TSTP Solution File: SYN656-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN656-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 23:56:49 EDT 2022

% Result   : Unsatisfiable 0.22s 0.46s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  116 (  34 unt;  15 typ;   0 def)
%            Number of atoms       :  496 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  651 ( 292   ~; 306   |;   0   &)
%                                         (  53 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of FOOLs       :   36 (  36 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :  297 ( 265   !;   0   ?; 297   :)

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

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

tff(c34_type,type,
    c34: $i ).

tff(c31_type,type,
    c31: $i ).

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

tff(c35_type,type,
    c35: $i ).

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

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

tff(p25_type,type,
    p25: ( $i * $i ) > $o ).

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

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

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

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

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

tff(p4_type,type,
    p4: ( $i * $i ) > $o ).

tff(1,plain,
    ^ [X64: $i] :
      refl(
        ( p3(X64,X64)
      <=> p3(X64,X64) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X64: $i] : p3(X64,X64)
  <=> ! [X64: $i] : p3(X64,X64) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [X64: $i] : p3(X64,X64)
  <=> ! [X64: $i] : p3(X64,X64) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [X64: $i] : p3(X64,X64),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_6) ).

tff(5,plain,
    ! [X64: $i] : p3(X64,X64),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [X64: $i] : p3(X64,X64),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [X64: $i] : p3(X64,X64),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [X64: $i] : p3(X64,X64)
    | p3(f13(c31,c34),f13(c31,c34)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    p3(f13(c31,c34),f13(c31,c34)),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    ^ [X58: $i] :
      refl(
        ( p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
      <=> p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) )),
    inference(bind,[status(th)],]) ).

tff(11,plain,
    ( ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
  <=> ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) ),
    inference(quant_intro,[status(thm)],[10]) ).

tff(12,plain,
    ( ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
  <=> ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)) ),
    inference(rewrite,[status(thm)],]) ).

tff(13,axiom,
    ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_31) ).

tff(14,plain,
    ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58)),
    inference(modus_ponens,[status(thm)],[15,11]) ).

tff(17,plain,
    ( ~ ! [X58: $i] : p25(f5(c29,f13(c31,f15(c32,X58))),f13(c31,X58))
    | p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ^ [X62: $i,X57: $i,X56: $i,X55: $i] :
      refl(
        ( ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(f7(c28,X55),X62),X57)
          | ~ p25(f5(X55,X56),X62) )
      <=> ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(f7(c28,X55),X62),X57)
          | ~ p25(f5(X55,X56),X62) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(f7(c28,X55),X62),X57)
        | ~ p25(f5(X55,X56),X62) )
  <=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(f7(c28,X55),X62),X57)
        | ~ p25(f5(X55,X56),X62) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(f7(c28,X55),X62),X57)
        | ~ p25(f5(X55,X56),X62) )
  <=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(f7(c28,X55),X62),X57)
        | ~ p25(f5(X55,X56),X62) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ^ [X62: $i,X57: $i,X56: $i,X55: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p25(f5(f7(c28,X55),X56),X57)
              | ~ p25(f5(X55,X56),X62) )
          <=> ( p25(f5(f7(c28,X55),X56),X57)
              | ~ p25(f5(X55,X56),X62) ) )),
          ( ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(X55,X56),X62)
            | ~ p25(f5(f7(c28,X55),X62),X57) )
        <=> ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(X55,X56),X62)
            | ~ p25(f5(f7(c28,X55),X62),X57) ) )),
        rewrite(
          ( ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(X55,X56),X62)
            | ~ p25(f5(f7(c28,X55),X62),X57) )
        <=> ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(f7(c28,X55),X62),X57)
            | ~ p25(f5(X55,X56),X62) ) )),
        ( ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(X55,X56),X62)
          | ~ p25(f5(f7(c28,X55),X62),X57) )
      <=> ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(f7(c28,X55),X62),X57)
          | ~ p25(f5(X55,X56),X62) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(X55,X56),X62)
        | ~ p25(f5(f7(c28,X55),X62),X57) )
  <=> ! [X62: $i,X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(f7(c28,X55),X62),X57)
        | ~ p25(f5(X55,X56),X62) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,axiom,
    ! [X62: $i,X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(X55,X56),X62)
      | ~ p25(f5(f7(c28,X55),X62),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_46) ).

tff(25,plain,
    ! [X62: $i,X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(f7(c28,X55),X62),X57)
      | ~ p25(f5(X55,X56),X62) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [X62: $i,X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(f7(c28,X55),X62),X57)
      | ~ p25(f5(X55,X56),X62) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ! [X62: $i,X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(f7(c28,X55),X62),X57)
      | ~ p25(f5(X55,X56),X62) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [X62: $i,X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(f7(c28,X55),X62),X57)
      | ~ p25(f5(X55,X56),X62) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ( ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
  <=> ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) ),
    inference(rewrite,[status(thm)],]) ).

tff(30,axiom,
    ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p25_45) ).

tff(31,plain,
    ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)),
    inference(modus_ponens,[status(thm)],[30,29]) ).

tff(32,plain,
    ( ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
            ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(f7(c28,X55),X62),X57)
            | ~ p25(f5(X55,X56),X62) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
      | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) )
  <=> ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
            ( p25(f5(f7(c28,X55),X56),X57)
            | ~ p25(f5(f7(c28,X55),X62),X57)
            | ~ p25(f5(X55,X56),X62) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
      | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(33,plain,
    ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
          ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(f7(c28,X55),X62),X57)
          | ~ p25(f5(X55,X56),X62) )
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
    | ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
    | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    ( ~ ! [X62: $i,X57: $i,X56: $i,X55: $i] :
          ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(f7(c28,X55),X62),X57)
          | ~ p25(f5(X55,X56),X62) )
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
    | ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34))
    | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
    inference(modus_ponens,[status(thm)],[33,32]) ).

tff(35,plain,
    ~ p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)),
    inference(unit_resolution,[status(thm)],[34,31,28,18]) ).

tff(36,plain,
    ^ [X63: $i] :
      refl(
        ( ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
          | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
      <=> ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
          | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) )),
    inference(bind,[status(th)],]) ).

tff(37,plain,
    ( ! [X63: $i] :
        ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
        | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
  <=> ! [X63: $i] :
        ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
        | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [X63: $i] :
        ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
        | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
  <=> ! [X63: $i] :
        ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
        | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,axiom,
    ! [X63: $i] :
      ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_49) ).

tff(40,plain,
    ! [X63: $i] :
      ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    ! [X63: $i] :
      ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
    inference(skolemize,[status(sab)],[40]) ).

tff(42,plain,
    ! [X63: $i] :
      ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) ),
    inference(modus_ponens,[status(thm)],[41,37]) ).

tff(43,plain,
    ( ( ~ ! [X63: $i] :
            ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
            | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
      | p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) )
  <=> ( ~ ! [X63: $i] :
            ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
            | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
      | p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
      | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,plain,
    ( ~ ! [X63: $i] :
          ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
          | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
    | p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
    | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(45,plain,
    ( ~ ! [X63: $i] :
          ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),X63)))
          | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),X63))),f13(c31,c34)) )
    | p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
    | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ( p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
    | p25(f5(f7(c28,c29),f13(c31,f15(f17(c33,c34),c35))),f13(c31,c34)) ),
    inference(unit_resolution,[status(thm)],[45,42]) ).

tff(47,plain,
    p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35))),
    inference(unit_resolution,[status(thm)],[46,35]) ).

tff(48,plain,
    ^ [X64: $i,X66: $i,X65: $i] :
      refl(
        ( ( ~ p3(X64,X66)
          | ~ p3(X64,X65)
          | p3(X65,X66) )
      <=> ( ~ p3(X64,X66)
          | ~ p3(X64,X65)
          | p3(X65,X66) ) )),
    inference(bind,[status(th)],]) ).

tff(49,plain,
    ( ! [X64: $i,X66: $i,X65: $i] :
        ( ~ p3(X64,X66)
        | ~ p3(X64,X65)
        | p3(X65,X66) )
  <=> ! [X64: $i,X66: $i,X65: $i] :
        ( ~ p3(X64,X66)
        | ~ p3(X64,X65)
        | p3(X65,X66) ) ),
    inference(quant_intro,[status(thm)],[48]) ).

tff(50,plain,
    ( ! [X64: $i,X66: $i,X65: $i] :
        ( ~ p3(X64,X66)
        | ~ p3(X64,X65)
        | p3(X65,X66) )
  <=> ! [X64: $i,X66: $i,X65: $i] :
        ( ~ p3(X64,X66)
        | ~ p3(X64,X65)
        | p3(X65,X66) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ^ [X64: $i,X66: $i,X65: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( p3(X65,X66)
              | ~ p3(X64,X65) )
          <=> ( ~ p3(X64,X65)
              | p3(X65,X66) ) )),
          ( ( p3(X65,X66)
            | ~ p3(X64,X65)
            | ~ p3(X64,X66) )
        <=> ( ~ p3(X64,X65)
            | p3(X65,X66)
            | ~ p3(X64,X66) ) )),
        rewrite(
          ( ( ~ p3(X64,X65)
            | p3(X65,X66)
            | ~ p3(X64,X66) )
        <=> ( ~ p3(X64,X66)
            | ~ p3(X64,X65)
            | p3(X65,X66) ) )),
        ( ( p3(X65,X66)
          | ~ p3(X64,X65)
          | ~ p3(X64,X66) )
      <=> ( ~ p3(X64,X66)
          | ~ p3(X64,X65)
          | p3(X65,X66) ) )),
    inference(bind,[status(th)],]) ).

tff(52,plain,
    ( ! [X64: $i,X66: $i,X65: $i] :
        ( p3(X65,X66)
        | ~ p3(X64,X65)
        | ~ p3(X64,X66) )
  <=> ! [X64: $i,X66: $i,X65: $i] :
        ( ~ p3(X64,X66)
        | ~ p3(X64,X65)
        | p3(X65,X66) ) ),
    inference(quant_intro,[status(thm)],[51]) ).

tff(53,axiom,
    ! [X64: $i,X66: $i,X65: $i] :
      ( p3(X65,X66)
      | ~ p3(X64,X65)
      | ~ p3(X64,X66) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_22) ).

tff(54,plain,
    ! [X64: $i,X66: $i,X65: $i] :
      ( ~ p3(X64,X66)
      | ~ p3(X64,X65)
      | p3(X65,X66) ),
    inference(modus_ponens,[status(thm)],[53,52]) ).

tff(55,plain,
    ! [X64: $i,X66: $i,X65: $i] :
      ( ~ p3(X64,X66)
      | ~ p3(X64,X65)
      | p3(X65,X66) ),
    inference(modus_ponens,[status(thm)],[54,50]) ).

tff(56,plain,
    ! [X64: $i,X66: $i,X65: $i] :
      ( ~ p3(X64,X66)
      | ~ p3(X64,X65)
      | p3(X65,X66) ),
    inference(skolemize,[status(sab)],[55]) ).

tff(57,plain,
    ! [X64: $i,X66: $i,X65: $i] :
      ( ~ p3(X64,X66)
      | ~ p3(X64,X65)
      | p3(X65,X66) ),
    inference(modus_ponens,[status(thm)],[56,49]) ).

tff(58,plain,
    ( ( ~ ! [X64: $i,X66: $i,X65: $i] :
            ( ~ p3(X64,X66)
            | ~ p3(X64,X65)
            | p3(X65,X66) )
      | ~ p3(f13(c31,c34),f13(c31,c34))
      | ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
      | p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) )
  <=> ( ~ ! [X64: $i,X66: $i,X65: $i] :
            ( ~ p3(X64,X66)
            | ~ p3(X64,X65)
            | p3(X65,X66) )
      | ~ p3(f13(c31,c34),f13(c31,c34))
      | ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
      | p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ( ~ ! [X64: $i,X66: $i,X65: $i] :
          ( ~ p3(X64,X66)
          | ~ p3(X64,X65)
          | p3(X65,X66) )
    | ~ p3(f13(c31,c34),f13(c31,c34))
    | ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
    | p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(60,plain,
    ( ~ ! [X64: $i,X66: $i,X65: $i] :
          ( ~ p3(X64,X66)
          | ~ p3(X64,X65)
          | p3(X65,X66) )
    | ~ p3(f13(c31,c34),f13(c31,c34))
    | ~ p3(f13(c31,c34),f13(c31,f15(f17(c33,c34),c35)))
    | p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
    inference(modus_ponens,[status(thm)],[59,58]) ).

tff(61,plain,
    p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)),
    inference(unit_resolution,[status(thm)],[60,57,47,9]) ).

tff(62,plain,
    ^ [X57: $i,X56: $i,X55: $i] :
      refl(
        ( ( ~ p25(f5(X55,X56),X57)
          | p25(f5(f7(c28,X55),X56),X57) )
      <=> ( ~ p25(f5(X55,X56),X57)
          | p25(f5(f7(c28,X55),X56),X57) ) )),
    inference(bind,[status(th)],]) ).

tff(63,plain,
    ( ! [X57: $i,X56: $i,X55: $i] :
        ( ~ p25(f5(X55,X56),X57)
        | p25(f5(f7(c28,X55),X56),X57) )
  <=> ! [X57: $i,X56: $i,X55: $i] :
        ( ~ p25(f5(X55,X56),X57)
        | p25(f5(f7(c28,X55),X56),X57) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,plain,
    ( ! [X57: $i,X56: $i,X55: $i] :
        ( ~ p25(f5(X55,X56),X57)
        | p25(f5(f7(c28,X55),X56),X57) )
  <=> ! [X57: $i,X56: $i,X55: $i] :
        ( ~ p25(f5(X55,X56),X57)
        | p25(f5(f7(c28,X55),X56),X57) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(65,plain,
    ^ [X57: $i,X56: $i,X55: $i] :
      rewrite(
        ( ( p25(f5(f7(c28,X55),X56),X57)
          | ~ p25(f5(X55,X56),X57) )
      <=> ( ~ p25(f5(X55,X56),X57)
          | p25(f5(f7(c28,X55),X56),X57) ) )),
    inference(bind,[status(th)],]) ).

tff(66,plain,
    ( ! [X57: $i,X56: $i,X55: $i] :
        ( p25(f5(f7(c28,X55),X56),X57)
        | ~ p25(f5(X55,X56),X57) )
  <=> ! [X57: $i,X56: $i,X55: $i] :
        ( ~ p25(f5(X55,X56),X57)
        | p25(f5(f7(c28,X55),X56),X57) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,axiom,
    ! [X57: $i,X56: $i,X55: $i] :
      ( p25(f5(f7(c28,X55),X56),X57)
      | ~ p25(f5(X55,X56),X57) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_32) ).

tff(68,plain,
    ! [X57: $i,X56: $i,X55: $i] :
      ( ~ p25(f5(X55,X56),X57)
      | p25(f5(f7(c28,X55),X56),X57) ),
    inference(modus_ponens,[status(thm)],[67,66]) ).

tff(69,plain,
    ! [X57: $i,X56: $i,X55: $i] :
      ( ~ p25(f5(X55,X56),X57)
      | p25(f5(f7(c28,X55),X56),X57) ),
    inference(modus_ponens,[status(thm)],[68,64]) ).

tff(70,plain,
    ! [X57: $i,X56: $i,X55: $i] :
      ( ~ p25(f5(X55,X56),X57)
      | p25(f5(f7(c28,X55),X56),X57) ),
    inference(skolemize,[status(sab)],[69]) ).

tff(71,plain,
    ! [X57: $i,X56: $i,X55: $i] :
      ( ~ p25(f5(X55,X56),X57)
      | p25(f5(f7(c28,X55),X56),X57) ),
    inference(modus_ponens,[status(thm)],[70,63]) ).

tff(72,plain,
    ( ( ~ ! [X57: $i,X56: $i,X55: $i] :
            ( ~ p25(f5(X55,X56),X57)
            | p25(f5(f7(c28,X55),X56),X57) )
      | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) )
  <=> ( ~ ! [X57: $i,X56: $i,X55: $i] :
            ( ~ p25(f5(X55,X56),X57)
            | p25(f5(f7(c28,X55),X56),X57) )
      | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [X57: $i,X56: $i,X55: $i] :
          ( ~ p25(f5(X55,X56),X57)
          | p25(f5(f7(c28,X55),X56),X57) )
    | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(74,plain,
    ( ~ ! [X57: $i,X56: $i,X55: $i] :
          ( ~ p25(f5(X55,X56),X57)
          | p25(f5(f7(c28,X55),X56),X57) )
    | ~ p25(f5(c29,f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))) ),
    inference(modus_ponens,[status(thm)],[73,72]) ).

tff(75,plain,
    p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35))),
    inference(unit_resolution,[status(thm)],[74,71,18]) ).

tff(76,plain,
    ^ [X75: $i] :
      refl(
        ( p4(X75,X75)
      <=> p4(X75,X75) )),
    inference(bind,[status(th)],]) ).

tff(77,plain,
    ( ! [X75: $i] : p4(X75,X75)
  <=> ! [X75: $i] : p4(X75,X75) ),
    inference(quant_intro,[status(thm)],[76]) ).

tff(78,plain,
    ( ! [X75: $i] : p4(X75,X75)
  <=> ! [X75: $i] : p4(X75,X75) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,axiom,
    ! [X75: $i] : p4(X75,X75),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4_5) ).

tff(80,plain,
    ! [X75: $i] : p4(X75,X75),
    inference(modus_ponens,[status(thm)],[79,78]) ).

tff(81,plain,
    ! [X75: $i] : p4(X75,X75),
    inference(skolemize,[status(sab)],[80]) ).

tff(82,plain,
    ! [X75: $i] : p4(X75,X75),
    inference(modus_ponens,[status(thm)],[81,77]) ).

tff(83,plain,
    ( ~ ! [X75: $i] : p4(X75,X75)
    | p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(84,plain,
    p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35))))),
    inference(unit_resolution,[status(thm)],[83,82]) ).

tff(85,plain,
    ^ [X53: $i,X52: $i,X51: $i,X54: $i] :
      refl(
        ( ( ~ p25(X53,X54)
          | ~ p4(X53,X51)
          | ~ p3(X54,X52)
          | p25(X51,X52) )
      <=> ( ~ p25(X53,X54)
          | ~ p4(X53,X51)
          | ~ p3(X54,X52)
          | p25(X51,X52) ) )),
    inference(bind,[status(th)],]) ).

tff(86,plain,
    ( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( ~ p25(X53,X54)
        | ~ p4(X53,X51)
        | ~ p3(X54,X52)
        | p25(X51,X52) )
  <=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( ~ p25(X53,X54)
        | ~ p4(X53,X51)
        | ~ p3(X54,X52)
        | p25(X51,X52) ) ),
    inference(quant_intro,[status(thm)],[85]) ).

tff(87,plain,
    ( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( ~ p25(X53,X54)
        | ~ p4(X53,X51)
        | ~ p3(X54,X52)
        | p25(X51,X52) )
  <=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( ~ p25(X53,X54)
        | ~ p4(X53,X51)
        | ~ p3(X54,X52)
        | p25(X51,X52) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(88,plain,
    ^ [X53: $i,X52: $i,X51: $i,X54: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( p25(X51,X52)
                  | ~ p3(X54,X52) )
              <=> ( ~ p3(X54,X52)
                  | p25(X51,X52) ) )),
              ( ( p25(X51,X52)
                | ~ p3(X54,X52)
                | ~ p4(X53,X51) )
            <=> ( ~ p3(X54,X52)
                | p25(X51,X52)
                | ~ p4(X53,X51) ) )),
            rewrite(
              ( ( ~ p3(X54,X52)
                | p25(X51,X52)
                | ~ p4(X53,X51) )
            <=> ( ~ p4(X53,X51)
                | ~ p3(X54,X52)
                | p25(X51,X52) ) )),
            ( ( p25(X51,X52)
              | ~ p3(X54,X52)
              | ~ p4(X53,X51) )
          <=> ( ~ p4(X53,X51)
              | ~ p3(X54,X52)
              | p25(X51,X52) ) )),
          ( ( p25(X51,X52)
            | ~ p3(X54,X52)
            | ~ p4(X53,X51)
            | ~ p25(X53,X54) )
        <=> ( ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52)
            | ~ p25(X53,X54) ) )),
        rewrite(
          ( ( ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52)
            | ~ p25(X53,X54) )
        <=> ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) ) )),
        ( ( p25(X51,X52)
          | ~ p3(X54,X52)
          | ~ p4(X53,X51)
          | ~ p25(X53,X54) )
      <=> ( ~ p25(X53,X54)
          | ~ p4(X53,X51)
          | ~ p3(X54,X52)
          | p25(X51,X52) ) )),
    inference(bind,[status(th)],]) ).

tff(89,plain,
    ( ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( p25(X51,X52)
        | ~ p3(X54,X52)
        | ~ p4(X53,X51)
        | ~ p25(X53,X54) )
  <=> ! [X53: $i,X52: $i,X51: $i,X54: $i] :
        ( ~ p25(X53,X54)
        | ~ p4(X53,X51)
        | ~ p3(X54,X52)
        | p25(X51,X52) ) ),
    inference(quant_intro,[status(thm)],[88]) ).

tff(90,axiom,
    ! [X53: $i,X52: $i,X51: $i,X54: $i] :
      ( p25(X51,X52)
      | ~ p3(X54,X52)
      | ~ p4(X53,X51)
      | ~ p25(X53,X54) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25_35) ).

tff(91,plain,
    ! [X53: $i,X52: $i,X51: $i,X54: $i] :
      ( ~ p25(X53,X54)
      | ~ p4(X53,X51)
      | ~ p3(X54,X52)
      | p25(X51,X52) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    ! [X53: $i,X52: $i,X51: $i,X54: $i] :
      ( ~ p25(X53,X54)
      | ~ p4(X53,X51)
      | ~ p3(X54,X52)
      | p25(X51,X52) ),
    inference(modus_ponens,[status(thm)],[91,87]) ).

tff(93,plain,
    ! [X53: $i,X52: $i,X51: $i,X54: $i] :
      ( ~ p25(X53,X54)
      | ~ p4(X53,X51)
      | ~ p3(X54,X52)
      | p25(X51,X52) ),
    inference(skolemize,[status(sab)],[92]) ).

tff(94,plain,
    ! [X53: $i,X52: $i,X51: $i,X54: $i] :
      ( ~ p25(X53,X54)
      | ~ p4(X53,X51)
      | ~ p3(X54,X52)
      | p25(X51,X52) ),
    inference(modus_ponens,[status(thm)],[93,86]) ).

tff(95,plain,
    ( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) )
  <=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ( ( ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
  <=> ( p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(97,plain,
    ( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
  <=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
    inference(monotonicity,[status(thm)],[96]) ).

tff(98,plain,
    ( ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) )
  <=> ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
            ( ~ p25(X53,X54)
            | ~ p4(X53,X51)
            | ~ p3(X54,X52)
            | p25(X51,X52) )
      | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
      | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
      | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
      | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ) ),
    inference(transitivity,[status(thm)],[97,95]) ).

tff(99,plain,
    ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
          ( ~ p25(X53,X54)
          | ~ p4(X53,X51)
          | ~ p3(X54,X52)
          | p25(X51,X52) )
    | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
    | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
    | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34))
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(100,plain,
    ( ~ ! [X53: $i,X52: $i,X51: $i,X54: $i] :
          ( ~ p25(X53,X54)
          | ~ p4(X53,X51)
          | ~ p3(X54,X52)
          | p25(X51,X52) )
    | p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,c34))
    | ~ p25(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f13(c31,f15(f17(c33,c34),c35)))
    | ~ p4(f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))),f5(f7(c28,c29),f13(c31,f15(c32,f15(f17(c33,c34),c35)))))
    | ~ p3(f13(c31,f15(f17(c33,c34),c35)),f13(c31,c34)) ),
    inference(modus_ponens,[status(thm)],[99,98]) ).

tff(101,plain,
    $false,
    inference(unit_resolution,[status(thm)],[100,94,31,84,75,61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SYN656-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n022.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Sep  5 06:25:39 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.22/0.46  % SZS status Unsatisfiable
% 0.22/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------