TSTP Solution File: SYN582-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN582-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 23:56:31 EDT 2022

% Result   : Unsatisfiable 1.00s 0.89s
% Output   : Proof 1.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   78 (  27 unt;   9 typ;   0 def)
%            Number of atoms       :  319 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  416 ( 192   ~; 188   |;   0   &)
%                                         (  36 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   26 (  26 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  190 ( 168   !;   0   ?; 190   :)

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

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

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

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

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

tff(c15_type,type,
    c15: $i ).

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

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

tff(p11_type,type,
    p11: ( $i * $i ) > $o ).

tff(1,plain,
    ^ [X18: $i] :
      refl(
        ( p2(X18,X18)
      <=> p2(X18,X18) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X18: $i] : p2(X18,X18)
  <=> ! [X18: $i] : p2(X18,X18) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X18: $i] : p2(X18,X18)
  <=> ! [X18: $i] : p2(X18,X18) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X18: $i] : p2(X18,X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_2) ).

tff(5,plain,
    ! [X18: $i] : p2(X18,X18),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X18: $i] : p2(X18,X18),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X18: $i] : p2(X18,X18),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X18: $i] : p2(X18,X18)
    | p2(c16,c16) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p2(c16,c16),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X31: $i] :
      refl(
        ( p5(X31,X31)
      <=> p5(X31,X31) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X31: $i] : p5(X31,X31)
  <=> ! [X31: $i] : p5(X31,X31) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X31: $i] : p5(X31,X31)
  <=> ! [X31: $i] : p5(X31,X31) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [X31: $i] : p5(X31,X31),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_3) ).

tff(14,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X31: $i] : p5(X31,X31),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [X31: $i] : p5(X31,X31)
    | p5(c15,c15) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    p5(c15,c15),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ^ [X25: $i,X27: $i,X28: $i,X26: $i] :
      refl(
        ( ( ~ p2(X26,X28)
          | ~ p5(X25,X27)
          | p2(f6(X25,X26),f6(X27,X28)) )
      <=> ( ~ p2(X26,X28)
          | ~ p5(X25,X27)
          | p2(f6(X25,X26),f6(X27,X28)) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( ~ p2(X26,X28)
        | ~ p5(X25,X27)
        | p2(f6(X25,X26),f6(X27,X28)) )
  <=> ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( ~ p2(X26,X28)
        | ~ p5(X25,X27)
        | p2(f6(X25,X26),f6(X27,X28)) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( ~ p2(X26,X28)
        | ~ p5(X25,X27)
        | p2(f6(X25,X26),f6(X27,X28)) )
  <=> ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( ~ p2(X26,X28)
        | ~ p5(X25,X27)
        | p2(f6(X25,X26),f6(X27,X28)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ^ [X25: $i,X27: $i,X28: $i,X26: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p2(f6(X25,X26),f6(X27,X28))
              | ~ p2(X26,X28) )
          <=> ( ~ p2(X26,X28)
              | p2(f6(X25,X26),f6(X27,X28)) ) )),
          ( ( p2(f6(X25,X26),f6(X27,X28))
            | ~ p2(X26,X28)
            | ~ p5(X25,X27) )
        <=> ( ~ p2(X26,X28)
            | p2(f6(X25,X26),f6(X27,X28))
            | ~ p5(X25,X27) ) )),
        rewrite(
          ( ( ~ p2(X26,X28)
            | p2(f6(X25,X26),f6(X27,X28))
            | ~ p5(X25,X27) )
        <=> ( ~ p2(X26,X28)
            | ~ p5(X25,X27)
            | p2(f6(X25,X26),f6(X27,X28)) ) )),
        ( ( p2(f6(X25,X26),f6(X27,X28))
          | ~ p2(X26,X28)
          | ~ p5(X25,X27) )
      <=> ( ~ p2(X26,X28)
          | ~ p5(X25,X27)
          | p2(f6(X25,X26),f6(X27,X28)) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( p2(f6(X25,X26),f6(X27,X28))
        | ~ p2(X26,X28)
        | ~ p5(X25,X27) )
  <=> ! [X25: $i,X27: $i,X28: $i,X26: $i] :
        ( ~ p2(X26,X28)
        | ~ p5(X25,X27)
        | p2(f6(X25,X26),f6(X27,X28)) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,axiom,
    ! [X25: $i,X27: $i,X28: $i,X26: $i] :
      ( p2(f6(X25,X26),f6(X27,X28))
      | ~ p2(X26,X28)
      | ~ p5(X25,X27) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_23) ).

tff(25,plain,
    ! [X25: $i,X27: $i,X28: $i,X26: $i] :
      ( ~ p2(X26,X28)
      | ~ p5(X25,X27)
      | p2(f6(X25,X26),f6(X27,X28)) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X25: $i,X27: $i,X28: $i,X26: $i] :
      ( ~ p2(X26,X28)
      | ~ p5(X25,X27)
      | p2(f6(X25,X26),f6(X27,X28)) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ! [X25: $i,X27: $i,X28: $i,X26: $i] :
      ( ~ p2(X26,X28)
      | ~ p5(X25,X27)
      | p2(f6(X25,X26),f6(X27,X28)) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [X25: $i,X27: $i,X28: $i,X26: $i] :
      ( ~ p2(X26,X28)
      | ~ p5(X25,X27)
      | p2(f6(X25,X26),f6(X27,X28)) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ( p2(c13,c18)
  <=> p2(c13,c18) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    p2(c13,c18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).

tff(31,plain,
    p2(c13,c18),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ( ( ~ ! [X25: $i,X27: $i,X28: $i,X26: $i] :
            ( ~ p2(X26,X28)
            | ~ p5(X25,X27)
            | p2(f6(X25,X26),f6(X27,X28)) )
      | ~ p2(c13,c18)
      | ~ p5(c15,c15)
      | p2(f6(c15,c13),f6(c15,c18)) )
  <=> ( ~ ! [X25: $i,X27: $i,X28: $i,X26: $i] :
            ( ~ p2(X26,X28)
            | ~ p5(X25,X27)
            | p2(f6(X25,X26),f6(X27,X28)) )
      | ~ p2(c13,c18)
      | ~ p5(c15,c15)
      | p2(f6(c15,c13),f6(c15,c18)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [X25: $i,X27: $i,X28: $i,X26: $i] :
          ( ~ p2(X26,X28)
          | ~ p5(X25,X27)
          | p2(f6(X25,X26),f6(X27,X28)) )
    | ~ p2(c13,c18)
    | ~ p5(c15,c15)
    | p2(f6(c15,c13),f6(c15,c18)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X25: $i,X27: $i,X28: $i,X26: $i] :
          ( ~ p2(X26,X28)
          | ~ p5(X25,X27)
          | p2(f6(X25,X26),f6(X27,X28)) )
    | ~ p2(c13,c18)
    | ~ p5(c15,c15)
    | p2(f6(c15,c13),f6(c15,c18)) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    p2(f6(c15,c13),f6(c15,c18)),
    inference(unit_resolution,[status(thm)],[34,31,28,18]) ).

tff(36,plain,
    ^ [X23: $i,X24: $i] :
      refl(
        ( ( ~ p2(X23,X24)
          | p2(f4(X23),f4(X24)) )
      <=> ( ~ p2(X23,X24)
          | p2(f4(X23),f4(X24)) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X23: $i,X24: $i] :
        ( ~ p2(X23,X24)
        | p2(f4(X23),f4(X24)) )
  <=> ! [X23: $i,X24: $i] :
        ( ~ p2(X23,X24)
        | p2(f4(X23),f4(X24)) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X23: $i,X24: $i] :
        ( ~ p2(X23,X24)
        | p2(f4(X23),f4(X24)) )
  <=> ! [X23: $i,X24: $i] :
        ( ~ p2(X23,X24)
        | p2(f4(X23),f4(X24)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ^ [X23: $i,X24: $i] :
      rewrite(
        ( ( p2(f4(X23),f4(X24))
          | ~ p2(X23,X24) )
      <=> ( ~ p2(X23,X24)
          | p2(f4(X23),f4(X24)) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [X23: $i,X24: $i] :
        ( p2(f4(X23),f4(X24))
        | ~ p2(X23,X24) )
  <=> ! [X23: $i,X24: $i] :
        ( ~ p2(X23,X24)
        | p2(f4(X23),f4(X24)) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,axiom,
    ! [X23: $i,X24: $i] :
      ( p2(f4(X23),f4(X24))
      | ~ p2(X23,X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_14) ).

tff(42,plain,
    ! [X23: $i,X24: $i] :
      ( ~ p2(X23,X24)
      | p2(f4(X23),f4(X24)) ),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ! [X23: $i,X24: $i] :
      ( ~ p2(X23,X24)
      | p2(f4(X23),f4(X24)) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ! [X23: $i,X24: $i] :
      ( ~ p2(X23,X24)
      | p2(f4(X23),f4(X24)) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [X23: $i,X24: $i] :
      ( ~ p2(X23,X24)
      | p2(f4(X23),f4(X24)) ),
    inference(modus_ponens,[status(thm)],[44,37]) ).

tff(46,plain,
    ( ( ~ ! [X23: $i,X24: $i] :
            ( ~ p2(X23,X24)
            | p2(f4(X23),f4(X24)) )
      | ~ p2(f6(c15,c13),f6(c15,c18))
      | p2(f4(f6(c15,c13)),f4(f6(c15,c18))) )
  <=> ( ~ ! [X23: $i,X24: $i] :
            ( ~ p2(X23,X24)
            | p2(f4(X23),f4(X24)) )
      | ~ p2(f6(c15,c13),f6(c15,c18))
      | p2(f4(f6(c15,c13)),f4(f6(c15,c18))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(47,plain,
    ( ~ ! [X23: $i,X24: $i] :
          ( ~ p2(X23,X24)
          | p2(f4(X23),f4(X24)) )
    | ~ p2(f6(c15,c13),f6(c15,c18))
    | p2(f4(f6(c15,c13)),f4(f6(c15,c18))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(48,plain,
    ( ~ ! [X23: $i,X24: $i] :
          ( ~ p2(X23,X24)
          | p2(f4(X23),f4(X24)) )
    | ~ p2(f6(c15,c13),f6(c15,c18))
    | p2(f4(f6(c15,c13)),f4(f6(c15,c18))) ),
    inference(modus_ponens,[status(thm)],[47,46]) ).

tff(49,plain,
    p2(f4(f6(c15,c13)),f4(f6(c15,c18))),
    inference(unit_resolution,[status(thm)],[48,45,35]) ).

tff(50,plain,
    ^ [X9: $i,X10: $i,X7: $i,X8: $i] :
      refl(
        ( ( ~ p2(X10,X8)
          | ~ p11(X9,X10)
          | ~ p2(X9,X7)
          | p11(X7,X8) )
      <=> ( ~ p2(X10,X8)
          | ~ p11(X9,X10)
          | ~ p2(X9,X7)
          | p11(X7,X8) ) )),
    inference(bind,[status(th)],]) ).

tff(51,plain,
    ( ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( ~ p2(X10,X8)
        | ~ p11(X9,X10)
        | ~ p2(X9,X7)
        | p11(X7,X8) )
  <=> ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( ~ p2(X10,X8)
        | ~ p11(X9,X10)
        | ~ p2(X9,X7)
        | p11(X7,X8) ) ),
    inference(quant_intro,[status(thm)],[50]) ).

tff(52,plain,
    ( ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( ~ p2(X10,X8)
        | ~ p11(X9,X10)
        | ~ p2(X9,X7)
        | p11(X7,X8) )
  <=> ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( ~ p2(X10,X8)
        | ~ p11(X9,X10)
        | ~ p2(X9,X7)
        | p11(X7,X8) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(53,plain,
    ^ [X9: $i,X10: $i,X7: $i,X8: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p11(X7,X8)
                  | ~ p2(X9,X7) )
              <=> ( ~ p2(X9,X7)
                  | p11(X7,X8) ) )),
              ( ( p11(X7,X8)
                | ~ p2(X9,X7)
                | ~ p2(X10,X8) )
            <=> ( ~ p2(X9,X7)
                | p11(X7,X8)
                | ~ p2(X10,X8) ) )),
            rewrite(
              ( ( ~ p2(X9,X7)
                | p11(X7,X8)
                | ~ p2(X10,X8) )
            <=> ( ~ p2(X10,X8)
                | ~ p2(X9,X7)
                | p11(X7,X8) ) )),
            ( ( p11(X7,X8)
              | ~ p2(X9,X7)
              | ~ p2(X10,X8) )
          <=> ( ~ p2(X10,X8)
              | ~ p2(X9,X7)
              | p11(X7,X8) ) )),
          ( ( p11(X7,X8)
            | ~ p2(X9,X7)
            | ~ p2(X10,X8)
            | ~ p11(X9,X10) )
        <=> ( ~ p2(X10,X8)
            | ~ p2(X9,X7)
            | p11(X7,X8)
            | ~ p11(X9,X10) ) )),
        rewrite(
          ( ( ~ p2(X10,X8)
            | ~ p2(X9,X7)
            | p11(X7,X8)
            | ~ p11(X9,X10) )
        <=> ( ~ p2(X10,X8)
            | ~ p11(X9,X10)
            | ~ p2(X9,X7)
            | p11(X7,X8) ) )),
        ( ( p11(X7,X8)
          | ~ p2(X9,X7)
          | ~ p2(X10,X8)
          | ~ p11(X9,X10) )
      <=> ( ~ p2(X10,X8)
          | ~ p11(X9,X10)
          | ~ p2(X9,X7)
          | p11(X7,X8) ) )),
    inference(bind,[status(th)],]) ).

tff(54,plain,
    ( ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( p11(X7,X8)
        | ~ p2(X9,X7)
        | ~ p2(X10,X8)
        | ~ p11(X9,X10) )
  <=> ! [X9: $i,X10: $i,X7: $i,X8: $i] :
        ( ~ p2(X10,X8)
        | ~ p11(X9,X10)
        | ~ p2(X9,X7)
        | p11(X7,X8) ) ),
    inference(quant_intro,[status(thm)],[53]) ).

tff(55,axiom,
    ! [X9: $i,X10: $i,X7: $i,X8: $i] :
      ( p11(X7,X8)
      | ~ p2(X9,X7)
      | ~ p2(X10,X8)
      | ~ p11(X9,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_21) ).

tff(56,plain,
    ! [X9: $i,X10: $i,X7: $i,X8: $i] :
      ( ~ p2(X10,X8)
      | ~ p11(X9,X10)
      | ~ p2(X9,X7)
      | p11(X7,X8) ),
    inference(modus_ponens,[status(thm)],[55,54]) ).

tff(57,plain,
    ! [X9: $i,X10: $i,X7: $i,X8: $i] :
      ( ~ p2(X10,X8)
      | ~ p11(X9,X10)
      | ~ p2(X9,X7)
      | p11(X7,X8) ),
    inference(modus_ponens,[status(thm)],[56,52]) ).

tff(58,plain,
    ! [X9: $i,X10: $i,X7: $i,X8: $i] :
      ( ~ p2(X10,X8)
      | ~ p11(X9,X10)
      | ~ p2(X9,X7)
      | p11(X7,X8) ),
    inference(skolemize,[status(sab)],[57]) ).

tff(59,plain,
    ! [X9: $i,X10: $i,X7: $i,X8: $i] :
      ( ~ p2(X10,X8)
      | ~ p11(X9,X10)
      | ~ p2(X9,X7)
      | p11(X7,X8) ),
    inference(modus_ponens,[status(thm)],[58,51]) ).

tff(60,plain,
    ( ~ p11(f4(f6(c15,c18)),c16)
  <=> ~ p11(f4(f6(c15,c18)),c16) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,axiom,
    ~ p11(f4(f6(c15,c18)),c16),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p11_9) ).

tff(62,plain,
    ~ p11(f4(f6(c15,c18)),c16),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    ( p11(f4(f6(c15,c13)),c16)
  <=> p11(f4(f6(c15,c13)),c16) ),
    inference(rewrite,[status(thm)],]) ).

tff(64,axiom,
    p11(f4(f6(c15,c13)),c16),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_7) ).

tff(65,plain,
    p11(f4(f6(c15,c13)),c16),
    inference(modus_ponens,[status(thm)],[64,63]) ).

tff(66,plain,
    ( ( ~ ! [X9: $i,X10: $i,X7: $i,X8: $i] :
            ( ~ p2(X10,X8)
            | ~ p11(X9,X10)
            | ~ p2(X9,X7)
            | p11(X7,X8) )
      | ~ p2(c16,c16)
      | ~ p11(f4(f6(c15,c13)),c16)
      | ~ p2(f4(f6(c15,c13)),f4(f6(c15,c18)))
      | p11(f4(f6(c15,c18)),c16) )
  <=> ( ~ ! [X9: $i,X10: $i,X7: $i,X8: $i] :
            ( ~ p2(X10,X8)
            | ~ p11(X9,X10)
            | ~ p2(X9,X7)
            | p11(X7,X8) )
      | ~ p2(c16,c16)
      | ~ p11(f4(f6(c15,c13)),c16)
      | ~ p2(f4(f6(c15,c13)),f4(f6(c15,c18)))
      | p11(f4(f6(c15,c18)),c16) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(67,plain,
    ( ~ ! [X9: $i,X10: $i,X7: $i,X8: $i] :
          ( ~ p2(X10,X8)
          | ~ p11(X9,X10)
          | ~ p2(X9,X7)
          | p11(X7,X8) )
    | ~ p2(c16,c16)
    | ~ p11(f4(f6(c15,c13)),c16)
    | ~ p2(f4(f6(c15,c13)),f4(f6(c15,c18)))
    | p11(f4(f6(c15,c18)),c16) ),
    inference(quant_inst,[status(thm)],]) ).

tff(68,plain,
    ( ~ ! [X9: $i,X10: $i,X7: $i,X8: $i] :
          ( ~ p2(X10,X8)
          | ~ p11(X9,X10)
          | ~ p2(X9,X7)
          | p11(X7,X8) )
    | ~ p2(c16,c16)
    | ~ p11(f4(f6(c15,c13)),c16)
    | ~ p2(f4(f6(c15,c13)),f4(f6(c15,c18)))
    | p11(f4(f6(c15,c18)),c16) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    $false,
    inference(unit_resolution,[status(thm)],[68,65,62,59,49,9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN582-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n020.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 05:54:13 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 1.00/0.89  % SZS status Unsatisfiable
% 1.00/0.89  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------