TSTP Solution File: SYN595-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN595-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 23:56:34 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   63
% Syntax   : Number of formulae    :  116 (  32 unt;  20 typ;   0 def)
%            Number of atoms       :  549 (   0 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  824 ( 405   ~; 364   |;   0   &)
%                                         (  55 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    9 (   3 avg)
%            Number of FOOLs       :   34 (  34 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  14   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-2 aty)
%            Number of variables   :  264 ( 238   !;   0   ?; 264   :)

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

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

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

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

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

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

tff(f3_type,type,
    f3: $i > $i ).

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

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

tff(c17_type,type,
    c17: $i ).

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

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

tff(c16_type,type,
    c16: $i ).

tff(c18_type,type,
    c18: $i ).

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

tff(p15_type,type,
    p15: ( $i * $i ) > $o ).

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

tff(c19_type,type,
    c19: $i ).

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

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

tff(1,plain,
    ^ [X10: $i] :
      refl(
        ( p2(X10,X10)
      <=> p2(X10,X10) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X10: $i] : p2(X10,X10)
  <=> ! [X10: $i] : p2(X10,X10) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X10: $i] : p2(X10,X10)
  <=> ! [X10: $i] : p2(X10,X10) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X10: $i] : p2(X10,X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).

tff(5,plain,
    ! [X10: $i] : p2(X10,X10),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X10: $i] : p2(X10,X10),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X10: $i] : p2(X10,X10),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X10: $i] : p2(X10,X10)
    | p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ( p14(c19,f6(f3(f4(f5(c17))),c16))
  <=> p14(c19,f6(f3(f4(f5(c17))),c16)) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,axiom,
    p14(c19,f6(f3(f4(f5(c17))),c16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_8) ).

tff(12,plain,
    p14(c19,f6(f3(f4(f5(c17))),c16)),
    inference(modus_ponens,[status(thm)],[11,10]) ).

tff(13,plain,
    ^ [X4: $i,X5: $i] :
      refl(
        ( ( ~ p14(X4,X5)
          | p15(X4,X5) )
      <=> ( ~ p14(X4,X5)
          | p15(X4,X5) ) )),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ( ! [X4: $i,X5: $i] :
        ( ~ p14(X4,X5)
        | p15(X4,X5) )
  <=> ! [X4: $i,X5: $i] :
        ( ~ p14(X4,X5)
        | p15(X4,X5) ) ),
    inference(quant_intro,[status(thm)],[13]) ).

tff(15,plain,
    ( ! [X4: $i,X5: $i] :
        ( ~ p14(X4,X5)
        | p15(X4,X5) )
  <=> ! [X4: $i,X5: $i] :
        ( ~ p14(X4,X5)
        | p15(X4,X5) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,plain,
    ^ [X4: $i,X5: $i] :
      rewrite(
        ( ( p15(X4,X5)
          | ~ p14(X4,X5) )
      <=> ( ~ p14(X4,X5)
          | p15(X4,X5) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [X4: $i,X5: $i] :
        ( p15(X4,X5)
        | ~ p14(X4,X5) )
  <=> ! [X4: $i,X5: $i] :
        ( ~ p14(X4,X5)
        | p15(X4,X5) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,axiom,
    ! [X4: $i,X5: $i] :
      ( p15(X4,X5)
      | ~ p14(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_6) ).

tff(19,plain,
    ! [X4: $i,X5: $i] :
      ( ~ p14(X4,X5)
      | p15(X4,X5) ),
    inference(modus_ponens,[status(thm)],[18,17]) ).

tff(20,plain,
    ! [X4: $i,X5: $i] :
      ( ~ p14(X4,X5)
      | p15(X4,X5) ),
    inference(modus_ponens,[status(thm)],[19,15]) ).

tff(21,plain,
    ! [X4: $i,X5: $i] :
      ( ~ p14(X4,X5)
      | p15(X4,X5) ),
    inference(skolemize,[status(sab)],[20]) ).

tff(22,plain,
    ! [X4: $i,X5: $i] :
      ( ~ p14(X4,X5)
      | p15(X4,X5) ),
    inference(modus_ponens,[status(thm)],[21,14]) ).

tff(23,plain,
    ( ( ~ ! [X4: $i,X5: $i] :
            ( ~ p14(X4,X5)
            | p15(X4,X5) )
      | ~ p14(c19,f6(f3(f4(f5(c17))),c16))
      | p15(c19,f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ ! [X4: $i,X5: $i] :
            ( ~ p14(X4,X5)
            | p15(X4,X5) )
      | ~ p14(c19,f6(f3(f4(f5(c17))),c16))
      | p15(c19,f6(f3(f4(f5(c17))),c16)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ~ ! [X4: $i,X5: $i] :
          ( ~ p14(X4,X5)
          | p15(X4,X5) )
    | ~ p14(c19,f6(f3(f4(f5(c17))),c16))
    | p15(c19,f6(f3(f4(f5(c17))),c16)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [X4: $i,X5: $i] :
          ( ~ p14(X4,X5)
          | p15(X4,X5) )
    | ~ p14(c19,f6(f3(f4(f5(c17))),c16))
    | p15(c19,f6(f3(f4(f5(c17))),c16)) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    p15(c19,f6(f3(f4(f5(c17))),c16)),
    inference(unit_resolution,[status(thm)],[25,22,12]) ).

tff(27,plain,
    ^ [X9: $i,X6: $i,X7: $i,X8: $i] :
      refl(
        ( ( ~ p2(X8,X6)
          | ~ p15(X8,X9)
          | ~ p2(X9,X7)
          | p15(X6,X7) )
      <=> ( ~ p2(X8,X6)
          | ~ p15(X8,X9)
          | ~ p2(X9,X7)
          | p15(X6,X7) ) )),
    inference(bind,[status(th)],]) ).

tff(28,plain,
    ( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( ~ p2(X8,X6)
        | ~ p15(X8,X9)
        | ~ p2(X9,X7)
        | p15(X6,X7) )
  <=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( ~ p2(X8,X6)
        | ~ p15(X8,X9)
        | ~ p2(X9,X7)
        | p15(X6,X7) ) ),
    inference(quant_intro,[status(thm)],[27]) ).

tff(29,plain,
    ( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( ~ p2(X8,X6)
        | ~ p15(X8,X9)
        | ~ p2(X9,X7)
        | p15(X6,X7) )
  <=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( ~ p2(X8,X6)
        | ~ p15(X8,X9)
        | ~ p2(X9,X7)
        | p15(X6,X7) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,plain,
    ^ [X9: $i,X6: $i,X7: $i,X8: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p15(X6,X7)
                  | ~ p2(X8,X6) )
              <=> ( ~ p2(X8,X6)
                  | p15(X6,X7) ) )),
              ( ( p15(X6,X7)
                | ~ p2(X8,X6)
                | ~ p2(X9,X7) )
            <=> ( ~ p2(X8,X6)
                | p15(X6,X7)
                | ~ p2(X9,X7) ) )),
            rewrite(
              ( ( ~ p2(X8,X6)
                | p15(X6,X7)
                | ~ p2(X9,X7) )
            <=> ( ~ p2(X8,X6)
                | ~ p2(X9,X7)
                | p15(X6,X7) ) )),
            ( ( p15(X6,X7)
              | ~ p2(X8,X6)
              | ~ p2(X9,X7) )
          <=> ( ~ p2(X8,X6)
              | ~ p2(X9,X7)
              | p15(X6,X7) ) )),
          ( ( p15(X6,X7)
            | ~ p2(X8,X6)
            | ~ p2(X9,X7)
            | ~ p15(X8,X9) )
        <=> ( ~ p2(X8,X6)
            | ~ p2(X9,X7)
            | p15(X6,X7)
            | ~ p15(X8,X9) ) )),
        rewrite(
          ( ( ~ p2(X8,X6)
            | ~ p2(X9,X7)
            | p15(X6,X7)
            | ~ p15(X8,X9) )
        <=> ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) ) )),
        ( ( p15(X6,X7)
          | ~ p2(X8,X6)
          | ~ p2(X9,X7)
          | ~ p15(X8,X9) )
      <=> ( ~ p2(X8,X6)
          | ~ p15(X8,X9)
          | ~ p2(X9,X7)
          | p15(X6,X7) ) )),
    inference(bind,[status(th)],]) ).

tff(31,plain,
    ( ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( p15(X6,X7)
        | ~ p2(X8,X6)
        | ~ p2(X9,X7)
        | ~ p15(X8,X9) )
  <=> ! [X9: $i,X6: $i,X7: $i,X8: $i] :
        ( ~ p2(X8,X6)
        | ~ p15(X8,X9)
        | ~ p2(X9,X7)
        | p15(X6,X7) ) ),
    inference(quant_intro,[status(thm)],[30]) ).

tff(32,axiom,
    ! [X9: $i,X6: $i,X7: $i,X8: $i] :
      ( p15(X6,X7)
      | ~ p2(X8,X6)
      | ~ p2(X9,X7)
      | ~ p15(X8,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_19) ).

tff(33,plain,
    ! [X9: $i,X6: $i,X7: $i,X8: $i] :
      ( ~ p2(X8,X6)
      | ~ p15(X8,X9)
      | ~ p2(X9,X7)
      | p15(X6,X7) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [X9: $i,X6: $i,X7: $i,X8: $i] :
      ( ~ p2(X8,X6)
      | ~ p15(X8,X9)
      | ~ p2(X9,X7)
      | p15(X6,X7) ),
    inference(modus_ponens,[status(thm)],[33,29]) ).

tff(35,plain,
    ! [X9: $i,X6: $i,X7: $i,X8: $i] :
      ( ~ p2(X8,X6)
      | ~ p15(X8,X9)
      | ~ p2(X9,X7)
      | p15(X6,X7) ),
    inference(skolemize,[status(sab)],[34]) ).

tff(36,plain,
    ! [X9: $i,X6: $i,X7: $i,X8: $i] :
      ( ~ p2(X8,X6)
      | ~ p15(X8,X9)
      | ~ p2(X9,X7)
      | p15(X6,X7) ),
    inference(modus_ponens,[status(thm)],[35,28]) ).

tff(37,plain,
    ( p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
  <=> p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))) ),
    inference(rewrite,[status(thm)],]) ).

tff(38,axiom,
    p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_17) ).

tff(39,plain,
    p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    ( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(41,plain,
    ( ( ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(monotonicity,[status(thm)],[41]) ).

tff(43,plain,
    ( ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
            ( ~ p2(X8,X6)
            | ~ p15(X8,X9)
            | ~ p2(X9,X7)
            | p15(X6,X7) )
      | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
      | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
      | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(transitivity,[status(thm)],[42,40]) ).

tff(44,plain,
    ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
          ( ~ p2(X8,X6)
          | ~ p15(X8,X9)
          | ~ p2(X9,X7)
          | p15(X6,X7) )
    | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
    | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
    | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16))
    | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [X9: $i,X6: $i,X7: $i,X8: $i] :
          ( ~ p2(X8,X6)
          | ~ p15(X8,X9)
          | ~ p2(X9,X7)
          | p15(X6,X7) )
    | ~ p2(c19,f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))))
    | ~ p15(c19,f6(f3(f4(f5(c17))),c16))
    | p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
    | ~ p2(f6(f3(f4(f5(c17))),c16),f6(f3(f4(f5(c17))),c16)) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)),
    inference(unit_resolution,[status(thm)],[45,39,36,26,9]) ).

tff(47,plain,
    ^ [X12: $i,X11: $i,X10: $i] :
      refl(
        ( ( ~ p2(X10,X11)
          | ~ p2(X10,X12)
          | p2(X11,X12) )
      <=> ( ~ p2(X10,X11)
          | ~ p2(X10,X12)
          | p2(X11,X12) ) )),
    inference(bind,[status(th)],]) ).

tff(48,plain,
    ( ! [X12: $i,X11: $i,X10: $i] :
        ( ~ p2(X10,X11)
        | ~ p2(X10,X12)
        | p2(X11,X12) )
  <=> ! [X12: $i,X11: $i,X10: $i] :
        ( ~ p2(X10,X11)
        | ~ p2(X10,X12)
        | p2(X11,X12) ) ),
    inference(quant_intro,[status(thm)],[47]) ).

tff(49,plain,
    ( ! [X12: $i,X11: $i,X10: $i] :
        ( ~ p2(X10,X11)
        | ~ p2(X10,X12)
        | p2(X11,X12) )
  <=> ! [X12: $i,X11: $i,X10: $i] :
        ( ~ p2(X10,X11)
        | ~ p2(X10,X12)
        | p2(X11,X12) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ^ [X12: $i,X11: $i,X10: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p2(X11,X12)
              | ~ p2(X10,X11) )
          <=> ( ~ p2(X10,X11)
              | p2(X11,X12) ) )),
          ( ( p2(X11,X12)
            | ~ p2(X10,X11)
            | ~ p2(X10,X12) )
        <=> ( ~ p2(X10,X11)
            | p2(X11,X12)
            | ~ p2(X10,X12) ) )),
        rewrite(
          ( ( ~ p2(X10,X11)
            | p2(X11,X12)
            | ~ p2(X10,X12) )
        <=> ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) ) )),
        ( ( p2(X11,X12)
          | ~ p2(X10,X11)
          | ~ p2(X10,X12) )
      <=> ( ~ p2(X10,X11)
          | ~ p2(X10,X12)
          | p2(X11,X12) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [X12: $i,X11: $i,X10: $i] :
        ( p2(X11,X12)
        | ~ p2(X10,X11)
        | ~ p2(X10,X12) )
  <=> ! [X12: $i,X11: $i,X10: $i] :
        ( ~ p2(X10,X11)
        | ~ p2(X10,X12)
        | p2(X11,X12) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,axiom,
    ! [X12: $i,X11: $i,X10: $i] :
      ( p2(X11,X12)
      | ~ p2(X10,X11)
      | ~ p2(X10,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_16) ).

tff(53,plain,
    ! [X12: $i,X11: $i,X10: $i] :
      ( ~ p2(X10,X11)
      | ~ p2(X10,X12)
      | p2(X11,X12) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ! [X12: $i,X11: $i,X10: $i] :
      ( ~ p2(X10,X11)
      | ~ p2(X10,X12)
      | p2(X11,X12) ),
    inference(modus_ponens,[status(thm)],[53,49]) ).

tff(55,plain,
    ! [X12: $i,X11: $i,X10: $i] :
      ( ~ p2(X10,X11)
      | ~ p2(X10,X12)
      | p2(X11,X12) ),
    inference(skolemize,[status(sab)],[54]) ).

tff(56,plain,
    ! [X12: $i,X11: $i,X10: $i] :
      ( ~ p2(X10,X11)
      | ~ p2(X10,X12)
      | p2(X11,X12) ),
    inference(modus_ponens,[status(thm)],[55,48]) ).

tff(57,plain,
    ( p2(c21,f3(c17))
  <=> p2(c21,f3(c17)) ),
    inference(rewrite,[status(thm)],]) ).

tff(58,axiom,
    p2(c21,f3(c17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_3) ).

tff(59,plain,
    p2(c21,f3(c17)),
    inference(modus_ponens,[status(thm)],[58,57]) ).

tff(60,plain,
    ( ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) )
  <=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ( ( ~ p2(c21,f3(c17))
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) )
  <=> ( ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    ( ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) )
  <=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) ) ),
    inference(monotonicity,[status(thm)],[61]) ).

tff(63,plain,
    ( ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) )
  <=> ( ~ ! [X12: $i,X11: $i,X10: $i] :
            ( ~ p2(X10,X11)
            | ~ p2(X10,X12)
            | p2(X11,X12) )
      | ~ p2(c21,f3(c17))
      | p2(f3(c17),f3(c17)) ) ),
    inference(transitivity,[status(thm)],[62,60]) ).

tff(64,plain,
    ( ~ ! [X12: $i,X11: $i,X10: $i] :
          ( ~ p2(X10,X11)
          | ~ p2(X10,X12)
          | p2(X11,X12) )
    | ~ p2(c21,f3(c17))
    | ~ p2(c21,f3(c17))
    | p2(f3(c17),f3(c17)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(65,plain,
    ( ~ ! [X12: $i,X11: $i,X10: $i] :
          ( ~ p2(X10,X11)
          | ~ p2(X10,X12)
          | p2(X11,X12) )
    | ~ p2(c21,f3(c17))
    | p2(f3(c17),f3(c17)) ),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    p2(f3(c17),f3(c17)),
    inference(unit_resolution,[status(thm)],[65,59,56]) ).

tff(67,plain,
    ^ [X47: $i,X46: $i,X48: $i] :
      refl(
        ( ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p2(X48,f3(c17)) )
      <=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p2(X48,f3(c17)) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p2(X48,f3(c17)) )
  <=> ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p2(X48,f3(c17)) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ( ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p2(X48,f3(c17)) )
  <=> ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p2(X48,f3(c17)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ^ [X47: $i,X46: $i,X48: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ p2(X48,f3(c17))
              | ~ p14(X46,f3(f4(f5(c17))))
              | ~ p15(X47,f6(f3(f4(f5(c17))),c16)) )
          <=> ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
              | ~ p14(X46,f3(f4(f5(c17))))
              | ~ p2(X48,f3(c17)) ) )),
          ( ( ~ p2(X48,f3(c17))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
        <=> ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17))
            | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) ) )),
        rewrite(
          ( ( ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17))
            | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
        <=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) ) )),
        ( ( ~ p2(X48,f3(c17))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
      <=> ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p2(X48,f3(c17)) ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p2(X48,f3(c17))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) )
  <=> ! [X47: $i,X46: $i,X48: $i] :
        ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
        | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
        | ~ p14(X46,f3(f4(f5(c17))))
        | ~ p2(X48,f3(c17)) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,axiom,
    ! [X47: $i,X46: $i,X48: $i] :
      ( ~ p2(X48,f3(c17))
      | ~ p14(X46,f3(f4(f5(c17))))
      | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_26) ).

tff(73,plain,
    ! [X47: $i,X46: $i,X48: $i] :
      ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
      | ~ p14(X46,f3(f4(f5(c17))))
      | ~ p2(X48,f3(c17)) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ! [X47: $i,X46: $i,X48: $i] :
      ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
      | ~ p14(X46,f3(f4(f5(c17))))
      | ~ p2(X48,f3(c17)) ),
    inference(modus_ponens,[status(thm)],[73,69]) ).

tff(75,plain,
    ! [X47: $i,X46: $i,X48: $i] :
      ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
      | ~ p14(X46,f3(f4(f5(c17))))
      | ~ p2(X48,f3(c17)) ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [X47: $i,X46: $i,X48: $i] :
      ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
      | ~ p14(X46,f3(f4(f5(c17))))
      | ~ p2(X48,f3(c17)) ),
    inference(modus_ponens,[status(thm)],[75,68]) ).

tff(77,plain,
    ( p14(c18,f3(f4(f5(c17))))
  <=> p14(c18,f3(f4(f5(c17)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,axiom,
    p14(c18,f3(f4(f5(c17)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14_5) ).

tff(79,plain,
    p14(c18,f3(f4(f5(c17)))),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ( ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) )
  <=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(81,plain,
    ( ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17)) )
  <=> ( ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(82,plain,
    ( ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17)) )
  <=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(monotonicity,[status(thm)],[81]) ).

tff(83,plain,
    ( ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17)) )
  <=> ( ~ ! [X47: $i,X46: $i,X48: $i] :
            ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
            | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
            | ~ p14(X46,f3(f4(f5(c17))))
            | ~ p2(X48,f3(c17)) )
      | ~ p14(c18,f3(f4(f5(c17))))
      | ~ p2(f3(c17),f3(c17))
      | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
      | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ) ),
    inference(transitivity,[status(thm)],[82,80]) ).

tff(84,plain,
    ( ~ ! [X47: $i,X46: $i,X48: $i] :
          ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p2(X48,f3(c17)) )
    | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16))
    | ~ p14(c18,f3(f4(f5(c17))))
    | ~ p2(f3(c17),f3(c17)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(85,plain,
    ( ~ ! [X47: $i,X46: $i,X48: $i] :
          ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),X46),f8(f10(f11(f3(f4(f5(c17)))),X48),f9(f11(X47),f10(f11(f3(f4(f5(c17)))),c22)))))
          | ~ p15(X47,f6(f3(f4(f5(c17))),c16))
          | ~ p14(X46,f3(f4(f5(c17))))
          | ~ p2(X48,f3(c17)) )
    | ~ p14(c18,f3(f4(f5(c17))))
    | ~ p2(f3(c17),f3(c17))
    | ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
    inference(modus_ponens,[status(thm)],[84,83]) ).

tff(86,plain,
    ( ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))))
    | ~ p15(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17)))),f6(f3(f4(f5(c17))),c16)) ),
    inference(unit_resolution,[status(thm)],[85,79,76,66]) ).

tff(87,plain,
    ~ p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22))))),
    inference(unit_resolution,[status(thm)],[86,46]) ).

tff(88,plain,
    ^ [X27: $i] :
      refl(
        ( p7(X27,X27)
      <=> p7(X27,X27) )),
    inference(bind,[status(th)],]) ).

tff(89,plain,
    ( ! [X27: $i] : p7(X27,X27)
  <=> ! [X27: $i] : p7(X27,X27) ),
    inference(quant_intro,[status(thm)],[88]) ).

tff(90,plain,
    ( ! [X27: $i] : p7(X27,X27)
  <=> ! [X27: $i] : p7(X27,X27) ),
    inference(rewrite,[status(thm)],]) ).

tff(91,axiom,
    ! [X27: $i] : p7(X27,X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7_2) ).

tff(92,plain,
    ! [X27: $i] : p7(X27,X27),
    inference(modus_ponens,[status(thm)],[91,90]) ).

tff(93,plain,
    ! [X27: $i] : p7(X27,X27),
    inference(skolemize,[status(sab)],[92]) ).

tff(94,plain,
    ! [X27: $i] : p7(X27,X27),
    inference(modus_ponens,[status(thm)],[93,89]) ).

tff(95,plain,
    ( ~ ! [X27: $i] : p7(X27,X27)
    | p7(f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22)))),f8(f10(f12(f11(f3(f5(c17)))),c18),f8(f10(f11(f3(f4(f5(c17)))),f3(c17)),f9(f11(f6(f3(f4(f5(c17))),f13(c16,f3(f5(c17))))),f10(f11(f3(f4(f5(c17)))),c22))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(96,plain,
    $false,
    inference(unit_resolution,[status(thm)],[95,94,87]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN595-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Sep  5 06:01:16 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 0.19/0.51  % SZS status Unsatisfiable
% 0.19/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------