) )),
        ( ( p12(X14,X15)
          | ~ p12(X13,X14)
          | ~ p12(X13,X15) )
      <=> ( ~ p12(X13,X15)
          | ~ p12(X13,X14)
          | p12(X14,X15) ) )),
    inference(bind,[status(th)],]) ).

tff(34,plain,
    ( ! [X14: $i,X13: $i,X15: $i] :
        ( p12(X14,X15)
        | ~ p12(X13,X14)
        | ~ p12(X13,X15) )
  <=> ! [X14: $i,X13: $i,X15: $i] :
        ( ~ p12(X13,X15)
        | ~ p12(X13,X14)
        | p12(X14,X15) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,axiom,
    ! [X14: $i,X13: $i,X15: $i] :
      ( p12(X14,X15)
      | ~ p12(X13,X14)
      | ~ p12(X13,X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_38) ).

tff(36,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p12(X13,X15)
      | ~ p12(X13,X14)
      | p12(X14,X15) ),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p12(X13,X15)
      | ~ p12(X13,X14)
      | p12(X14,X15) ),
    inference(modus_ponens,[status(thm)],[36,32]) ).

tff(38,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p12(X13,X15)
      | ~ p12(X13,X14)
      | p12(X14,X15) ),
    inference(skolemize,[status(sab)],[37]) ).

tff(39,plain,
    ! [X14: $i,X13: $i,X15: $i] :
      ( ~ p12(X13,X15)
      | ~ p12(X13,X14)
      | p12(X14,X15) ),
    inference(modus_ponens,[status(thm)],[38,31]) ).

tff(40,plain,
    ( p12(f13(f16(c39),f17(c39)),f13(c40,c41))
  <=> p12(f13(f16(c39),f17(c39)),f13(c40,c41)) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,axiom,
    p12(f13(f16(c39),f17(c39)),f13(c40,c41)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_29) ).

tff(42,plain,
    p12(f13(f16(c39),f17(c39)),f13(c40,c41)),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) )
  <=> ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) ) ),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    ( ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) )
  <=> ( ~ ! [X14: $i,X13: $i,X15: $i] :
            ( ~ p12(X13,X15)
            | ~ p12(X13,X14)
            | p12(X14,X15) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p12(f13(c40,c41),f13(c40,c41)) ) ),
    inference(transitivity,[status(thm)],[45,43]) ).

tff(47,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p12(X13,X15)
          | ~ p12(X13,X14)
          | p12(X14,X15) )
    | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
    | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
    | p12(f13(c40,c41),f13(c40,c41)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    ( ~ ! [X14: $i,X13: $i,X15: $i] :
          ( ~ p12(X13,X15)
          | ~ p12(X13,X14)
          | p12(X14,X15) )
    | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
    | p12(f13(c40,c41),f13(c40,c41)) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    p12(f13(c40,c41),f13(c40,c41)),
    inference(unit_resolution,[status(thm)],[48,42,39]) ).

tff(50,plain,
    ^ [X25: $i,X23: $i,X26: $i,X24: $i] :
      refl(
        ( ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) )
      <=> ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( ~ p12(X24,X26)
        | ~ p7(X23,X25)
        | p14(f15(X23,X24),f15(X25,X26)) )
  <=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( ~ p12(X24,X26)
        | ~ p7(X23,X25)
        | p14(f15(X23,X24),f15(X25,X26)) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,plain,
    ( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( ~ p12(X24,X26)
        | ~ p7(X23,X25)
        | p14(f15(X23,X24),f15(X25,X26)) )
  <=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( ~ p12(X24,X26)
        | ~ p7(X23,X25)
        | p14(f15(X23,X24),f15(X25,X26)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ^ [X25: $i,X23: $i,X26: $i,X24: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p14(f15(X23,X24),f15(X25,X26))
              | ~ p12(X24,X26) )
          <=> ( ~ p12(X24,X26)
              | p14(f15(X23,X24),f15(X25,X26)) ) )),
          ( ( p14(f15(X23,X24),f15(X25,X26))
            | ~ p12(X24,X26)
            | ~ p7(X23,X25) )
        <=> ( ~ p12(X24,X26)
            | p14(f15(X23,X24),f15(X25,X26))
            | ~ p7(X23,X25) ) )),
        rewrite(
          ( ( ~ p12(X24,X26)
            | p14(f15(X23,X24),f15(X25,X26))
            | ~ p7(X23,X25) )
        <=> ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) ) )),
        ( ( p14(f15(X23,X24),f15(X25,X26))
          | ~ p12(X24,X26)
          | ~ p7(X23,X25) )
      <=> ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( p14(f15(X23,X24),f15(X25,X26))
        | ~ p12(X24,X26)
        | ~ p7(X23,X25) )
  <=> ! [X25: $i,X23: $i,X26: $i,X24: $i] :
        ( ~ p12(X24,X26)
        | ~ p7(X23,X25)
        | p14(f15(X23,X24),f15(X25,X26)) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,axiom,
    ! [X25: $i,X23: $i,X26: $i,X24: $i] :
      ( p14(f15(X23,X24),f15(X25,X26))
      | ~ p12(X24,X26)
      | ~ p7(X23,X25) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_45) ).

tff(56,plain,
    ! [X25: $i,X23: $i,X26: $i,X24: $i] :
      ( ~ p12(X24,X26)
      | ~ p7(X23,X25)
      | p14(f15(X23,X24),f15(X25,X26)) ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    ! [X25: $i,X23: $i,X26: $i,X24: $i] :
      ( ~ p12(X24,X26)
      | ~ p7(X23,X25)
      | p14(f15(X23,X24),f15(X25,X26)) ),
    inference(modus_ponens,[status(thm)],[56,52]) ).

tff(58,plain,
    ! [X25: $i,X23: $i,X26: $i,X24: $i] :
      ( ~ p12(X24,X26)
      | ~ p7(X23,X25)
      | p14(f15(X23,X24),f15(X25,X26)) ),
    inference(skolemize,[status(sab)],[57]) ).

tff(59,plain,
    ! [X25: $i,X23: $i,X26: $i,X24: $i] :
      ( ~ p12(X24,X26)
      | ~ p7(X23,X25)
      | p14(f15(X23,X24),f15(X25,X26)) ),
    inference(modus_ponens,[status(thm)],[58,51]) ).

tff(60,plain,
    ( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(c40,c41),f13(c40,c41))
      | ~ p7(c29,f8(c28))
      | p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(c40,c41),f13(c40,c41))
      | ~ p7(c29,f8(c28))
      | p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
          ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) )
    | ~ p12(f13(c40,c41),f13(c40,c41))
    | ~ p7(c29,f8(c28))
    | p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
          ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) )
    | ~ p12(f13(c40,c41),f13(c40,c41))
    | ~ p7(c29,f8(c28))
    | p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))),
    inference(unit_resolution,[status(thm)],[62,59,49,29]) ).

tff(64,plain,
    ^ [X13: $i] :
      refl(
        ( p12(X13,X13)
      <=> p12(X13,X13) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [X13: $i] : p12(X13,X13)
  <=> ! [X13: $i] : p12(X13,X13) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [X13: $i] : p12(X13,X13)
  <=> ! [X13: $i] : p12(X13,X13) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,axiom,
    ! [X13: $i] : p12(X13,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_10) ).

tff(68,plain,
    ! [X13: $i] : p12(X13,X13),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ! [X13: $i] : p12(X13,X13),
    inference(skolemize,[status(sab)],[68]) ).

tff(70,plain,
    ! [X13: $i] : p12(X13,X13),
    inference(modus_ponens,[status(thm)],[69,65]) ).

tff(71,plain,
    ( ~ ! [X13: $i] : p12(X13,X13)
    | p12(f13(c32,c33),f13(c32,c33)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(72,plain,
    p12(f13(c32,c33),f13(c32,c33)),
    inference(unit_resolution,[status(thm)],[71,70]) ).

tff(73,plain,
    ^ [X67: $i,X68: $i,X70: $i,X69: $i] :
      refl(
        ( ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) )
      <=> ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) ) )),
    inference(bind,[status(th)],]) ).

tff(74,plain,
    ( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( ~ p12(X69,X68)
        | ~ p24(X70,X69)
        | ~ p14(X70,X67)
        | p24(X67,X68) )
  <=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( ~ p12(X69,X68)
        | ~ p24(X70,X69)
        | ~ p14(X70,X67)
        | p24(X67,X68) ) ),
    inference(quant_intro,[status(thm)],[73]) ).

tff(75,plain,
    ( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( ~ p12(X69,X68)
        | ~ p24(X70,X69)
        | ~ p14(X70,X67)
        | p24(X67,X68) )
  <=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( ~ p12(X69,X68)
        | ~ p24(X70,X69)
        | ~ p14(X70,X67)
        | p24(X67,X68) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ^ [X67: $i,X68: $i,X70: $i,X69: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p24(X67,X68)
                  | ~ p14(X70,X67) )
              <=> ( ~ p14(X70,X67)
                  | p24(X67,X68) ) )),
              ( ( p24(X67,X68)
                | ~ p14(X70,X67)
                | ~ p24(X70,X69) )
            <=> ( ~ p14(X70,X67)
                | p24(X67,X68)
                | ~ p24(X70,X69) ) )),
            rewrite(
              ( ( ~ p14(X70,X67)
                | p24(X67,X68)
                | ~ p24(X70,X69) )
            <=> ( ~ p24(X70,X69)
                | ~ p14(X70,X67)
                | p24(X67,X68) ) )),
            ( ( p24(X67,X68)
              | ~ p14(X70,X67)
              | ~ p24(X70,X69) )
          <=> ( ~ p24(X70,X69)
              | ~ p14(X70,X67)
              | p24(X67,X68) ) )),
          ( ( p24(X67,X68)
            | ~ p14(X70,X67)
            | ~ p24(X70,X69)
            | ~ p12(X69,X68) )
        <=> ( ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68)
            | ~ p12(X69,X68) ) )),
        rewrite(
          ( ( ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68)
            | ~ p12(X69,X68) )
        <=> ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) ) )),
        ( ( p24(X67,X68)
          | ~ p14(X70,X67)
          | ~ p24(X70,X69)
          | ~ p12(X69,X68) )
      <=> ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) ) )),
    inference(bind,[status(th)],]) ).

tff(77,plain,
    ( ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( p24(X67,X68)
        | ~ p14(X70,X67)
        | ~ p24(X70,X69)
        | ~ p12(X69,X68) )
  <=> ! [X67: $i,X68: $i,X70: $i,X69: $i] :
        ( ~ p12(X69,X68)
        | ~ p24(X70,X69)
        | ~ p14(X70,X67)
        | p24(X67,X68) ) ),
    inference(quant_intro,[status(thm)],[76]) ).

tff(78,axiom,
    ! [X67: $i,X68: $i,X70: $i,X69: $i] :
      ( p24(X67,X68)
      | ~ p14(X70,X67)
      | ~ p24(X70,X69)
      | ~ p12(X69,X68) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_41) ).

tff(79,plain,
    ! [X67: $i,X68: $i,X70: $i,X69: $i] :
      ( ~ p12(X69,X68)
      | ~ p24(X70,X69)
      | ~ p14(X70,X67)
      | p24(X67,X68) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ! [X67: $i,X68: $i,X70: $i,X69: $i] :
      ( ~ p12(X69,X68)
      | ~ p24(X70,X69)
      | ~ p14(X70,X67)
      | p24(X67,X68) ),
    inference(modus_ponens,[status(thm)],[79,75]) ).

tff(81,plain,
    ! [X67: $i,X68: $i,X70: $i,X69: $i] :
      ( ~ p12(X69,X68)
      | ~ p24(X70,X69)
      | ~ p14(X70,X67)
      | p24(X67,X68) ),
    inference(skolemize,[status(sab)],[80]) ).

tff(82,plain,
    ! [X67: $i,X68: $i,X70: $i,X69: $i] :
      ( ~ p12(X69,X68)
      | ~ p24(X70,X69)
      | ~ p14(X70,X67)
      | p24(X67,X68) ),
    inference(modus_ponens,[status(thm)],[81,74]) ).

tff(83,plain,
    ( p24(f15(c29,f13(c40,c41)),f13(c32,c33))
  <=> p24(f15(c29,f13(c40,c41)),f13(c32,c33)) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,axiom,
    p24(f15(c29,f13(c40,c41)),f13(c32,c33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24_27) ).

tff(85,plain,
    p24(f15(c29,f13(c40,c41)),f13(c32,c33)),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(87,plain,
    ( ( ~ p12(f13(c32,c33),f13(c32,c33))
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
  <=> ( ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(88,plain,
    ( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
  <=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
    inference(monotonicity,[status(thm)],[87]) ).

tff(89,plain,
    ( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) )
  <=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ) ),
    inference(transitivity,[status(thm)],[88,86]) ).

tff(90,plain,
    ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
          ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) )
    | ~ p12(f13(c32,c33),f13(c32,c33))
    | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
    | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41)))
    | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(91,plain,
    ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
          ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) )
    | ~ p24(f15(c29,f13(c40,c41)),f13(c32,c33))
    | ~ p12(f13(c32,c33),f13(c32,c33))
    | p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
    | ~ p14(f15(c29,f13(c40,c41)),f15(f8(c28),f13(c40,c41))) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33)),
    inference(unit_resolution,[status(thm)],[91,85,82,72,63]) ).

tff(93,plain,
    ( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | ~ p7(c29,f8(c28)) )
  <=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | ~ p7(c29,f8(c28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(94,plain,
    ( ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p7(c29,f8(c28))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | ~ p7(c29,f8(c28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(95,plain,
    ( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p7(c29,f8(c28))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | ~ p7(c29,f8(c28)) ) ),
    inference(monotonicity,[status(thm)],[94]) ).

tff(96,plain,
    ( ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | ~ p7(c29,f8(c28))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
            ( ~ p12(X24,X26)
            | ~ p7(X23,X25)
            | p14(f15(X23,X24),f15(X25,X26)) )
      | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
      | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | ~ p7(c29,f8(c28)) ) ),
    inference(transitivity,[status(thm)],[95,93]) ).

tff(97,plain,
    ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
          ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) )
    | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
    | ~ p7(c29,f8(c28))
    | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(98,plain,
    ( ~ ! [X25: $i,X23: $i,X26: $i,X24: $i] :
          ( ~ p12(X24,X26)
          | ~ p7(X23,X25)
          | p14(f15(X23,X24),f15(X25,X26)) )
    | ~ p12(f13(f16(c39),f17(c39)),f13(c40,c41))
    | p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
    | ~ p7(c29,f8(c28)) ),
    inference(modus_ponens,[status(thm)],[97,96]) ).

tff(99,plain,
    p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))),
    inference(unit_resolution,[status(thm)],[98,42,59,29]) ).

tff(100,plain,
    ^ [X20: $i] :
      refl(
        ( p14(X20,X20)
      <=> p14(X20,X20) )),
    inference(bind,[status(th)],]) ).

tff(101,plain,
    ( ! [X20: $i] : p14(X20,X20)
  <=> ! [X20: $i] : p14(X20,X20) ),
    inference(quant_intro,[status(thm)],[100]) ).

tff(102,plain,
    ( ! [X20: $i] : p14(X20,X20)
  <=> ! [X20: $i] : p14(X20,X20) ),
    inference(rewrite,[status(thm)],]) ).

tff(103,axiom,
    ! [X20: $i] : p14(X20,X20),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_9) ).

tff(104,plain,
    ! [X20: $i] : p14(X20,X20),
    inference(modus_ponens,[status(thm)],[103,102]) ).

tff(105,plain,
    ! [X20: $i] : p14(X20,X20),
    inference(skolemize,[status(sab)],[104]) ).

tff(106,plain,
    ! [X20: $i] : p14(X20,X20),
    inference(modus_ponens,[status(thm)],[105,101]) ).

tff(107,plain,
    ( ~ ! [X20: $i] : p14(X20,X20)
    | p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(108,plain,
    p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39)))),
    inference(unit_resolution,[status(thm)],[107,106]) ).

tff(109,plain,
    ^ [X22: $i,X21: $i,X20: $i] :
      refl(
        ( ( ~ p14(X20,X22)
          | ~ p14(X20,X21)
          | p14(X21,X22) )
      <=> ( ~ p14(X20,X22)
          | ~ p14(X20,X21)
          | p14(X21,X22) ) )),
    inference(bind,[status(th)],]) ).

tff(110,plain,
    ( ! [X22: $i,X21: $i,X20: $i] :
        ( ~ p14(X20,X22)
        | ~ p14(X20,X21)
        | p14(X21,X22) )
  <=> ! [X22: $i,X21: $i,X20: $i] :
        ( ~ p14(X20,X22)
        | ~ p14(X20,X21)
        | p14(X21,X22) ) ),
    inference(quant_intro,[status(thm)],[109]) ).

tff(111,plain,
    ( ! [X22: $i,X21: $i,X20: $i] :
        ( ~ p14(X20,X22)
        | ~ p14(X20,X21)
        | p14(X21,X22) )
  <=> ! [X22: $i,X21: $i,X20: $i] :
        ( ~ p14(X20,X22)
        | ~ p14(X20,X21)
        | p14(X21,X22) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(112,plain,
    ^ [X22: $i,X21: $i,X20: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p14(X21,X22)
              | ~ p14(X20,X21) )
          <=> ( ~ p14(X20,X21)
              | p14(X21,X22) ) )),
          ( ( p14(X21,X22)
            | ~ p14(X20,X21)
            | ~ p14(X20,X22) )
        <=> ( ~ p14(X20,X21)
            | p14(X21,X22)
            | ~ p14(X20,X22) ) )),
        rewrite(
          ( ( ~ p14(X20,X21)
            | p14(X21,X22)
            | ~ p14(X20,X22) )
        <=> ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) ) )),
        ( ( p14(X21,X22)
          | ~ p14(X20,X21)
          | ~ p14(X20,X22) )
      <=> ( ~ p14(X20,X22)
          | ~ p14(X20,X21)
          | p14(X21,X22) ) )),
    inference(bind,[status(th)],]) ).

tff(113,plain,
    ( ! [X22: $i,X21: $i,X20: $i] :
        ( p14(X21,X22)
        | ~ p14(X20,X21)
        | ~ p14(X20,X22) )
  <=> ! [X22: $i,X21: $i,X20: $i] :
        ( ~ p14(X20,X22)
        | ~ p14(X20,X21)
        | p14(X21,X22) ) ),
    inference(quant_intro,[status(thm)],[112]) ).

tff(114,axiom,
    ! [X22: $i,X21: $i,X20: $i] :
      ( p14(X21,X22)
      | ~ p14(X20,X21)
      | ~ p14(X20,X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_37) ).

tff(115,plain,
    ! [X22: $i,X21: $i,X20: $i] :
      ( ~ p14(X20,X22)
      | ~ p14(X20,X21)
      | p14(X21,X22) ),
    inference(modus_ponens,[status(thm)],[114,113]) ).

tff(116,plain,
    ! [X22: $i,X21: $i,X20: $i] :
      ( ~ p14(X20,X22)
      | ~ p14(X20,X21)
      | p14(X21,X22) ),
    inference(modus_ponens,[status(thm)],[115,111]) ).

tff(117,plain,
    ! [X22: $i,X21: $i,X20: $i] :
      ( ~ p14(X20,X22)
      | ~ p14(X20,X21)
      | p14(X21,X22) ),
    inference(skolemize,[status(sab)],[116]) ).

tff(118,plain,
    ! [X22: $i,X21: $i,X20: $i] :
      ( ~ p14(X20,X22)
      | ~ p14(X20,X21)
      | p14(X21,X22) ),
    inference(modus_ponens,[status(thm)],[117,110]) ).

tff(119,plain,
    ( ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) )
  <=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(120,plain,
    ( ( ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
  <=> ( ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(121,plain,
    ( ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
  <=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
    inference(monotonicity,[status(thm)],[120]) ).

tff(122,plain,
    ( ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) )
  <=> ( ~ ! [X22: $i,X21: $i,X20: $i] :
            ( ~ p14(X20,X22)
            | ~ p14(X20,X21)
            | p14(X21,X22) )
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
      | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ) ),
    inference(transitivity,[status(thm)],[121,119]) ).

tff(123,plain,
    ( ~ ! [X22: $i,X21: $i,X20: $i] :
          ( ~ p14(X20,X22)
          | ~ p14(X20,X21)
          | p14(X21,X22) )
    | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
    | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41)))
    | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(124,plain,
    ( ~ ! [X22: $i,X21: $i,X20: $i] :
          ( ~ p14(X20,X22)
          | ~ p14(X20,X21)
          | p14(X21,X22) )
    | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(c29,f13(f16(c39),f17(c39))))
    | p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
    | ~ p14(f15(c29,f13(f16(c39),f17(c39))),f15(f8(c28),f13(c40,c41))) ),
    inference(modus_ponens,[status(thm)],[123,122]) ).

tff(125,plain,
    p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39)))),
    inference(unit_resolution,[status(thm)],[124,118,108,99]) ).

tff(126,plain,
    ( ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33))
  <=> ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
    inference(rewrite,[status(thm)],]) ).

tff(127,axiom,
    ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p24_39) ).

tff(128,plain,
    ~ p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)),
    inference(modus_ponens,[status(thm)],[127,126]) ).

tff(129,plain,
    ( ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) )
  <=> ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
            ( ~ p12(X69,X68)
            | ~ p24(X70,X69)
            | ~ p14(X70,X67)
            | p24(X67,X68) )
      | ~ p12(f13(c32,c33),f13(c32,c33))
      | ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
      | ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
      | p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(130,plain,
    ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
          ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) )
    | ~ p12(f13(c32,c33),f13(c32,c33))
    | ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
    | ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
    | p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(131,plain,
    ( ~ ! [X67: $i,X68: $i,X70: $i,X69: $i] :
          ( ~ p12(X69,X68)
          | ~ p24(X70,X69)
          | ~ p14(X70,X67)
          | p24(X67,X68) )
    | ~ p12(f13(c32,c33),f13(c32,c33))
    | ~ p24(f15(f8(c28),f13(c40,c41)),f13(c32,c33))
    | ~ p14(f15(f8(c28),f13(c40,c41)),f15(c29,f13(f16(c39),f17(c39))))
    | p24(f15(c29,f13(f16(c39),f17(c39))),f13(c32,c33)) ),
    inference(modus_ponens,[status(thm)],[130,129]) ).

tff(132,plain,
    $false,
    inference(unit_resolution,[status(thm)],[131,128,82,72,125,92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYN659-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Sep  5 06:24:38 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 1.72/1.33  % SZS status Unsatisfiable
% 1.72/1.33  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------