TSTP Solution File: SYN598-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN598-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 23:56:35 EDT 2022

% Result   : Unsatisfiable 7.74s 5.22s
% Output   : Proof 7.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   78
% Syntax   : Number of formulae    :  152 (  45 unt;  18 typ;   0 def)
%            Number of atoms       :  571 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  730 ( 334   ~; 330   |;   0   &)
%                                         (  66 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of FOOLs       :   41 (  41 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  15   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :  353 ( 312   !;   0   ?; 353   :)

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

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

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

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

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

tff(c23_type,type,
    c23: $i ).

tff(f14_type,type,
    f14: $i > $i ).

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

tff(c22_type,type,
    c22: $i ).

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

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

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

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

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

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

tff(p5_type,type,
    p5: ( $i * $i ) > $o ).

tff(p19_type,type,
    p19: ( $i * $i ) > $o ).

tff(p18_type,type,
    p18: $i > $o ).

tff(1,plain,
    ^ [X18: $i] :
      refl(
        ( p3(X18,X18)
      <=> p3(X18,X18) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X18: $i] : p3(X18,X18)
  <=> ! [X18: $i] : p3(X18,X18) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X18: $i] : p3(X18,X18)
  <=> ! [X18: $i] : p3(X18,X18) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X18: $i] : p3(X18,X18),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_5) ).

tff(5,plain,
    ! [X18: $i] : p3(X18,X18),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X18: $i] : p3(X18,X18),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X18: $i] : p3(X18,X18),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X18: $i] : p3(X18,X18)
    | p3(f12(f15(f13(c23))),f12(f15(f13(c23)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p3(f12(f15(f13(c23))),f12(f15(f13(c23)))),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X45: $i,X46: $i] :
      refl(
        ( ( ~ p3(X45,X46)
          | p7(f14(X45),f14(X46)) )
      <=> ( ~ p3(X45,X46)
          | p7(f14(X45),f14(X46)) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X45: $i,X46: $i] :
        ( ~ p3(X45,X46)
        | p7(f14(X45),f14(X46)) )
  <=> ! [X45: $i,X46: $i] :
        ( ~ p3(X45,X46)
        | p7(f14(X45),f14(X46)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X45: $i,X46: $i] :
        ( ~ p3(X45,X46)
        | p7(f14(X45),f14(X46)) )
  <=> ! [X45: $i,X46: $i] :
        ( ~ p3(X45,X46)
        | p7(f14(X45),f14(X46)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X45: $i,X46: $i] :
      rewrite(
        ( ( p7(f14(X45),f14(X46))
          | ~ p3(X45,X46) )
      <=> ( ~ p3(X45,X46)
          | p7(f14(X45),f14(X46)) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X45: $i,X46: $i] :
        ( p7(f14(X45),f14(X46))
        | ~ p3(X45,X46) )
  <=> ! [X45: $i,X46: $i] :
        ( ~ p3(X45,X46)
        | p7(f14(X45),f14(X46)) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X45: $i,X46: $i] :
      ( p7(f14(X45),f14(X46))
      | ~ p3(X45,X46) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_17) ).

tff(16,plain,
    ! [X45: $i,X46: $i] :
      ( ~ p3(X45,X46)
      | p7(f14(X45),f14(X46)) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X45: $i,X46: $i] :
      ( ~ p3(X45,X46)
      | p7(f14(X45),f14(X46)) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X45: $i,X46: $i] :
      ( ~ p3(X45,X46)
      | p7(f14(X45),f14(X46)) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X45: $i,X46: $i] :
      ( ~ p3(X45,X46)
      | p7(f14(X45),f14(X46)) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( ( ~ ! [X45: $i,X46: $i] :
            ( ~ p3(X45,X46)
            | p7(f14(X45),f14(X46)) )
      | ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
      | p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) )
  <=> ( ~ ! [X45: $i,X46: $i] :
            ( ~ p3(X45,X46)
            | p7(f14(X45),f14(X46)) )
      | ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
      | p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [X45: $i,X46: $i] :
          ( ~ p3(X45,X46)
          | p7(f14(X45),f14(X46)) )
    | ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
    | p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(22,plain,
    ( ~ ! [X45: $i,X46: $i] :
          ( ~ p3(X45,X46)
          | p7(f14(X45),f14(X46)) )
    | ~ p3(f12(f15(f13(c23))),f12(f15(f13(c23))))
    | p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))) ),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23))))),
    inference(unit_resolution,[status(thm)],[22,19,9]) ).

tff(24,plain,
    ^ [X43: $i,X42: $i,X41: $i,X44: $i] :
      refl(
        ( ( ~ p3(X42,X44)
          | ~ p7(X41,X43)
          | p7(f11(X41,X42),f11(X43,X44)) )
      <=> ( ~ p3(X42,X44)
          | ~ p7(X41,X43)
          | p7(f11(X41,X42),f11(X43,X44)) ) )),
    inference(bind,[status(th)],]) ).

tff(25,plain,
    ( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( ~ p3(X42,X44)
        | ~ p7(X41,X43)
        | p7(f11(X41,X42),f11(X43,X44)) )
  <=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( ~ p3(X42,X44)
        | ~ p7(X41,X43)
        | p7(f11(X41,X42),f11(X43,X44)) ) ),
    inference(quant_intro,[status(thm)],[24]) ).

tff(26,plain,
    ( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( ~ p3(X42,X44)
        | ~ p7(X41,X43)
        | p7(f11(X41,X42),f11(X43,X44)) )
  <=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( ~ p3(X42,X44)
        | ~ p7(X41,X43)
        | p7(f11(X41,X42),f11(X43,X44)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    ^ [X43: $i,X42: $i,X41: $i,X44: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p7(f11(X41,X42),f11(X43,X44))
              | ~ p3(X42,X44) )
          <=> ( ~ p3(X42,X44)
              | p7(f11(X41,X42),f11(X43,X44)) ) )),
          ( ( p7(f11(X41,X42),f11(X43,X44))
            | ~ p3(X42,X44)
            | ~ p7(X41,X43) )
        <=> ( ~ p3(X42,X44)
            | p7(f11(X41,X42),f11(X43,X44))
            | ~ p7(X41,X43) ) )),
        rewrite(
          ( ( ~ p3(X42,X44)
            | p7(f11(X41,X42),f11(X43,X44))
            | ~ p7(X41,X43) )
        <=> ( ~ p3(X42,X44)
            | ~ p7(X41,X43)
            | p7(f11(X41,X42),f11(X43,X44)) ) )),
        ( ( p7(f11(X41,X42),f11(X43,X44))
          | ~ p3(X42,X44)
          | ~ p7(X41,X43) )
      <=> ( ~ p3(X42,X44)
          | ~ p7(X41,X43)
          | p7(f11(X41,X42),f11(X43,X44)) ) )),
    inference(bind,[status(th)],]) ).

tff(28,plain,
    ( ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( p7(f11(X41,X42),f11(X43,X44))
        | ~ p3(X42,X44)
        | ~ p7(X41,X43) )
  <=> ! [X43: $i,X42: $i,X41: $i,X44: $i] :
        ( ~ p3(X42,X44)
        | ~ p7(X41,X43)
        | p7(f11(X41,X42),f11(X43,X44)) ) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,axiom,
    ! [X43: $i,X42: $i,X41: $i,X44: $i] :
      ( p7(f11(X41,X42),f11(X43,X44))
      | ~ p3(X42,X44)
      | ~ p7(X41,X43) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_25) ).

tff(30,plain,
    ! [X43: $i,X42: $i,X41: $i,X44: $i] :
      ( ~ p3(X42,X44)
      | ~ p7(X41,X43)
      | p7(f11(X41,X42),f11(X43,X44)) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [X43: $i,X42: $i,X41: $i,X44: $i] :
      ( ~ p3(X42,X44)
      | ~ p7(X41,X43)
      | p7(f11(X41,X42),f11(X43,X44)) ),
    inference(modus_ponens,[status(thm)],[30,26]) ).

tff(32,plain,
    ! [X43: $i,X42: $i,X41: $i,X44: $i] :
      ( ~ p3(X42,X44)
      | ~ p7(X41,X43)
      | p7(f11(X41,X42),f11(X43,X44)) ),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [X43: $i,X42: $i,X41: $i,X44: $i] :
      ( ~ p3(X42,X44)
      | ~ p7(X41,X43)
      | p7(f11(X41,X42),f11(X43,X44)) ),
    inference(modus_ponens,[status(thm)],[32,25]) ).

tff(34,plain,
    ( p3(f4(f6(c21)),c22)
  <=> p3(f4(f6(c21)),c22) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,axiom,
    p3(f4(f6(c21)),c22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).

tff(36,plain,
    p3(f4(f6(c21)),c22),
    inference(modus_ponens,[status(thm)],[35,34]) ).

tff(37,plain,
    ( ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
            ( ~ p3(X42,X44)
            | ~ p7(X41,X43)
            | p7(f11(X41,X42),f11(X43,X44)) )
      | ~ p3(f4(f6(c21)),c22)
      | ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
      | p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) )
  <=> ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
            ( ~ p3(X42,X44)
            | ~ p7(X41,X43)
            | p7(f11(X41,X42),f11(X43,X44)) )
      | ~ p3(f4(f6(c21)),c22)
      | ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
      | p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
          ( ~ p3(X42,X44)
          | ~ p7(X41,X43)
          | p7(f11(X41,X42),f11(X43,X44)) )
    | ~ p3(f4(f6(c21)),c22)
    | ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
    | p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [X43: $i,X42: $i,X41: $i,X44: $i] :
          ( ~ p3(X42,X44)
          | ~ p7(X41,X43)
          | p7(f11(X41,X42),f11(X43,X44)) )
    | ~ p3(f4(f6(c21)),c22)
    | ~ p7(f14(f12(f15(f13(c23)))),f14(f12(f15(f13(c23)))))
    | p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22)),
    inference(unit_resolution,[status(thm)],[39,36,33,23]) ).

tff(41,plain,
    ^ [X34: $i] :
      refl(
        ( p7(X34,X34)
      <=> p7(X34,X34) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [X34: $i] : p7(X34,X34)
  <=> ! [X34: $i] : p7(X34,X34) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [X34: $i] : p7(X34,X34)
  <=> ! [X34: $i] : p7(X34,X34) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,axiom,
    ! [X34: $i] : p7(X34,X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_3) ).

tff(45,plain,
    ! [X34: $i] : p7(X34,X34),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [X34: $i] : p7(X34,X34),
    inference(skolemize,[status(sab)],[45]) ).

tff(47,plain,
    ! [X34: $i] : p7(X34,X34),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ( ~ ! [X34: $i] : p7(X34,X34)
    | p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),
    inference(unit_resolution,[status(thm)],[48,47]) ).

tff(50,plain,
    ^ [X39: $i,X38: $i,X37: $i,X40: $i] :
      refl(
        ( ( ~ p7(X38,X40)
          | ~ p7(X37,X39)
          | p7(f10(X37,X38),f10(X39,X40)) )
      <=> ( ~ p7(X38,X40)
          | ~ p7(X37,X39)
          | p7(f10(X37,X38),f10(X39,X40)) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( ~ p7(X38,X40)
        | ~ p7(X37,X39)
        | p7(f10(X37,X38),f10(X39,X40)) )
  <=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( ~ p7(X38,X40)
        | ~ p7(X37,X39)
        | p7(f10(X37,X38),f10(X39,X40)) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,plain,
    ( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( ~ p7(X38,X40)
        | ~ p7(X37,X39)
        | p7(f10(X37,X38),f10(X39,X40)) )
  <=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( ~ p7(X38,X40)
        | ~ p7(X37,X39)
        | p7(f10(X37,X38),f10(X39,X40)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ^ [X39: $i,X38: $i,X37: $i,X40: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p7(f10(X37,X38),f10(X39,X40))
              | ~ p7(X38,X40) )
          <=> ( ~ p7(X38,X40)
              | p7(f10(X37,X38),f10(X39,X40)) ) )),
          ( ( p7(f10(X37,X38),f10(X39,X40))
            | ~ p7(X38,X40)
            | ~ p7(X37,X39) )
        <=> ( ~ p7(X38,X40)
            | p7(f10(X37,X38),f10(X39,X40))
            | ~ p7(X37,X39) ) )),
        rewrite(
          ( ( ~ p7(X38,X40)
            | p7(f10(X37,X38),f10(X39,X40))
            | ~ p7(X37,X39) )
        <=> ( ~ p7(X38,X40)
            | ~ p7(X37,X39)
            | p7(f10(X37,X38),f10(X39,X40)) ) )),
        ( ( p7(f10(X37,X38),f10(X39,X40))
          | ~ p7(X38,X40)
          | ~ p7(X37,X39) )
      <=> ( ~ p7(X38,X40)
          | ~ p7(X37,X39)
          | p7(f10(X37,X38),f10(X39,X40)) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( p7(f10(X37,X38),f10(X39,X40))
        | ~ p7(X38,X40)
        | ~ p7(X37,X39) )
  <=> ! [X39: $i,X38: $i,X37: $i,X40: $i] :
        ( ~ p7(X38,X40)
        | ~ p7(X37,X39)
        | p7(f10(X37,X38),f10(X39,X40)) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,axiom,
    ! [X39: $i,X38: $i,X37: $i,X40: $i] :
      ( p7(f10(X37,X38),f10(X39,X40))
      | ~ p7(X38,X40)
      | ~ p7(X37,X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_26) ).

tff(56,plain,
    ! [X39: $i,X38: $i,X37: $i,X40: $i] :
      ( ~ p7(X38,X40)
      | ~ p7(X37,X39)
      | p7(f10(X37,X38),f10(X39,X40)) ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    ! [X39: $i,X38: $i,X37: $i,X40: $i] :
      ( ~ p7(X38,X40)
      | ~ p7(X37,X39)
      | p7(f10(X37,X38),f10(X39,X40)) ),
    inference(modus_ponens,[status(thm)],[56,52]) ).

tff(58,plain,
    ! [X39: $i,X38: $i,X37: $i,X40: $i] :
      ( ~ p7(X38,X40)
      | ~ p7(X37,X39)
      | p7(f10(X37,X38),f10(X39,X40)) ),
    inference(skolemize,[status(sab)],[57]) ).

tff(59,plain,
    ! [X39: $i,X38: $i,X37: $i,X40: $i] :
      ( ~ p7(X38,X40)
      | ~ p7(X37,X39)
      | p7(f10(X37,X38),f10(X39,X40)) ),
    inference(modus_ponens,[status(thm)],[58,51]) ).

tff(60,plain,
    ( ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
            ( ~ p7(X38,X40)
            | ~ p7(X37,X39)
            | p7(f10(X37,X38),f10(X39,X40)) )
      | ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
      | ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
      | p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) )
  <=> ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
            ( ~ p7(X38,X40)
            | ~ p7(X37,X39)
            | p7(f10(X37,X38),f10(X39,X40)) )
      | ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
      | ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
      | p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
          ( ~ p7(X38,X40)
          | ~ p7(X37,X39)
          | p7(f10(X37,X38),f10(X39,X40)) )
    | ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
    | ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
    | p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(62,plain,
    ( ~ ! [X39: $i,X38: $i,X37: $i,X40: $i] :
          ( ~ p7(X38,X40)
          | ~ p7(X37,X39)
          | p7(f10(X37,X38),f10(X39,X40)) )
    | ~ p7(f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))
    | ~ p7(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),c22))
    | p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))) ),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23))))))))))),
    inference(unit_resolution,[status(thm)],[62,59,49,40]) ).

tff(64,plain,
    ^ [X31: $i] :
      refl(
        ( p5(X31,X31)
      <=> p5(X31,X31) )),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ( ! [X31: $i] : p5(X31,X31)
  <=> ! [X31: $i] : p5(X31,X31) ),
    inference(quant_intro,[status(thm)],[64]) ).

tff(66,plain,
    ( ! [X31: $i] : p5(X31,X31)
  <=> ! [X31: $i] : p5(X31,X31) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,axiom,
    ! [X31: $i] : p5(X31,X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_6) ).

tff(68,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(skolemize,[status(sab)],[68]) ).

tff(70,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(modus_ponens,[status(thm)],[69,65]) ).

tff(71,plain,
    ( ~ ! [X31: $i] : p5(X31,X31)
    | p5(c21,c21) ),
    inference(quant_inst,[status(thm)],]) ).

tff(72,plain,
    p5(c21,c21),
    inference(unit_resolution,[status(thm)],[71,70]) ).

tff(73,plain,
    ^ [X49: $i,X50: $i] :
      refl(
        ( ( ~ p5(X49,X50)
          | p7(f9(X49),f9(X50)) )
      <=> ( ~ p5(X49,X50)
          | p7(f9(X49),f9(X50)) ) )),
    inference(bind,[status(th)],]) ).

tff(74,plain,
    ( ! [X49: $i,X50: $i] :
        ( ~ p5(X49,X50)
        | p7(f9(X49),f9(X50)) )
  <=> ! [X49: $i,X50: $i] :
        ( ~ p5(X49,X50)
        | p7(f9(X49),f9(X50)) ) ),
    inference(quant_intro,[status(thm)],[73]) ).

tff(75,plain,
    ( ! [X49: $i,X50: $i] :
        ( ~ p5(X49,X50)
        | p7(f9(X49),f9(X50)) )
  <=> ! [X49: $i,X50: $i] :
        ( ~ p5(X49,X50)
        | p7(f9(X49),f9(X50)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    ^ [X49: $i,X50: $i] :
      rewrite(
        ( ( p7(f9(X49),f9(X50))
          | ~ p5(X49,X50) )
      <=> ( ~ p5(X49,X50)
          | p7(f9(X49),f9(X50)) ) )),
    inference(bind,[status(th)],]) ).

tff(77,plain,
    ( ! [X49: $i,X50: $i] :
        ( p7(f9(X49),f9(X50))
        | ~ p5(X49,X50) )
  <=> ! [X49: $i,X50: $i] :
        ( ~ p5(X49,X50)
        | p7(f9(X49),f9(X50)) ) ),
    inference(quant_intro,[status(thm)],[76]) ).

tff(78,axiom,
    ! [X49: $i,X50: $i] :
      ( p7(f9(X49),f9(X50))
      | ~ p5(X49,X50) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_10) ).

tff(79,plain,
    ! [X49: $i,X50: $i] :
      ( ~ p5(X49,X50)
      | p7(f9(X49),f9(X50)) ),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ! [X49: $i,X50: $i] :
      ( ~ p5(X49,X50)
      | p7(f9(X49),f9(X50)) ),
    inference(modus_ponens,[status(thm)],[79,75]) ).

tff(81,plain,
    ! [X49: $i,X50: $i] :
      ( ~ p5(X49,X50)
      | p7(f9(X49),f9(X50)) ),
    inference(skolemize,[status(sab)],[80]) ).

tff(82,plain,
    ! [X49: $i,X50: $i] :
      ( ~ p5(X49,X50)
      | p7(f9(X49),f9(X50)) ),
    inference(modus_ponens,[status(thm)],[81,74]) ).

tff(83,plain,
    ( ( ~ ! [X49: $i,X50: $i] :
            ( ~ p5(X49,X50)
            | p7(f9(X49),f9(X50)) )
      | ~ p5(c21,c21)
      | p7(f9(c21),f9(c21)) )
  <=> ( ~ ! [X49: $i,X50: $i] :
            ( ~ p5(X49,X50)
            | p7(f9(X49),f9(X50)) )
      | ~ p5(c21,c21)
      | p7(f9(c21),f9(c21)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(84,plain,
    ( ~ ! [X49: $i,X50: $i] :
          ( ~ p5(X49,X50)
          | p7(f9(X49),f9(X50)) )
    | ~ p5(c21,c21)
    | p7(f9(c21),f9(c21)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(85,plain,
    ( ~ ! [X49: $i,X50: $i] :
          ( ~ p5(X49,X50)
          | p7(f9(X49),f9(X50)) )
    | ~ p5(c21,c21)
    | p7(f9(c21),f9(c21)) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    p7(f9(c21),f9(c21)),
    inference(unit_resolution,[status(thm)],[85,82,72]) ).

tff(87,plain,
    ^ [X47: $i,X48: $i] :
      refl(
        ( ( ~ p7(X47,X48)
          | p7(f8(X47),f8(X48)) )
      <=> ( ~ p7(X47,X48)
          | p7(f8(X47),f8(X48)) ) )),
    inference(bind,[status(th)],]) ).

tff(88,plain,
    ( ! [X47: $i,X48: $i] :
        ( ~ p7(X47,X48)
        | p7(f8(X47),f8(X48)) )
  <=> ! [X47: $i,X48: $i] :
        ( ~ p7(X47,X48)
        | p7(f8(X47),f8(X48)) ) ),
    inference(quant_intro,[status(thm)],[87]) ).

tff(89,plain,
    ( ! [X47: $i,X48: $i] :
        ( ~ p7(X47,X48)
        | p7(f8(X47),f8(X48)) )
  <=> ! [X47: $i,X48: $i] :
        ( ~ p7(X47,X48)
        | p7(f8(X47),f8(X48)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(90,plain,
    ^ [X47: $i,X48: $i] :
      rewrite(
        ( ( p7(f8(X47),f8(X48))
          | ~ p7(X47,X48) )
      <=> ( ~ p7(X47,X48)
          | p7(f8(X47),f8(X48)) ) )),
    inference(bind,[status(th)],]) ).

tff(91,plain,
    ( ! [X47: $i,X48: $i] :
        ( p7(f8(X47),f8(X48))
        | ~ p7(X47,X48) )
  <=> ! [X47: $i,X48: $i] :
        ( ~ p7(X47,X48)
        | p7(f8(X47),f8(X48)) ) ),
    inference(quant_intro,[status(thm)],[90]) ).

tff(92,axiom,
    ! [X47: $i,X48: $i] :
      ( p7(f8(X47),f8(X48))
      | ~ p7(X47,X48) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_18) ).

tff(93,plain,
    ! [X47: $i,X48: $i] :
      ( ~ p7(X47,X48)
      | p7(f8(X47),f8(X48)) ),
    inference(modus_ponens,[status(thm)],[92,91]) ).

tff(94,plain,
    ! [X47: $i,X48: $i] :
      ( ~ p7(X47,X48)
      | p7(f8(X47),f8(X48)) ),
    inference(modus_ponens,[status(thm)],[93,89]) ).

tff(95,plain,
    ! [X47: $i,X48: $i] :
      ( ~ p7(X47,X48)
      | p7(f8(X47),f8(X48)) ),
    inference(skolemize,[status(sab)],[94]) ).

tff(96,plain,
    ! [X47: $i,X48: $i] :
      ( ~ p7(X47,X48)
      | p7(f8(X47),f8(X48)) ),
    inference(modus_ponens,[status(thm)],[95,88]) ).

tff(97,plain,
    ( ( ~ ! [X47: $i,X48: $i] :
            ( ~ p7(X47,X48)
            | p7(f8(X47),f8(X48)) )
      | ~ p7(f9(c21),f9(c21))
      | p7(f8(f9(c21)),f8(f9(c21))) )
  <=> ( ~ ! [X47: $i,X48: $i] :
            ( ~ p7(X47,X48)
            | p7(f8(X47),f8(X48)) )
      | ~ p7(f9(c21),f9(c21))
      | p7(f8(f9(c21)),f8(f9(c21))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(98,plain,
    ( ~ ! [X47: $i,X48: $i] :
          ( ~ p7(X47,X48)
          | p7(f8(X47),f8(X48)) )
    | ~ p7(f9(c21),f9(c21))
    | p7(f8(f9(c21)),f8(f9(c21))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(99,plain,
    ( ~ ! [X47: $i,X48: $i] :
          ( ~ p7(X47,X48)
          | p7(f8(X47),f8(X48)) )
    | ~ p7(f9(c21),f9(c21))
    | p7(f8(f9(c21)),f8(f9(c21))) ),
    inference(modus_ponens,[status(thm)],[98,97]) ).

tff(100,plain,
    p7(f8(f9(c21)),f8(f9(c21))),
    inference(unit_resolution,[status(thm)],[99,96,86]) ).

tff(101,plain,
    ^ [X8: $i] :
      refl(
        ( ( ~ p18(X8)
          | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
      <=> ( ~ p18(X8)
          | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) )),
    inference(bind,[status(th)],]) ).

tff(102,plain,
    ( ! [X8: $i] :
        ( ~ p18(X8)
        | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
  <=> ! [X8: $i] :
        ( ~ p18(X8)
        | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
    inference(quant_intro,[status(thm)],[101]) ).

tff(103,plain,
    ( ! [X8: $i] :
        ( ~ p18(X8)
        | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
  <=> ! [X8: $i] :
        ( ~ p18(X8)
        | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(104,plain,
    ^ [X8: $i] :
      rewrite(
        ( ( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
          | ~ p18(X8) )
      <=> ( ~ p18(X8)
          | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) )),
    inference(bind,[status(th)],]) ).

tff(105,plain,
    ( ! [X8: $i] :
        ( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
        | ~ p18(X8) )
  <=> ! [X8: $i] :
        ( ~ p18(X8)
        | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ) ),
    inference(quant_intro,[status(thm)],[104]) ).

tff(106,axiom,
    ! [X8: $i] :
      ( p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8)))
      | ~ p18(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_28) ).

tff(107,plain,
    ! [X8: $i] :
      ( ~ p18(X8)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
    inference(modus_ponens,[status(thm)],[106,105]) ).

tff(108,plain,
    ! [X8: $i] :
      ( ~ p18(X8)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
    inference(modus_ponens,[status(thm)],[107,103]) ).

tff(109,plain,
    ! [X8: $i] :
      ( ~ p18(X8)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
    inference(skolemize,[status(sab)],[108]) ).

tff(110,plain,
    ! [X8: $i] :
      ( ~ p18(X8)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) ),
    inference(modus_ponens,[status(thm)],[109,102]) ).

tff(111,plain,
    ( p18(c21)
  <=> p18(c21) ),
    inference(rewrite,[status(thm)],]) ).

tff(112,axiom,
    p18(c21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c21_is_p18_2) ).

tff(113,plain,
    p18(c21),
    inference(modus_ponens,[status(thm)],[112,111]) ).

tff(114,plain,
    ( ( ~ ! [X8: $i] :
            ( ~ p18(X8)
            | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
      | ~ p18(c21)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) )
  <=> ( ~ ! [X8: $i] :
            ( ~ p18(X8)
            | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
      | ~ p18(c21)
      | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(115,plain,
    ( ~ ! [X8: $i] :
          ( ~ p18(X8)
          | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
    | ~ p18(c21)
    | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(116,plain,
    ( ~ ! [X8: $i] :
          ( ~ p18(X8)
          | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(X8))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(X8))) )
    | ~ p18(c21)
    | p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
    inference(modus_ponens,[status(thm)],[115,114]) ).

tff(117,plain,
    p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
    inference(unit_resolution,[status(thm)],[116,113,110]) ).

tff(118,plain,
    ( ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
  <=> ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
    inference(rewrite,[status(thm)],]) ).

tff(119,axiom,
    ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p19_27) ).

tff(120,plain,
    ~ p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))),
    inference(modus_ponens,[status(thm)],[119,118]) ).

tff(121,plain,
    ^ [X6: $i,X4: $i,X7: $i,X5: $i] :
      refl(
        ( ( ~ p7(X7,X5)
          | ~ p19(X6,X7)
          | ~ p7(X6,X4)
          | p19(X4,X5) )
      <=> ( ~ p7(X7,X5)
          | ~ p19(X6,X7)
          | ~ p7(X6,X4)
          | p19(X4,X5) ) )),
    inference(bind,[status(th)],]) ).

tff(122,plain,
    ( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( ~ p7(X7,X5)
        | ~ p19(X6,X7)
        | ~ p7(X6,X4)
        | p19(X4,X5) )
  <=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( ~ p7(X7,X5)
        | ~ p19(X6,X7)
        | ~ p7(X6,X4)
        | p19(X4,X5) ) ),
    inference(quant_intro,[status(thm)],[121]) ).

tff(123,plain,
    ( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( ~ p7(X7,X5)
        | ~ p19(X6,X7)
        | ~ p7(X6,X4)
        | p19(X4,X5) )
  <=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( ~ p7(X7,X5)
        | ~ p19(X6,X7)
        | ~ p7(X6,X4)
        | p19(X4,X5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(124,plain,
    ^ [X6: $i,X4: $i,X7: $i,X5: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p19(X4,X5)
                  | ~ p7(X6,X4) )
              <=> ( ~ p7(X6,X4)
                  | p19(X4,X5) ) )),
              ( ( p19(X4,X5)
                | ~ p7(X6,X4)
                | ~ p7(X7,X5) )
            <=> ( ~ p7(X6,X4)
                | p19(X4,X5)
                | ~ p7(X7,X5) ) )),
            rewrite(
              ( ( ~ p7(X6,X4)
                | p19(X4,X5)
                | ~ p7(X7,X5) )
            <=> ( ~ p7(X7,X5)
                | ~ p7(X6,X4)
                | p19(X4,X5) ) )),
            ( ( p19(X4,X5)
              | ~ p7(X6,X4)
              | ~ p7(X7,X5) )
          <=> ( ~ p7(X7,X5)
              | ~ p7(X6,X4)
              | p19(X4,X5) ) )),
          ( ( p19(X4,X5)
            | ~ p7(X6,X4)
            | ~ p7(X7,X5)
            | ~ p19(X6,X7) )
        <=> ( ~ p7(X7,X5)
            | ~ p7(X6,X4)
            | p19(X4,X5)
            | ~ p19(X6,X7) ) )),
        rewrite(
          ( ( ~ p7(X7,X5)
            | ~ p7(X6,X4)
            | p19(X4,X5)
            | ~ p19(X6,X7) )
        <=> ( ~ p7(X7,X5)
            | ~ p19(X6,X7)
            | ~ p7(X6,X4)
            | p19(X4,X5) ) )),
        ( ( p19(X4,X5)
          | ~ p7(X6,X4)
          | ~ p7(X7,X5)
          | ~ p19(X6,X7) )
      <=> ( ~ p7(X7,X5)
          | ~ p19(X6,X7)
          | ~ p7(X6,X4)
          | p19(X4,X5) ) )),
    inference(bind,[status(th)],]) ).

tff(125,plain,
    ( ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( p19(X4,X5)
        | ~ p7(X6,X4)
        | ~ p7(X7,X5)
        | ~ p19(X6,X7) )
  <=> ! [X6: $i,X4: $i,X7: $i,X5: $i] :
        ( ~ p7(X7,X5)
        | ~ p19(X6,X7)
        | ~ p7(X6,X4)
        | p19(X4,X5) ) ),
    inference(quant_intro,[status(thm)],[124]) ).

tff(126,axiom,
    ! [X6: $i,X4: $i,X7: $i,X5: $i] :
      ( p19(X4,X5)
      | ~ p7(X6,X4)
      | ~ p7(X7,X5)
      | ~ p19(X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_23) ).

tff(127,plain,
    ! [X6: $i,X4: $i,X7: $i,X5: $i] :
      ( ~ p7(X7,X5)
      | ~ p19(X6,X7)
      | ~ p7(X6,X4)
      | p19(X4,X5) ),
    inference(modus_ponens,[status(thm)],[126,125]) ).

tff(128,plain,
    ! [X6: $i,X4: $i,X7: $i,X5: $i] :
      ( ~ p7(X7,X5)
      | ~ p19(X6,X7)
      | ~ p7(X6,X4)
      | p19(X4,X5) ),
    inference(modus_ponens,[status(thm)],[127,123]) ).

tff(129,plain,
    ! [X6: $i,X4: $i,X7: $i,X5: $i] :
      ( ~ p7(X7,X5)
      | ~ p19(X6,X7)
      | ~ p7(X6,X4)
      | p19(X4,X5) ),
    inference(skolemize,[status(sab)],[128]) ).

tff(130,plain,
    ! [X6: $i,X4: $i,X7: $i,X5: $i] :
      ( ~ p7(X7,X5)
      | ~ p19(X6,X7)
      | ~ p7(X6,X4)
      | p19(X4,X5) ),
    inference(modus_ponens,[status(thm)],[129,122]) ).

tff(131,plain,
    ( ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
            ( ~ p7(X7,X5)
            | ~ p19(X6,X7)
            | ~ p7(X6,X4)
            | p19(X4,X5) )
      | ~ p7(f8(f9(c21)),f8(f9(c21)))
      | ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
      | ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
      | p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) )
  <=> ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
            ( ~ p7(X7,X5)
            | ~ p19(X6,X7)
            | ~ p7(X6,X4)
            | p19(X4,X5) )
      | ~ p7(f8(f9(c21)),f8(f9(c21)))
      | ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
      | ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
      | p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(132,plain,
    ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
          ( ~ p7(X7,X5)
          | ~ p19(X6,X7)
          | ~ p7(X6,X4)
          | p19(X4,X5) )
    | ~ p7(f8(f9(c21)),f8(f9(c21)))
    | ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
    | ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
    | p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(133,plain,
    ( ~ ! [X6: $i,X4: $i,X7: $i,X5: $i] :
          ( ~ p7(X7,X5)
          | ~ p19(X6,X7)
          | ~ p7(X6,X4)
          | p19(X4,X5) )
    | ~ p7(f8(f9(c21)),f8(f9(c21)))
    | ~ p19(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21)))
    | ~ p7(f10(f11(f14(f12(f15(f13(c23)))),f4(f6(c21))),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))))
    | p19(f10(f11(f14(f12(f15(f13(c23)))),c22),f11(f14(f12(f15(f13(c23)))),f12(f13(f13(f13(f13(f13(f13(f13(c23)))))))))),f8(f9(c21))) ),
    inference(modus_ponens,[status(thm)],[132,131]) ).

tff(134,plain,
    $false,
    inference(unit_resolution,[status(thm)],[133,130,120,117,100,63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN598-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 05:43:35 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 7.74/5.22  % SZS status Unsatisfiable
% 7.74/5.22  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------