TSTP Solution File: SYN556-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN556-1 : 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 23:56:24 EDT 2022

% Result   : Unsatisfiable 0.87s 0.86s
% Output   : Proof 1.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   64
% Syntax   : Number of formulae    :  126 (  38 unt;  12 typ;   0 def)
%            Number of atoms       :  632 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  882 ( 412   ~; 408   |;   0   &)
%                                         (  62 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of FOOLs       :   48 (  48 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   7   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :  399 ( 357   !;   0   ?; 399   :)

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

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

tff(c11_type,type,
    c11: $i ).

tff(f5_type,type,
    f5: ( $i * $i ) > $i ).

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

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

tff(c12_type,type,
    c12: $i ).

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

tff(c10_type,type,
    c10: $i ).

tff(c13_type,type,
    c13: $i ).

tff(p2_type,type,
    p2: ( $i * $i ) > $o ).

tff(c9_type,type,
    c9: $i ).

tff(1,plain,
    ^ [X15: $i] :
      refl(
        ( p3(X15,X15)
      <=> p3(X15,X15) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X15: $i] : p3(X15,X15)
  <=> ! [X15: $i] : p3(X15,X15) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X15: $i] : p3(X15,X15)
  <=> ! [X15: $i] : p3(X15,X15) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X15: $i] : p3(X15,X15),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_2) ).

tff(5,plain,
    ! [X15: $i] : p3(X15,X15),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X15: $i] : p3(X15,X15),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X15: $i] : p3(X15,X15),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X15: $i] : p3(X15,X15)
    | p3(c11,c11) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p3(c11,c11),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X14: $i,X12: $i,X11: $i,X13: $i] :
      refl(
        ( ( ~ p2(X12,X14)
          | ~ p3(X11,X13)
          | p2(f8(X11,X12),f8(X13,X14)) )
      <=> ( ~ p2(X12,X14)
          | ~ p3(X11,X13)
          | p2(f8(X11,X12),f8(X13,X14)) ) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( ~ p2(X12,X14)
        | ~ p3(X11,X13)
        | p2(f8(X11,X12),f8(X13,X14)) )
  <=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( ~ p2(X12,X14)
        | ~ p3(X11,X13)
        | p2(f8(X11,X12),f8(X13,X14)) ) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( ~ p2(X12,X14)
        | ~ p3(X11,X13)
        | p2(f8(X11,X12),f8(X13,X14)) )
  <=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( ~ p2(X12,X14)
        | ~ p3(X11,X13)
        | p2(f8(X11,X12),f8(X13,X14)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,plain,
    ^ [X14: $i,X12: $i,X11: $i,X13: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p2(f8(X11,X12),f8(X13,X14))
              | ~ p2(X12,X14) )
          <=> ( ~ p2(X12,X14)
              | p2(f8(X11,X12),f8(X13,X14)) ) )),
          ( ( p2(f8(X11,X12),f8(X13,X14))
            | ~ p2(X12,X14)
            | ~ p3(X11,X13) )
        <=> ( ~ p2(X12,X14)
            | p2(f8(X11,X12),f8(X13,X14))
            | ~ p3(X11,X13) ) )),
        rewrite(
          ( ( ~ p2(X12,X14)
            | p2(f8(X11,X12),f8(X13,X14))
            | ~ p3(X11,X13) )
        <=> ( ~ p2(X12,X14)
            | ~ p3(X11,X13)
            | p2(f8(X11,X12),f8(X13,X14)) ) )),
        ( ( p2(f8(X11,X12),f8(X13,X14))
          | ~ p2(X12,X14)
          | ~ p3(X11,X13) )
      <=> ( ~ p2(X12,X14)
          | ~ p3(X11,X13)
          | p2(f8(X11,X12),f8(X13,X14)) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( p2(f8(X11,X12),f8(X13,X14))
        | ~ p2(X12,X14)
        | ~ p3(X11,X13) )
  <=> ! [X14: $i,X12: $i,X11: $i,X13: $i] :
        ( ~ p2(X12,X14)
        | ~ p3(X11,X13)
        | p2(f8(X11,X12),f8(X13,X14)) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,axiom,
    ! [X14: $i,X12: $i,X11: $i,X13: $i] :
      ( p2(f8(X11,X12),f8(X13,X14))
      | ~ p2(X12,X14)
      | ~ p3(X11,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_11) ).

tff(16,plain,
    ! [X14: $i,X12: $i,X11: $i,X13: $i] :
      ( ~ p2(X12,X14)
      | ~ p3(X11,X13)
      | p2(f8(X11,X12),f8(X13,X14)) ),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ! [X14: $i,X12: $i,X11: $i,X13: $i] :
      ( ~ p2(X12,X14)
      | ~ p3(X11,X13)
      | p2(f8(X11,X12),f8(X13,X14)) ),
    inference(modus_ponens,[status(thm)],[16,12]) ).

tff(18,plain,
    ! [X14: $i,X12: $i,X11: $i,X13: $i] :
      ( ~ p2(X12,X14)
      | ~ p3(X11,X13)
      | p2(f8(X11,X12),f8(X13,X14)) ),
    inference(skolemize,[status(sab)],[17]) ).

tff(19,plain,
    ! [X14: $i,X12: $i,X11: $i,X13: $i] :
      ( ~ p2(X12,X14)
      | ~ p3(X11,X13)
      | p2(f8(X11,X12),f8(X13,X14)) ),
    inference(modus_ponens,[status(thm)],[18,11]) ).

tff(20,plain,
    ( p2(c10,c13)
  <=> p2(c10,c13) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    p2(c10,c13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_3) ).

tff(22,plain,
    p2(c10,c13),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    ( ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
            ( ~ p2(X12,X14)
            | ~ p3(X11,X13)
            | p2(f8(X11,X12),f8(X13,X14)) )
      | ~ p2(c10,c13)
      | ~ p3(c11,c11)
      | p2(f8(c11,c10),f8(c11,c13)) )
  <=> ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
            ( ~ p2(X12,X14)
            | ~ p3(X11,X13)
            | p2(f8(X11,X12),f8(X13,X14)) )
      | ~ p2(c10,c13)
      | ~ p3(c11,c11)
      | p2(f8(c11,c10),f8(c11,c13)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
          ( ~ p2(X12,X14)
          | ~ p3(X11,X13)
          | p2(f8(X11,X12),f8(X13,X14)) )
    | ~ p2(c10,c13)
    | ~ p3(c11,c11)
    | p2(f8(c11,c10),f8(c11,c13)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [X14: $i,X12: $i,X11: $i,X13: $i] :
          ( ~ p2(X12,X14)
          | ~ p3(X11,X13)
          | p2(f8(X11,X12),f8(X13,X14)) )
    | ~ p2(c10,c13)
    | ~ p3(c11,c11)
    | p2(f8(c11,c10),f8(c11,c13)) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    p2(f8(c11,c10),f8(c11,c13)),
    inference(unit_resolution,[status(thm)],[25,22,19,9]) ).

tff(27,plain,
    ^ [X0: $i] :
      refl(
        ( p2(X0,X0)
      <=> p2(X0,X0) )),
    inference(bind,[status(th)],]) ).

tff(28,plain,
    ( ! [X0: $i] : p2(X0,X0)
  <=> ! [X0: $i] : p2(X0,X0) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,plain,
    ( ! [X0: $i] : p2(X0,X0)
  <=> ! [X0: $i] : p2(X0,X0) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    ! [X0: $i] : p2(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).

tff(31,plain,
    ! [X0: $i] : p2(X0,X0),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ! [X0: $i] : p2(X0,X0),
    inference(skolemize,[status(sab)],[31]) ).

tff(33,plain,
    ! [X0: $i] : p2(X0,X0),
    inference(modus_ponens,[status(thm)],[32,28]) ).

tff(34,plain,
    ( ~ ! [X0: $i] : p2(X0,X0)
    | p2(f8(c11,c10),f8(c11,c10)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(35,plain,
    p2(f8(c11,c10),f8(c11,c10)),
    inference(unit_resolution,[status(thm)],[34,33]) ).

tff(36,plain,
    ^ [X0: $i,X2: $i,X1: $i] :
      refl(
        ( ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) )
      <=> ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X0: $i,X2: $i,X1: $i] :
        ( ~ p2(X0,X2)
        | ~ p2(X0,X1)
        | p2(X1,X2) )
  <=> ! [X0: $i,X2: $i,X1: $i] :
        ( ~ p2(X0,X2)
        | ~ p2(X0,X1)
        | p2(X1,X2) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X0: $i,X2: $i,X1: $i] :
        ( ~ p2(X0,X2)
        | ~ p2(X0,X1)
        | p2(X1,X2) )
  <=> ! [X0: $i,X2: $i,X1: $i] :
        ( ~ p2(X0,X2)
        | ~ p2(X0,X1)
        | p2(X1,X2) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ^ [X0: $i,X2: $i,X1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p2(X1,X2)
              | ~ p2(X0,X1) )
          <=> ( ~ p2(X0,X1)
              | p2(X1,X2) ) )),
          ( ( p2(X1,X2)
            | ~ p2(X0,X1)
            | ~ p2(X0,X2) )
        <=> ( ~ p2(X0,X1)
            | p2(X1,X2)
            | ~ p2(X0,X2) ) )),
        rewrite(
          ( ( ~ p2(X0,X1)
            | p2(X1,X2)
            | ~ p2(X0,X2) )
        <=> ( ~ p2(X0,X2)
            | ~ p2(X0,X1)
            | p2(X1,X2) ) )),
        ( ( p2(X1,X2)
          | ~ p2(X0,X1)
          | ~ p2(X0,X2) )
      <=> ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X0: $i,X2: $i,X1: $i] :
        ( p2(X1,X2)
        | ~ p2(X0,X1)
        | ~ p2(X0,X2) )
  <=> ! [X0: $i,X2: $i,X1: $i] :
        ( ~ p2(X0,X2)
        | ~ p2(X0,X1)
        | p2(X1,X2) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,axiom,
    ! [X0: $i,X2: $i,X1: $i] :
      ( p2(X1,X2)
      | ~ p2(X0,X1)
      | ~ p2(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).

tff(42,plain,
    ! [X0: $i,X2: $i,X1: $i] :
      ( ~ p2(X0,X2)
      | ~ p2(X0,X1)
      | p2(X1,X2) ),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ! [X0: $i,X2: $i,X1: $i] :
      ( ~ p2(X0,X2)
      | ~ p2(X0,X1)
      | p2(X1,X2) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ! [X0: $i,X2: $i,X1: $i] :
      ( ~ p2(X0,X2)
      | ~ p2(X0,X1)
      | p2(X1,X2) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [X0: $i,X2: $i,X1: $i] :
      ( ~ p2(X0,X2)
      | ~ p2(X0,X1)
      | p2(X1,X2) ),
    inference(modus_ponens,[status(thm)],[44,37]) ).

tff(46,plain,
    ( ( ~ ! [X0: $i,X2: $i,X1: $i] :
            ( ~ p2(X0,X2)
            | ~ p2(X0,X1)
            | p2(X1,X2) )
      | ~ p2(f8(c11,c10),f8(c11,c10))
      | ~ p2(f8(c11,c10),f8(c11,c13))
      | p2(f8(c11,c13),f8(c11,c10)) )
  <=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
            ( ~ p2(X0,X2)
            | ~ p2(X0,X1)
            | p2(X1,X2) )
      | ~ p2(f8(c11,c10),f8(c11,c10))
      | ~ p2(f8(c11,c10),f8(c11,c13))
      | p2(f8(c11,c13),f8(c11,c10)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ( ~ ! [X0: $i,X2: $i,X1: $i] :
          ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) )
    | ~ p2(f8(c11,c10),f8(c11,c10))
    | ~ p2(f8(c11,c10),f8(c11,c13))
    | p2(f8(c11,c13),f8(c11,c10)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    ( ~ ! [X0: $i,X2: $i,X1: $i] :
          ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) )
    | ~ p2(f8(c11,c10),f8(c11,c10))
    | ~ p2(f8(c11,c10),f8(c11,c13))
    | p2(f8(c11,c13),f8(c11,c10)) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    p2(f8(c11,c13),f8(c11,c10)),
    inference(unit_resolution,[status(thm)],[48,45,35,26]) ).

tff(50,plain,
    ( ~ ! [X0: $i] : p2(X0,X0)
    | p2(f6(f7(c12)),f6(f7(c12))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(51,plain,
    p2(f6(f7(c12)),f6(f7(c12))),
    inference(unit_resolution,[status(thm)],[50,33]) ).

tff(52,plain,
    ^ [X6: $i,X4: $i,X3: $i,X5: $i] :
      refl(
        ( ( ~ p2(X3,X5)
          | ~ p2(X4,X6)
          | p2(f5(X3,X4),f5(X5,X6)) )
      <=> ( ~ p2(X3,X5)
          | ~ p2(X4,X6)
          | p2(f5(X3,X4),f5(X5,X6)) ) )),
    inference(bind,[status(th)],]) ).

tff(53,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p2(X3,X5)
        | ~ p2(X4,X6)
        | p2(f5(X3,X4),f5(X5,X6)) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p2(X3,X5)
        | ~ p2(X4,X6)
        | p2(f5(X3,X4),f5(X5,X6)) ) ),
    inference(quant_intro,[status(thm)],[52]) ).

tff(54,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p2(X3,X5)
        | ~ p2(X4,X6)
        | p2(f5(X3,X4),f5(X5,X6)) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p2(X3,X5)
        | ~ p2(X4,X6)
        | p2(f5(X3,X4),f5(X5,X6)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(55,plain,
    ^ [X6: $i,X4: $i,X3: $i,X5: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p2(f5(X3,X4),f5(X5,X6))
              | ~ p2(X3,X5) )
          <=> ( ~ p2(X3,X5)
              | p2(f5(X3,X4),f5(X5,X6)) ) )),
          ( ( p2(f5(X3,X4),f5(X5,X6))
            | ~ p2(X3,X5)
            | ~ p2(X4,X6) )
        <=> ( ~ p2(X3,X5)
            | p2(f5(X3,X4),f5(X5,X6))
            | ~ p2(X4,X6) ) )),
        rewrite(
          ( ( ~ p2(X3,X5)
            | p2(f5(X3,X4),f5(X5,X6))
            | ~ p2(X4,X6) )
        <=> ( ~ p2(X3,X5)
            | ~ p2(X4,X6)
            | p2(f5(X3,X4),f5(X5,X6)) ) )),
        ( ( p2(f5(X3,X4),f5(X5,X6))
          | ~ p2(X3,X5)
          | ~ p2(X4,X6) )
      <=> ( ~ p2(X3,X5)
          | ~ p2(X4,X6)
          | p2(f5(X3,X4),f5(X5,X6)) ) )),
    inference(bind,[status(th)],]) ).

tff(56,plain,
    ( ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( p2(f5(X3,X4),f5(X5,X6))
        | ~ p2(X3,X5)
        | ~ p2(X4,X6) )
  <=> ! [X6: $i,X4: $i,X3: $i,X5: $i] :
        ( ~ p2(X3,X5)
        | ~ p2(X4,X6)
        | p2(f5(X3,X4),f5(X5,X6)) ) ),
    inference(quant_intro,[status(thm)],[55]) ).

tff(57,axiom,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( p2(f5(X3,X4),f5(X5,X6))
      | ~ p2(X3,X5)
      | ~ p2(X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).

tff(58,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p2(X3,X5)
      | ~ p2(X4,X6)
      | p2(f5(X3,X4),f5(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[57,56]) ).

tff(59,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p2(X3,X5)
      | ~ p2(X4,X6)
      | p2(f5(X3,X4),f5(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[58,54]) ).

tff(60,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p2(X3,X5)
      | ~ p2(X4,X6)
      | p2(f5(X3,X4),f5(X5,X6)) ),
    inference(skolemize,[status(sab)],[59]) ).

tff(61,plain,
    ! [X6: $i,X4: $i,X3: $i,X5: $i] :
      ( ~ p2(X3,X5)
      | ~ p2(X4,X6)
      | p2(f5(X3,X4),f5(X5,X6)) ),
    inference(modus_ponens,[status(thm)],[60,53]) ).

tff(62,plain,
    ( ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
            ( ~ p2(X3,X5)
            | ~ p2(X4,X6)
            | p2(f5(X3,X4),f5(X5,X6)) )
      | ~ p2(f8(c11,c13),f8(c11,c10))
      | ~ p2(f6(f7(c12)),f6(f7(c12)))
      | p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12)))) )
  <=> ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
            ( ~ p2(X3,X5)
            | ~ p2(X4,X6)
            | p2(f5(X3,X4),f5(X5,X6)) )
      | ~ p2(f8(c11,c13),f8(c11,c10))
      | ~ p2(f6(f7(c12)),f6(f7(c12)))
      | p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(63,plain,
    ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
          ( ~ p2(X3,X5)
          | ~ p2(X4,X6)
          | p2(f5(X3,X4),f5(X5,X6)) )
    | ~ p2(f8(c11,c13),f8(c11,c10))
    | ~ p2(f6(f7(c12)),f6(f7(c12)))
    | p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(64,plain,
    ( ~ ! [X6: $i,X4: $i,X3: $i,X5: $i] :
          ( ~ p2(X3,X5)
          | ~ p2(X4,X6)
          | p2(f5(X3,X4),f5(X5,X6)) )
    | ~ p2(f8(c11,c13),f8(c11,c10))
    | ~ p2(f6(f7(c12)),f6(f7(c12)))
    | p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12)))) ),
    inference(modus_ponens,[status(thm)],[63,62]) ).

tff(65,plain,
    p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12)))),
    inference(unit_resolution,[status(thm)],[64,61,51,49]) ).

tff(66,plain,
    ( ~ ! [X0: $i] : p2(X0,X0)
    | p2(c10,c10) ),
    inference(quant_inst,[status(thm)],]) ).

tff(67,plain,
    p2(c10,c10),
    inference(unit_resolution,[status(thm)],[66,33]) ).

tff(68,plain,
    ( ( ~ ! [X0: $i,X2: $i,X1: $i] :
            ( ~ p2(X0,X2)
            | ~ p2(X0,X1)
            | p2(X1,X2) )
      | ~ p2(c10,c10)
      | ~ p2(c10,c13)
      | p2(c13,c10) )
  <=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
            ( ~ p2(X0,X2)
            | ~ p2(X0,X1)
            | p2(X1,X2) )
      | ~ p2(c10,c10)
      | ~ p2(c10,c13)
      | p2(c13,c10) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,plain,
    ( ~ ! [X0: $i,X2: $i,X1: $i] :
          ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) )
    | ~ p2(c10,c10)
    | ~ p2(c10,c13)
    | p2(c13,c10) ),
    inference(quant_inst,[status(thm)],]) ).

tff(70,plain,
    ( ~ ! [X0: $i,X2: $i,X1: $i] :
          ( ~ p2(X0,X2)
          | ~ p2(X0,X1)
          | p2(X1,X2) )
    | ~ p2(c10,c10)
    | ~ p2(c10,c13)
    | p2(c13,c10) ),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    p2(c13,c10),
    inference(unit_resolution,[status(thm)],[70,22,45,67]) ).

tff(72,plain,
    ^ [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      refl(
        ( ( ~ p2(X18,X21)
          | ~ p3(X20,X23)
          | ~ p2(X19,X22)
          | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
      <=> ( ~ p2(X18,X21)
          | ~ p3(X20,X23)
          | ~ p2(X19,X22)
          | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
    inference(bind,[status(th)],]) ).

tff(73,plain,
    ( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( ~ p2(X18,X21)
        | ~ p3(X20,X23)
        | ~ p2(X19,X22)
        | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
  <=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( ~ p2(X18,X21)
        | ~ p3(X20,X23)
        | ~ p2(X19,X22)
        | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) ),
    inference(quant_intro,[status(thm)],[72]) ).

tff(74,plain,
    ( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( ~ p2(X18,X21)
        | ~ p3(X20,X23)
        | ~ p2(X19,X22)
        | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
  <=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( ~ p2(X18,X21)
        | ~ p3(X20,X23)
        | ~ p2(X19,X22)
        | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(75,plain,
    ^ [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
                  | ~ p2(X19,X22) )
              <=> ( ~ p2(X19,X22)
                  | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
              ( ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
                | ~ p2(X19,X22)
                | ~ p3(X20,X23) )
            <=> ( ~ p2(X19,X22)
                | p3(f4(X18,X19,X20),f4(X21,X22,X23))
                | ~ p3(X20,X23) ) )),
            rewrite(
              ( ( ~ p2(X19,X22)
                | p3(f4(X18,X19,X20),f4(X21,X22,X23))
                | ~ p3(X20,X23) )
            <=> ( ~ p3(X20,X23)
                | ~ p2(X19,X22)
                | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
            ( ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
              | ~ p2(X19,X22)
              | ~ p3(X20,X23) )
          <=> ( ~ p3(X20,X23)
              | ~ p2(X19,X22)
              | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
          ( ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
            | ~ p2(X19,X22)
            | ~ p3(X20,X23)
            | ~ p2(X18,X21) )
        <=> ( ~ p3(X20,X23)
            | ~ p2(X19,X22)
            | p3(f4(X18,X19,X20),f4(X21,X22,X23))
            | ~ p2(X18,X21) ) )),
        rewrite(
          ( ( ~ p3(X20,X23)
            | ~ p2(X19,X22)
            | p3(f4(X18,X19,X20),f4(X21,X22,X23))
            | ~ p2(X18,X21) )
        <=> ( ~ p2(X18,X21)
            | ~ p3(X20,X23)
            | ~ p2(X19,X22)
            | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
        ( ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
          | ~ p2(X19,X22)
          | ~ p3(X20,X23)
          | ~ p2(X18,X21) )
      <=> ( ~ p2(X18,X21)
          | ~ p3(X20,X23)
          | ~ p2(X19,X22)
          | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) )),
    inference(bind,[status(th)],]) ).

tff(76,plain,
    ( ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
        | ~ p2(X19,X22)
        | ~ p3(X20,X23)
        | ~ p2(X18,X21) )
  <=> ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
        ( ~ p2(X18,X21)
        | ~ p3(X20,X23)
        | ~ p2(X19,X22)
        | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ) ),
    inference(quant_intro,[status(thm)],[75]) ).

tff(77,axiom,
    ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      ( p3(f4(X18,X19,X20),f4(X21,X22,X23))
      | ~ p2(X19,X22)
      | ~ p3(X20,X23)
      | ~ p2(X18,X21) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_12) ).

tff(78,plain,
    ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      ( ~ p2(X18,X21)
      | ~ p3(X20,X23)
      | ~ p2(X19,X22)
      | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
    inference(modus_ponens,[status(thm)],[77,76]) ).

tff(79,plain,
    ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      ( ~ p2(X18,X21)
      | ~ p3(X20,X23)
      | ~ p2(X19,X22)
      | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
    inference(modus_ponens,[status(thm)],[78,74]) ).

tff(80,plain,
    ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      ( ~ p2(X18,X21)
      | ~ p3(X20,X23)
      | ~ p2(X19,X22)
      | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
    inference(skolemize,[status(sab)],[79]) ).

tff(81,plain,
    ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
      ( ~ p2(X18,X21)
      | ~ p3(X20,X23)
      | ~ p2(X19,X22)
      | p3(f4(X18,X19,X20),f4(X21,X22,X23)) ),
    inference(modus_ponens,[status(thm)],[80,73]) ).

tff(82,plain,
    ( ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
            ( ~ p2(X18,X21)
            | ~ p3(X20,X23)
            | ~ p2(X19,X22)
            | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
      | ~ p2(c13,c10)
      | ~ p3(c11,c11)
      | ~ p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12))))
      | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) )
  <=> ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
            ( ~ p2(X18,X21)
            | ~ p3(X20,X23)
            | ~ p2(X19,X22)
            | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
      | ~ p2(c13,c10)
      | ~ p3(c11,c11)
      | ~ p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12))))
      | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(83,plain,
    ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
          ( ~ p2(X18,X21)
          | ~ p3(X20,X23)
          | ~ p2(X19,X22)
          | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
    | ~ p2(c13,c10)
    | ~ p3(c11,c11)
    | ~ p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12))))
    | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(84,plain,
    ( ~ ! [X22: $i,X21: $i,X18: $i,X20: $i,X23: $i,X19: $i] :
          ( ~ p2(X18,X21)
          | ~ p3(X20,X23)
          | ~ p2(X19,X22)
          | p3(f4(X18,X19,X20),f4(X21,X22,X23)) )
    | ~ p2(c13,c10)
    | ~ p3(c11,c11)
    | ~ p2(f5(f8(c11,c13),f6(f7(c12))),f5(f8(c11,c10),f6(f7(c12))))
    | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ),
    inference(modus_ponens,[status(thm)],[83,82]) ).

tff(85,plain,
    p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
    inference(unit_resolution,[status(thm)],[84,81,9,71,65]) ).

tff(86,plain,
    ( ~ ! [X15: $i] : p3(X15,X15)
    | p3(c9,c9) ),
    inference(quant_inst,[status(thm)],]) ).

tff(87,plain,
    p3(c9,c9),
    inference(unit_resolution,[status(thm)],[86,7]) ).

tff(88,plain,
    ( p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11))
  <=> p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)) ),
    inference(rewrite,[status(thm)],]) ).

tff(89,axiom,
    p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_8) ).

tff(90,plain,
    p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11)),
    inference(modus_ponens,[status(thm)],[89,88]) ).

tff(91,plain,
    ^ [X17: $i,X16: $i,X15: $i] :
      refl(
        ( ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) )
      <=> ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) ) )),
    inference(bind,[status(th)],]) ).

tff(92,plain,
    ( ! [X17: $i,X16: $i,X15: $i] :
        ( ~ p3(X15,X17)
        | ~ p3(X15,X16)
        | p3(X16,X17) )
  <=> ! [X17: $i,X16: $i,X15: $i] :
        ( ~ p3(X15,X17)
        | ~ p3(X15,X16)
        | p3(X16,X17) ) ),
    inference(quant_intro,[status(thm)],[91]) ).

tff(93,plain,
    ( ! [X17: $i,X16: $i,X15: $i] :
        ( ~ p3(X15,X17)
        | ~ p3(X15,X16)
        | p3(X16,X17) )
  <=> ! [X17: $i,X16: $i,X15: $i] :
        ( ~ p3(X15,X17)
        | ~ p3(X15,X16)
        | p3(X16,X17) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(94,plain,
    ^ [X17: $i,X16: $i,X15: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p3(X16,X17)
              | ~ p3(X15,X16) )
          <=> ( ~ p3(X15,X16)
              | p3(X16,X17) ) )),
          ( ( p3(X16,X17)
            | ~ p3(X15,X16)
            | ~ p3(X15,X17) )
        <=> ( ~ p3(X15,X16)
            | p3(X16,X17)
            | ~ p3(X15,X17) ) )),
        rewrite(
          ( ( ~ p3(X15,X16)
            | p3(X16,X17)
            | ~ p3(X15,X17) )
        <=> ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) ) )),
        ( ( p3(X16,X17)
          | ~ p3(X15,X16)
          | ~ p3(X15,X17) )
      <=> ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) ) )),
    inference(bind,[status(th)],]) ).

tff(95,plain,
    ( ! [X17: $i,X16: $i,X15: $i] :
        ( p3(X16,X17)
        | ~ p3(X15,X16)
        | ~ p3(X15,X17) )
  <=> ! [X17: $i,X16: $i,X15: $i] :
        ( ~ p3(X15,X17)
        | ~ p3(X15,X16)
        | p3(X16,X17) ) ),
    inference(quant_intro,[status(thm)],[94]) ).

tff(96,axiom,
    ! [X17: $i,X16: $i,X15: $i] :
      ( p3(X16,X17)
      | ~ p3(X15,X16)
      | ~ p3(X15,X17) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_7) ).

tff(97,plain,
    ! [X17: $i,X16: $i,X15: $i] :
      ( ~ p3(X15,X17)
      | ~ p3(X15,X16)
      | p3(X16,X17) ),
    inference(modus_ponens,[status(thm)],[96,95]) ).

tff(98,plain,
    ! [X17: $i,X16: $i,X15: $i] :
      ( ~ p3(X15,X17)
      | ~ p3(X15,X16)
      | p3(X16,X17) ),
    inference(modus_ponens,[status(thm)],[97,93]) ).

tff(99,plain,
    ! [X17: $i,X16: $i,X15: $i] :
      ( ~ p3(X15,X17)
      | ~ p3(X15,X16)
      | p3(X16,X17) ),
    inference(skolemize,[status(sab)],[98]) ).

tff(100,plain,
    ! [X17: $i,X16: $i,X15: $i] :
      ( ~ p3(X15,X17)
      | ~ p3(X15,X16)
      | p3(X16,X17) ),
    inference(modus_ponens,[status(thm)],[99,92]) ).

tff(101,plain,
    ( ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | ~ p3(c9,c9)
      | ~ p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11))
      | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) )
  <=> ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | ~ p3(c9,c9)
      | ~ p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11))
      | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(102,plain,
    ( ~ ! [X17: $i,X16: $i,X15: $i] :
          ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) )
    | ~ p3(c9,c9)
    | ~ p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11))
    | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) ),
    inference(quant_inst,[status(thm)],]) ).

tff(103,plain,
    ( ~ ! [X17: $i,X16: $i,X15: $i] :
          ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) )
    | ~ p3(c9,c9)
    | ~ p3(c9,f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11))
    | p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9) ),
    inference(modus_ponens,[status(thm)],[102,101]) ).

tff(104,plain,
    p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9),
    inference(unit_resolution,[status(thm)],[103,100,90,87]) ).

tff(105,plain,
    ( ~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
  <=> ~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ),
    inference(rewrite,[status(thm)],]) ).

tff(106,axiom,
    ~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p3_9) ).

tff(107,plain,
    ~ p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)),
    inference(modus_ponens,[status(thm)],[106,105]) ).

tff(108,plain,
    ( ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) )
  <=> ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,plain,
    ( ( ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) )
  <=> ( p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(110,plain,
    ( ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) )
  <=> ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ) ),
    inference(monotonicity,[status(thm)],[109]) ).

tff(111,plain,
    ( ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) )
  <=> ( ~ ! [X17: $i,X16: $i,X15: $i] :
            ( ~ p3(X15,X17)
            | ~ p3(X15,X16)
            | p3(X16,X17) )
      | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
      | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ) ),
    inference(transitivity,[status(thm)],[110,108]) ).

tff(112,plain,
    ( ~ ! [X17: $i,X16: $i,X15: $i] :
          ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) )
    | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
    | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
    | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(113,plain,
    ( ~ ! [X17: $i,X16: $i,X15: $i] :
          ( ~ p3(X15,X17)
          | ~ p3(X15,X16)
          | p3(X16,X17) )
    | p3(c9,f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11))
    | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),c9)
    | ~ p3(f4(c13,f5(f8(c11,c13),f6(f7(c12))),c11),f4(c10,f5(f8(c11,c10),f6(f7(c12))),c11)) ),
    inference(modus_ponens,[status(thm)],[112,111]) ).

tff(114,plain,
    $false,
    inference(unit_resolution,[status(thm)],[113,100,107,104,85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYN556-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 05:41:03 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.
% 0.87/0.86  % SZS status Unsatisfiable
% 0.87/0.86  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------