TSTP Solution File: SYO038-1.003.003 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n004.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 : Fri Sep 30 01:39:22 EDT 2022

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   66
% Syntax   : Number of formulae    :  223 ( 109 unt;   4 typ;   0 def)
%            Number of atoms       :  499 ( 122 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  521 ( 246   ~; 223   |;   0   &)
%                                         (  52 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    8 (   3 avg)
%            Number of FOOLs       :    5 (   5 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :  129 ( 123   !;   0   ?; 129   :)

% Comments : 
%------------------------------------------------------------------------------
tff(d_type,type,
    d: $i > $o ).

tff(s_type,type,
    s: $i > $i ).

tff(f_type,type,
    f: ( $i * $i ) > $i ).

tff(one_type,type,
    one: $i ).

tff(1,plain,
    ^ [N: $i] :
      refl(
        ( ( f(N,one) = s(one) )
      <=> ( f(N,one) = s(one) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [N: $i] : ( f(N,one) = s(one) )
  <=> ! [N: $i] : ( f(N,one) = s(one) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [N: $i] : ( f(N,one) = s(one) )
  <=> ! [N: $i] : ( f(N,one) = s(one) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,axiom,
    ! [N: $i] : ( f(N,one) = s(one) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(5,plain,
    ! [N: $i] : ( f(N,one) = s(one) ),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ! [N: $i] : ( f(N,one) = s(one) ),
    inference(skolemize,[status(sab)],[5]) ).

tff(7,plain,
    ! [N: $i] : ( f(N,one) = s(one) ),
    inference(modus_ponens,[status(thm)],[6,2]) ).

tff(8,plain,
    ( ~ ! [N: $i] : ( f(N,one) = s(one) )
    | ( f(s(s(one)),one) = s(one) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(9,plain,
    f(s(s(one)),one) = s(one),
    inference(unit_resolution,[status(thm)],[8,7]) ).

tff(10,plain,
    s(one) = f(s(s(one)),one),
    inference(symmetry,[status(thm)],[9]) ).

tff(11,plain,
    f(s(one),s(one)) = f(s(one),f(s(s(one)),one)),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    f(s(one),f(s(s(one)),one)) = f(s(one),s(one)),
    inference(symmetry,[status(thm)],[11]) ).

tff(13,plain,
    f(one,f(s(one),f(s(s(one)),one))) = f(one,f(s(one),s(one))),
    inference(monotonicity,[status(thm)],[12]) ).

tff(14,plain,
    f(one,f(s(one),s(one))) = f(one,f(s(one),f(s(s(one)),one))),
    inference(symmetry,[status(thm)],[13]) ).

tff(15,plain,
    s(f(one,f(s(one),s(one)))) = s(f(one,f(s(one),f(s(s(one)),one)))),
    inference(monotonicity,[status(thm)],[14]) ).

tff(16,plain,
    ( d(s(f(one,f(s(one),s(one)))))
  <=> d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
    inference(monotonicity,[status(thm)],[15]) ).

tff(17,plain,
    ^ [X: $i] :
      refl(
        ( ( f(one,s(X)) = s(s(f(one,X))) )
      <=> ( f(one,s(X)) = s(s(f(one,X))) ) )),
    inference(bind,[status(th)],]) ).

tff(18,plain,
    ( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
  <=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
    inference(quant_intro,[status(thm)],[17]) ).

tff(19,plain,
    ( ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
  <=> ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,axiom,
    ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(21,plain,
    ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
    inference(skolemize,[status(sab)],[21]) ).

tff(23,plain,
    ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) ),
    inference(modus_ponens,[status(thm)],[22,18]) ).

tff(24,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(25,plain,
    f(one,s(s(s(one)))) = s(s(f(one,s(s(one))))),
    inference(unit_resolution,[status(thm)],[24,23]) ).

tff(26,plain,
    ^ [N: $i,X: $i] :
      refl(
        ( ( f(s(N),s(X)) = f(N,f(s(N),X)) )
      <=> ( f(s(N),s(X)) = f(N,f(s(N),X)) ) )),
    inference(bind,[status(th)],]) ).

tff(27,plain,
    ( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
  <=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
    inference(quant_intro,[status(thm)],[26]) ).

tff(28,plain,
    ( ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
  <=> ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,axiom,
    ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(30,plain,
    ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
    inference(modus_ponens,[status(thm)],[31,27]) ).

tff(33,plain,
    ( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
    | ( f(s(one),s(one)) = f(one,f(s(one),one)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(34,plain,
    f(s(one),s(one)) = f(one,f(s(one),one)),
    inference(unit_resolution,[status(thm)],[33,32]) ).

tff(35,plain,
    f(one,f(s(one),one)) = f(s(one),s(one)),
    inference(symmetry,[status(thm)],[34]) ).

tff(36,plain,
    ( ~ ! [N: $i] : ( f(N,one) = s(one) )
    | ( f(s(one),one) = s(one) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(37,plain,
    f(s(one),one) = s(one),
    inference(unit_resolution,[status(thm)],[36,7]) ).

tff(38,plain,
    s(one) = f(s(one),one),
    inference(symmetry,[status(thm)],[37]) ).

tff(39,plain,
    f(one,s(one)) = f(one,f(s(one),one)),
    inference(monotonicity,[status(thm)],[38]) ).

tff(40,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(one)) = s(s(f(one,one))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(41,plain,
    f(one,s(one)) = s(s(f(one,one))),
    inference(unit_resolution,[status(thm)],[40,23]) ).

tff(42,plain,
    s(s(f(one,one))) = f(one,s(one)),
    inference(symmetry,[status(thm)],[41]) ).

tff(43,plain,
    ( ~ ! [N: $i] : ( f(N,one) = s(one) )
    | ( f(one,one) = s(one) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(44,plain,
    f(one,one) = s(one),
    inference(unit_resolution,[status(thm)],[43,7]) ).

tff(45,plain,
    s(f(one,one)) = s(s(one)),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    s(s(one)) = s(f(one,one)),
    inference(symmetry,[status(thm)],[45]) ).

tff(47,plain,
    s(s(s(one))) = s(s(f(one,one))),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    s(s(s(one))) = f(s(one),s(one)),
    inference(transitivity,[status(thm)],[47,42,39,35]) ).

tff(49,plain,
    f(one,s(s(s(one)))) = f(one,f(s(one),s(one))),
    inference(monotonicity,[status(thm)],[48]) ).

tff(50,plain,
    f(one,f(s(one),s(one))) = f(one,s(s(s(one)))),
    inference(symmetry,[status(thm)],[49]) ).

tff(51,plain,
    f(one,f(s(one),s(one))) = s(s(f(one,s(s(one))))),
    inference(transitivity,[status(thm)],[50,25]) ).

tff(52,plain,
    ( d(f(one,f(s(one),s(one))))
  <=> d(s(s(f(one,s(s(one)))))) ),
    inference(monotonicity,[status(thm)],[51]) ).

tff(53,plain,
    ( d(s(s(f(one,s(s(one))))))
  <=> d(f(one,f(s(one),s(one)))) ),
    inference(symmetry,[status(thm)],[52]) ).

tff(54,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(s(one))) = s(s(f(one,s(one)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(55,plain,
    f(one,s(s(one))) = s(s(f(one,s(one)))),
    inference(unit_resolution,[status(thm)],[54,23]) ).

tff(56,plain,
    s(s(f(one,s(one)))) = f(one,s(s(one))),
    inference(symmetry,[status(thm)],[55]) ).

tff(57,plain,
    ( d(s(s(f(one,s(one)))))
  <=> d(f(one,s(s(one)))) ),
    inference(monotonicity,[status(thm)],[56]) ).

tff(58,plain,
    f(one,f(s(one),one)) = f(one,s(one)),
    inference(symmetry,[status(thm)],[39]) ).

tff(59,plain,
    f(s(one),f(s(s(one)),one)) = f(one,s(one)),
    inference(transitivity,[status(thm)],[12,34,58]) ).

tff(60,plain,
    s(f(s(one),f(s(s(one)),one))) = s(f(one,s(one))),
    inference(monotonicity,[status(thm)],[59]) ).

tff(61,plain,
    ( d(s(f(s(one),f(s(s(one)),one))))
  <=> d(s(f(one,s(one)))) ),
    inference(monotonicity,[status(thm)],[60]) ).

tff(62,plain,
    f(s(one),f(s(s(one)),one)) = s(s(f(one,one))),
    inference(transitivity,[status(thm)],[12,34,58,41]) ).

tff(63,plain,
    ( d(f(s(one),f(s(s(one)),one)))
  <=> d(s(s(f(one,one)))) ),
    inference(monotonicity,[status(thm)],[62]) ).

tff(64,plain,
    ( d(s(s(f(one,one))))
  <=> d(f(s(one),f(s(s(one)),one))) ),
    inference(symmetry,[status(thm)],[63]) ).

tff(65,plain,
    ( d(s(f(one,one)))
  <=> d(s(s(one))) ),
    inference(monotonicity,[status(thm)],[45]) ).

tff(66,plain,
    ( d(s(s(one)))
  <=> d(s(f(one,one))) ),
    inference(symmetry,[status(thm)],[65]) ).

tff(67,plain,
    ^ [X: $i] :
      refl(
        ( ( d(s(X))
          | ~ d(X) )
      <=> ( d(s(X))
          | ~ d(X) ) )),
    inference(bind,[status(th)],]) ).

tff(68,plain,
    ( ! [X: $i] :
        ( d(s(X))
        | ~ d(X) )
  <=> ! [X: $i] :
        ( d(s(X))
        | ~ d(X) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ( ! [X: $i] :
        ( d(s(X))
        | ~ d(X) )
  <=> ! [X: $i] :
        ( d(s(X))
        | ~ d(X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ^ [X: $i] :
      rewrite(
        ( ( ~ d(X)
          | d(s(X)) )
      <=> ( d(s(X))
          | ~ d(X) ) )),
    inference(bind,[status(th)],]) ).

tff(71,plain,
    ( ! [X: $i] :
        ( ~ d(X)
        | d(s(X)) )
  <=> ! [X: $i] :
        ( d(s(X))
        | ~ d(X) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,axiom,
    ! [X: $i] :
      ( ~ d(X)
      | d(s(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(73,plain,
    ! [X: $i] :
      ( d(s(X))
      | ~ d(X) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    ! [X: $i] :
      ( d(s(X))
      | ~ d(X) ),
    inference(modus_ponens,[status(thm)],[73,69]) ).

tff(75,plain,
    ! [X: $i] :
      ( d(s(X))
      | ~ d(X) ),
    inference(skolemize,[status(sab)],[74]) ).

tff(76,plain,
    ! [X: $i] :
      ( d(s(X))
      | ~ d(X) ),
    inference(modus_ponens,[status(thm)],[75,68]) ).

tff(77,plain,
    ( d(one)
  <=> d(one) ),
    inference(rewrite,[status(thm)],]) ).

tff(78,axiom,
    d(one),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(79,plain,
    d(one),
    inference(modus_ponens,[status(thm)],[78,77]) ).

tff(80,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(one))
      | ~ d(one) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(one))
      | ~ d(one) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(81,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(one))
    | ~ d(one) ),
    inference(quant_inst,[status(thm)],]) ).

tff(82,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(one))
    | ~ d(one) ),
    inference(modus_ponens,[status(thm)],[81,80]) ).

tff(83,plain,
    d(s(one)),
    inference(unit_resolution,[status(thm)],[82,79,76]) ).

tff(84,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(one)))
      | ~ d(s(one)) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(one)))
      | ~ d(s(one)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(one)))
    | ~ d(s(one)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(86,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(one)))
    | ~ d(s(one)) ),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    d(s(s(one))),
    inference(unit_resolution,[status(thm)],[86,76,83]) ).

tff(88,plain,
    d(s(f(one,one))),
    inference(modus_ponens,[status(thm)],[87,66]) ).

tff(89,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,one))))
      | ~ d(s(f(one,one))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,one))))
      | ~ d(s(f(one,one))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(90,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,one))))
    | ~ d(s(f(one,one))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(91,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,one))))
    | ~ d(s(f(one,one))) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    ( d(s(s(f(one,one))))
    | ~ d(s(f(one,one))) ),
    inference(unit_resolution,[status(thm)],[91,76]) ).

tff(93,plain,
    d(s(s(f(one,one)))),
    inference(unit_resolution,[status(thm)],[92,88]) ).

tff(94,plain,
    d(f(s(one),f(s(s(one)),one))),
    inference(modus_ponens,[status(thm)],[93,64]) ).

tff(95,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(s(one),f(s(s(one)),one))))
      | ~ d(f(s(one),f(s(s(one)),one))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(s(one),f(s(s(one)),one))))
      | ~ d(f(s(one),f(s(s(one)),one))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(s(one),f(s(s(one)),one))))
    | ~ d(f(s(one),f(s(s(one)),one))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(97,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(s(one),f(s(s(one)),one))))
    | ~ d(f(s(one),f(s(s(one)),one))) ),
    inference(modus_ponens,[status(thm)],[96,95]) ).

tff(98,plain,
    ( d(s(f(s(one),f(s(s(one)),one))))
    | ~ d(f(s(one),f(s(s(one)),one))) ),
    inference(unit_resolution,[status(thm)],[97,76]) ).

tff(99,plain,
    d(s(f(s(one),f(s(s(one)),one)))),
    inference(unit_resolution,[status(thm)],[98,94]) ).

tff(100,plain,
    d(s(f(one,s(one)))),
    inference(modus_ponens,[status(thm)],[99,61]) ).

tff(101,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(one)))))
      | ~ d(s(f(one,s(one)))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(one)))))
      | ~ d(s(f(one,s(one)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(102,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(one)))))
    | ~ d(s(f(one,s(one)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(103,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(one)))))
    | ~ d(s(f(one,s(one)))) ),
    inference(modus_ponens,[status(thm)],[102,101]) ).

tff(104,plain,
    ( d(s(s(f(one,s(one)))))
    | ~ d(s(f(one,s(one)))) ),
    inference(unit_resolution,[status(thm)],[103,76]) ).

tff(105,plain,
    d(s(s(f(one,s(one))))),
    inference(unit_resolution,[status(thm)],[104,100]) ).

tff(106,plain,
    d(f(one,s(s(one)))),
    inference(modus_ponens,[status(thm)],[105,57]) ).

tff(107,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(s(one)))))
      | ~ d(f(one,s(s(one)))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(s(one)))))
      | ~ d(f(one,s(s(one)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(108,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(s(one)))))
    | ~ d(f(one,s(s(one)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(109,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(s(one)))))
    | ~ d(f(one,s(s(one)))) ),
    inference(modus_ponens,[status(thm)],[108,107]) ).

tff(110,plain,
    ( d(s(f(one,s(s(one)))))
    | ~ d(f(one,s(s(one)))) ),
    inference(unit_resolution,[status(thm)],[109,76]) ).

tff(111,plain,
    d(s(f(one,s(s(one))))),
    inference(unit_resolution,[status(thm)],[110,106]) ).

tff(112,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(s(one))))))
      | ~ d(s(f(one,s(s(one))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(s(one))))))
      | ~ d(s(f(one,s(s(one))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(113,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(s(one))))))
    | ~ d(s(f(one,s(s(one))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(114,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(s(one))))))
    | ~ d(s(f(one,s(s(one))))) ),
    inference(modus_ponens,[status(thm)],[113,112]) ).

tff(115,plain,
    ( d(s(s(f(one,s(s(one))))))
    | ~ d(s(f(one,s(s(one))))) ),
    inference(unit_resolution,[status(thm)],[114,76]) ).

tff(116,plain,
    d(s(s(f(one,s(s(one)))))),
    inference(unit_resolution,[status(thm)],[115,111]) ).

tff(117,plain,
    d(f(one,f(s(one),s(one)))),
    inference(modus_ponens,[status(thm)],[116,53]) ).

tff(118,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,f(s(one),s(one)))))
      | ~ d(f(one,f(s(one),s(one)))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,f(s(one),s(one)))))
      | ~ d(f(one,f(s(one),s(one)))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(119,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,f(s(one),s(one)))))
    | ~ d(f(one,f(s(one),s(one)))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(120,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,f(s(one),s(one)))))
    | ~ d(f(one,f(s(one),s(one)))) ),
    inference(modus_ponens,[status(thm)],[119,118]) ).

tff(121,plain,
    ( d(s(f(one,f(s(one),s(one)))))
    | ~ d(f(one,f(s(one),s(one)))) ),
    inference(unit_resolution,[status(thm)],[120,76]) ).

tff(122,plain,
    d(s(f(one,f(s(one),s(one))))),
    inference(unit_resolution,[status(thm)],[121,117]) ).

tff(123,plain,
    d(s(f(one,f(s(one),f(s(s(one)),one))))),
    inference(modus_ponens,[status(thm)],[122,16]) ).

tff(124,plain,
    s(f(one,s(one))) = s(f(s(one),f(s(s(one)),one))),
    inference(symmetry,[status(thm)],[60]) ).

tff(125,plain,
    f(one,s(f(one,s(one)))) = f(one,s(f(s(one),f(s(s(one)),one)))),
    inference(monotonicity,[status(thm)],[124]) ).

tff(126,plain,
    f(one,s(f(s(one),f(s(s(one)),one)))) = f(one,s(f(one,s(one)))),
    inference(symmetry,[status(thm)],[125]) ).

tff(127,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(f(s(one),f(s(s(one)),one)))) = s(s(f(one,f(s(one),f(s(s(one)),one))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(128,plain,
    f(one,s(f(s(one),f(s(s(one)),one)))) = s(s(f(one,f(s(one),f(s(s(one)),one))))),
    inference(unit_resolution,[status(thm)],[127,23]) ).

tff(129,plain,
    s(s(f(one,f(s(one),f(s(s(one)),one))))) = f(one,s(f(s(one),f(s(s(one)),one)))),
    inference(symmetry,[status(thm)],[128]) ).

tff(130,plain,
    s(s(f(one,f(s(one),f(s(s(one)),one))))) = f(one,s(f(one,s(one)))),
    inference(transitivity,[status(thm)],[129,126]) ).

tff(131,plain,
    ( d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
  <=> d(f(one,s(f(one,s(one))))) ),
    inference(monotonicity,[status(thm)],[130]) ).

tff(132,plain,
    ( d(f(one,s(f(one,s(one)))))
  <=> d(s(s(f(one,f(s(one),f(s(s(one)),one)))))) ),
    inference(symmetry,[status(thm)],[131]) ).

tff(133,plain,
    ( ~ d(f(one,s(f(one,s(one)))))
  <=> ~ d(s(s(f(one,f(s(one),f(s(s(one)),one)))))) ),
    inference(monotonicity,[status(thm)],[132]) ).

tff(134,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(135,plain,
    f(one,s(s(f(one,s(one))))) = s(s(f(one,s(f(one,s(one)))))),
    inference(unit_resolution,[status(thm)],[134,23]) ).

tff(136,plain,
    s(s(f(one,s(f(one,s(one)))))) = f(one,s(s(f(one,s(one))))),
    inference(symmetry,[status(thm)],[135]) ).

tff(137,plain,
    ( d(s(s(f(one,s(f(one,s(one)))))))
  <=> d(f(one,s(s(f(one,s(one)))))) ),
    inference(monotonicity,[status(thm)],[136]) ).

tff(138,plain,
    ( d(f(one,s(s(f(one,s(one))))))
  <=> d(s(s(f(one,s(f(one,s(one))))))) ),
    inference(symmetry,[status(thm)],[137]) ).

tff(139,plain,
    ( ~ d(f(one,s(s(f(one,s(one))))))
  <=> ~ d(s(s(f(one,s(f(one,s(one))))))) ),
    inference(monotonicity,[status(thm)],[138]) ).

tff(140,plain,
    s(s(s(f(one,s(one))))) = s(f(one,s(s(one)))),
    inference(monotonicity,[status(thm)],[56]) ).

tff(141,plain,
    s(f(one,s(s(one)))) = s(s(s(f(one,s(one))))),
    inference(symmetry,[status(thm)],[140]) ).

tff(142,plain,
    f(one,s(f(one,s(s(one))))) = f(one,s(s(s(f(one,s(one)))))),
    inference(monotonicity,[status(thm)],[141]) ).

tff(143,plain,
    f(one,s(s(s(f(one,s(one)))))) = f(one,s(f(one,s(s(one))))),
    inference(symmetry,[status(thm)],[142]) ).

tff(144,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(145,plain,
    f(one,s(s(s(f(one,s(one)))))) = s(s(f(one,s(s(f(one,s(one))))))),
    inference(unit_resolution,[status(thm)],[144,23]) ).

tff(146,plain,
    s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(s(s(f(one,s(one)))))),
    inference(symmetry,[status(thm)],[145]) ).

tff(147,plain,
    s(s(f(one,s(s(f(one,s(one))))))) = f(one,s(f(one,s(s(one))))),
    inference(transitivity,[status(thm)],[146,143]) ).

tff(148,plain,
    ( d(s(s(f(one,s(s(f(one,s(one))))))))
  <=> d(f(one,s(f(one,s(s(one)))))) ),
    inference(monotonicity,[status(thm)],[147]) ).

tff(149,plain,
    ( d(f(one,s(f(one,s(s(one))))))
  <=> d(s(s(f(one,s(s(f(one,s(one)))))))) ),
    inference(symmetry,[status(thm)],[148]) ).

tff(150,plain,
    ( ~ d(f(one,s(f(one,s(s(one))))))
  <=> ~ d(s(s(f(one,s(s(f(one,s(one)))))))) ),
    inference(monotonicity,[status(thm)],[149]) ).

tff(151,plain,
    ( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
    | ( f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(152,plain,
    f(s(s(one)),s(s(one))) = f(s(one),f(s(s(one)),s(one))),
    inference(unit_resolution,[status(thm)],[151,32]) ).

tff(153,plain,
    f(s(one),f(s(s(one)),s(one))) = f(s(s(one)),s(s(one))),
    inference(symmetry,[status(thm)],[152]) ).

tff(154,plain,
    ( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
    | ( f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(155,plain,
    f(s(s(one)),s(one)) = f(s(one),f(s(s(one)),one)),
    inference(unit_resolution,[status(thm)],[154,32]) ).

tff(156,plain,
    f(s(one),f(s(s(one)),one)) = f(s(s(one)),s(one)),
    inference(symmetry,[status(thm)],[155]) ).

tff(157,plain,
    s(s(f(one,one))) = f(s(s(one)),s(one)),
    inference(transitivity,[status(thm)],[42,39,35,11,156]) ).

tff(158,plain,
    f(s(one),s(s(f(one,one)))) = f(s(one),f(s(s(one)),s(one))),
    inference(monotonicity,[status(thm)],[157]) ).

tff(159,plain,
    ( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
    | ( f(s(one),s(s(f(one,one)))) = f(one,f(s(one),s(f(one,one)))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(160,plain,
    f(s(one),s(s(f(one,one)))) = f(one,f(s(one),s(f(one,one)))),
    inference(unit_resolution,[status(thm)],[159,32]) ).

tff(161,plain,
    f(one,f(s(one),s(f(one,one)))) = f(s(one),s(s(f(one,one)))),
    inference(symmetry,[status(thm)],[160]) ).

tff(162,plain,
    f(s(one),s(f(one,one))) = f(s(one),s(s(one))),
    inference(monotonicity,[status(thm)],[45]) ).

tff(163,plain,
    f(s(one),s(s(one))) = f(s(one),s(f(one,one))),
    inference(symmetry,[status(thm)],[162]) ).

tff(164,plain,
    ( ~ ! [N: $i,X: $i] : ( f(s(N),s(X)) = f(N,f(s(N),X)) )
    | ( f(s(one),s(s(one))) = f(one,f(s(one),s(one))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(165,plain,
    f(s(one),s(s(one))) = f(one,f(s(one),s(one))),
    inference(unit_resolution,[status(thm)],[164,32]) ).

tff(166,plain,
    f(one,f(s(one),s(one))) = f(s(one),s(s(one))),
    inference(symmetry,[status(thm)],[165]) ).

tff(167,plain,
    s(s(f(one,s(s(one))))) = f(one,s(s(s(one)))),
    inference(symmetry,[status(thm)],[25]) ).

tff(168,plain,
    s(s(f(one,s(s(one))))) = f(s(one),s(f(one,one))),
    inference(transitivity,[status(thm)],[167,49,166,163]) ).

tff(169,plain,
    f(one,s(s(f(one,s(s(one)))))) = f(one,f(s(one),s(f(one,one)))),
    inference(monotonicity,[status(thm)],[168]) ).

tff(170,plain,
    ( ~ ! [X: $i] : ( f(one,s(X)) = s(s(f(one,X))) )
    | ( f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(171,plain,
    f(one,s(s(f(one,s(s(one)))))) = s(s(f(one,s(f(one,s(s(one))))))),
    inference(unit_resolution,[status(thm)],[170,23]) ).

tff(172,plain,
    s(s(f(one,s(f(one,s(s(one))))))) = f(one,s(s(f(one,s(s(one)))))),
    inference(symmetry,[status(thm)],[171]) ).

tff(173,plain,
    s(s(f(one,s(f(one,s(s(one))))))) = f(s(s(one)),s(s(one))),
    inference(transitivity,[status(thm)],[172,169,161,158,153]) ).

tff(174,plain,
    ( d(s(s(f(one,s(f(one,s(s(one))))))))
  <=> d(f(s(s(one)),s(s(one)))) ),
    inference(monotonicity,[status(thm)],[173]) ).

tff(175,plain,
    ( d(f(s(s(one)),s(s(one))))
  <=> d(s(s(f(one,s(f(one,s(s(one)))))))) ),
    inference(symmetry,[status(thm)],[174]) ).

tff(176,plain,
    ( ~ d(f(s(s(one)),s(s(one))))
  <=> ~ d(s(s(f(one,s(f(one,s(s(one)))))))) ),
    inference(monotonicity,[status(thm)],[175]) ).

tff(177,plain,
    ( ~ d(f(s(s(one)),s(s(one))))
  <=> ~ d(f(s(s(one)),s(s(one)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(178,axiom,
    ~ d(f(s(s(one)),s(s(one)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

tff(179,plain,
    ~ d(f(s(s(one)),s(s(one)))),
    inference(modus_ponens,[status(thm)],[178,177]) ).

tff(180,plain,
    ~ d(s(s(f(one,s(f(one,s(s(one)))))))),
    inference(modus_ponens,[status(thm)],[179,176]) ).

tff(181,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(f(one,s(s(one))))))))
      | ~ d(s(f(one,s(f(one,s(s(one))))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(f(one,s(s(one))))))))
      | ~ d(s(f(one,s(f(one,s(s(one))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(182,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(f(one,s(s(one))))))))
    | ~ d(s(f(one,s(f(one,s(s(one))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(183,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(f(one,s(s(one))))))))
    | ~ d(s(f(one,s(f(one,s(s(one))))))) ),
    inference(modus_ponens,[status(thm)],[182,181]) ).

tff(184,plain,
    ( d(s(s(f(one,s(f(one,s(s(one))))))))
    | ~ d(s(f(one,s(f(one,s(s(one))))))) ),
    inference(unit_resolution,[status(thm)],[183,76]) ).

tff(185,plain,
    ~ d(s(f(one,s(f(one,s(s(one))))))),
    inference(unit_resolution,[status(thm)],[184,180]) ).

tff(186,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(f(one,s(s(one)))))))
      | ~ d(f(one,s(f(one,s(s(one)))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(f(one,s(s(one)))))))
      | ~ d(f(one,s(f(one,s(s(one)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(187,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(f(one,s(s(one)))))))
    | ~ d(f(one,s(f(one,s(s(one)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(188,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(f(one,s(s(one)))))))
    | ~ d(f(one,s(f(one,s(s(one)))))) ),
    inference(modus_ponens,[status(thm)],[187,186]) ).

tff(189,plain,
    ( d(s(f(one,s(f(one,s(s(one)))))))
    | ~ d(f(one,s(f(one,s(s(one)))))) ),
    inference(unit_resolution,[status(thm)],[188,76]) ).

tff(190,plain,
    ~ d(f(one,s(f(one,s(s(one)))))),
    inference(unit_resolution,[status(thm)],[189,185]) ).

tff(191,plain,
    ~ d(s(s(f(one,s(s(f(one,s(one)))))))),
    inference(modus_ponens,[status(thm)],[190,150]) ).

tff(192,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(s(f(one,s(one))))))))
      | ~ d(s(f(one,s(s(f(one,s(one))))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(s(f(one,s(one))))))))
      | ~ d(s(f(one,s(s(f(one,s(one))))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(193,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(s(f(one,s(one))))))))
    | ~ d(s(f(one,s(s(f(one,s(one))))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(194,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(s(f(one,s(one))))))))
    | ~ d(s(f(one,s(s(f(one,s(one))))))) ),
    inference(modus_ponens,[status(thm)],[193,192]) ).

tff(195,plain,
    ( d(s(s(f(one,s(s(f(one,s(one))))))))
    | ~ d(s(f(one,s(s(f(one,s(one))))))) ),
    inference(unit_resolution,[status(thm)],[194,76]) ).

tff(196,plain,
    ~ d(s(f(one,s(s(f(one,s(one))))))),
    inference(unit_resolution,[status(thm)],[195,191]) ).

tff(197,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(s(f(one,s(one)))))))
      | ~ d(f(one,s(s(f(one,s(one)))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(s(f(one,s(one)))))))
      | ~ d(f(one,s(s(f(one,s(one)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(198,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(s(f(one,s(one)))))))
    | ~ d(f(one,s(s(f(one,s(one)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(199,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(s(f(one,s(one)))))))
    | ~ d(f(one,s(s(f(one,s(one)))))) ),
    inference(modus_ponens,[status(thm)],[198,197]) ).

tff(200,plain,
    ( d(s(f(one,s(s(f(one,s(one)))))))
    | ~ d(f(one,s(s(f(one,s(one)))))) ),
    inference(unit_resolution,[status(thm)],[199,76]) ).

tff(201,plain,
    ~ d(f(one,s(s(f(one,s(one)))))),
    inference(unit_resolution,[status(thm)],[200,196]) ).

tff(202,plain,
    ~ d(s(s(f(one,s(f(one,s(one))))))),
    inference(modus_ponens,[status(thm)],[201,139]) ).

tff(203,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(f(one,s(one)))))))
      | ~ d(s(f(one,s(f(one,s(one)))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,s(f(one,s(one)))))))
      | ~ d(s(f(one,s(f(one,s(one)))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(204,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(f(one,s(one)))))))
    | ~ d(s(f(one,s(f(one,s(one)))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(205,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,s(f(one,s(one)))))))
    | ~ d(s(f(one,s(f(one,s(one)))))) ),
    inference(modus_ponens,[status(thm)],[204,203]) ).

tff(206,plain,
    ( d(s(s(f(one,s(f(one,s(one)))))))
    | ~ d(s(f(one,s(f(one,s(one)))))) ),
    inference(unit_resolution,[status(thm)],[205,76]) ).

tff(207,plain,
    ~ d(s(f(one,s(f(one,s(one)))))),
    inference(unit_resolution,[status(thm)],[206,202]) ).

tff(208,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(f(one,s(one))))))
      | ~ d(f(one,s(f(one,s(one))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(f(one,s(f(one,s(one))))))
      | ~ d(f(one,s(f(one,s(one))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(209,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(f(one,s(one))))))
    | ~ d(f(one,s(f(one,s(one))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(210,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(f(one,s(f(one,s(one))))))
    | ~ d(f(one,s(f(one,s(one))))) ),
    inference(modus_ponens,[status(thm)],[209,208]) ).

tff(211,plain,
    ( d(s(f(one,s(f(one,s(one))))))
    | ~ d(f(one,s(f(one,s(one))))) ),
    inference(unit_resolution,[status(thm)],[210,76]) ).

tff(212,plain,
    ~ d(f(one,s(f(one,s(one))))),
    inference(unit_resolution,[status(thm)],[211,207]) ).

tff(213,plain,
    ~ d(s(s(f(one,f(s(one),f(s(s(one)),one)))))),
    inference(modus_ponens,[status(thm)],[212,133]) ).

tff(214,plain,
    ( ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
      | ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) )
  <=> ( ~ ! [X: $i] :
            ( d(s(X))
            | ~ d(X) )
      | d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
      | ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(215,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
    | ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
    inference(quant_inst,[status(thm)],]) ).

tff(216,plain,
    ( ~ ! [X: $i] :
          ( d(s(X))
          | ~ d(X) )
    | d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
    | ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
    inference(modus_ponens,[status(thm)],[215,214]) ).

tff(217,plain,
    ( d(s(s(f(one,f(s(one),f(s(s(one)),one))))))
    | ~ d(s(f(one,f(s(one),f(s(s(one)),one))))) ),
    inference(unit_resolution,[status(thm)],[216,76]) ).

tff(218,plain,
    ~ d(s(f(one,f(s(one),f(s(s(one)),one))))),
    inference(unit_resolution,[status(thm)],[217,213]) ).

tff(219,plain,
    $false,
    inference(unit_resolution,[status(thm)],[218,123]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SYO038-1.003.003 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n004.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 10:14:04 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.21/0.40  % SZS status Unsatisfiable
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------