%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : COL006-5 : TPTP v8.2.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n006.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 : Wed May 29 16:37:29 EDT 2024

% Result   : Unsatisfiable 0.20s 0.56s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : COL006-5 : TPTP v8.2.0. Released v2.1.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat May 25 22:34:39 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.20/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.elC5qQnQMX/cvc5---1.0.5_12314.smt2
% 0.20/0.56  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.elC5qQnQMX/cvc5---1.0.5_12314.smt2
% 0.20/0.69  (assume a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.69  (assume a1 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.apply tptp.k X) Y) X)))
% 0.20/0.69  (assume a2 (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))))
% 0.20/0.69  (assume a3 (not (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))))
% 0.20/0.69  (step t1 (cl (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule and_neg)
% 0.20/0.69  (step t2 (cl (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg1)
% 0.20/0.69  (anchor :step t3)
% 0.20/0.69  (assume t3.a0 (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))))
% 0.20/0.69  (assume t3.a1 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))
% 0.20/0.69  (assume t3.a2 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))
% 0.20/0.69  (assume t3.a3 (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.a4 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.a5 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))
% 0.20/0.69  (assume t3.a6 (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.a7 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.a8 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.a9 (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.a10 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.a11 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.a12 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.a13 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))
% 0.20/0.69  (assume t3.a14 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.a15 (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (step t3.t1 (cl (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg1)
% 0.20/0.69  (anchor :step t3.t2)
% 0.20/0.69  (assume t3.t2.a0 (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.t2.a1 (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))))
% 0.20/0.69  (assume t3.t2.a2 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))
% 0.20/0.69  (assume t3.t2.a3 (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.t2.a4 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.t2.a5 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.t2.a6 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.t2.a7 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))
% 0.20/0.69  (assume t3.t2.a8 (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.t2.a9 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))
% 0.20/0.69  (assume t3.t2.a10 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.t2.a11 (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (assume t3.t2.a12 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))
% 0.20/0.69  (assume t3.t2.a13 (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))
% 0.20/0.69  (assume t3.t2.a14 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))
% 0.20/0.69  (assume t3.t2.a15 (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.69  (step t3.t2.t1 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.strong_fixed_point)) :rule symm :premises (t3.t2.a1))
% 0.20/0.69  (step t3.t2.t2 (cl (= tptp.fixed_pt tptp.fixed_pt)) :rule refl)
% 0.20/0.69  (step t3.t2.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))) :rule cong :premises (t3.t2.t1 t3.t2.t2))
% 0.20/0.69  (step t3.t2.t4 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt))) :rule symm :premises (t3.t2.t3))
% 0.20/0.69  (step t3.t2.t5 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) :rule symm :premises (t3.t2.a3))
% 0.20/0.69  (step t3.t2.t6 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule symm :premises (t3.t2.t5))
% 0.20/0.69  (step t3.t2.t7 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) :rule refl)
% 0.20/0.69  (step t3.t2.t8 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule cong :premises (t3.t2.t6 t3.t2.t7))
% 0.20/0.69  (step t3.t2.t9 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule symm :premises (t3.t2.t8))
% 0.20/0.69  (step t3.t2.t10 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule symm :premises (t3.t2.a9))
% 0.20/0.69  (step t3.t2.t11 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) :rule symm :premises (t3.t2.a8))
% 0.20/0.69  (step t3.t2.t12 (cl (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule symm :premises (t3.t2.t11))
% 0.20/0.69  (step t3.t2.t13 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) :rule refl)
% 0.20/0.69  (step t3.t2.t14 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule cong :premises (t3.t2.t12 t3.t2.t13))
% 0.20/0.69  (step t3.t2.t15 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) :rule symm :premises (t3.t2.a7))
% 0.20/0.69  (step t3.t2.t16 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) :rule symm :premises (t3.t2.a6))
% 0.20/0.69  (step t3.t2.t17 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule symm :premises (t3.t2.t16))
% 0.20/0.69  (step t3.t2.t18 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule symm :premises (t3.t2.a5))
% 0.20/0.69  (step t3.t2.t19 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule trans :premises (t3.t2.t10 t3.t2.t14 t3.t2.t15 t3.t2.t17 t3.t2.t18))
% 0.20/0.69  (step t3.t2.t20 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule symm :premises (t3.t2.t19))
% 0.20/0.69  (step t3.t2.t21 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule refl)
% 0.20/0.69  (step t3.t2.t22 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule cong :premises (t3.t2.t20 t3.t2.t21))
% 0.20/0.69  (step t3.t2.t23 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule symm :premises (t3.t2.a15))
% 0.20/0.69  (step t3.t2.t24 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule symm :premises (t3.t2.t23))
% 0.20/0.69  (step t3.t2.t25 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) :rule symm :premises (t3.t2.a14))
% 0.20/0.69  (step t3.t2.t26 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule symm :premises (t3.t2.t25))
% 0.20/0.69  (step t3.t2.t27 (cl (= (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) tptp.s)) :rule symm :premises (t3.t2.a13))
% 0.20/0.69  (step t3.t2.t28 (cl (= (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) :rule refl)
% 0.20/0.69  (step t3.t2.t29 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)))) :rule cong :premises (t3.t2.t27 t3.t2.t28))
% 0.20/0.69  (step t3.t2.t30 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)))) :rule trans :premises (t3.t2.t26 t3.t2.t29))
% 0.20/0.69  (step t3.t2.t31 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule cong :premises (t3.t2.t30 t3.t2.t21))
% 0.20/0.69  (step t3.t2.t32 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule refl)
% 0.20/0.69  (step t3.t2.t33 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule cong :premises (t3.t2.t31 t3.t2.t32))
% 0.20/0.69  (step t3.t2.t34 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule symm :premises (t3.t2.a12))
% 0.20/0.69  (step t3.t2.t35 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule symm :premises (t3.t2.t34))
% 0.20/0.69  (step t3.t2.t36 (cl (= (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) tptp.fixed_pt)) :rule symm :premises (t3.t2.a0))
% 0.20/0.69  (step t3.t2.t37 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule cong :premises (t3.t2.t20 t3.t2.t32))
% 0.20/0.69  (step t3.t2.t38 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule symm :premises (t3.t2.a11))
% 0.20/0.69  (step t3.t2.t39 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule symm :premises (t3.t2.t38))
% 0.20/0.69  (step t3.t2.t40 (cl (= tptp.k tptp.k)) :rule refl)
% 0.20/0.69  (step t3.t2.t41 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) :rule trans :premises (t3.t2.a5 t3.t2.t16))
% 0.20/0.69  (step t3.t2.t42 (cl (= (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule cong :premises (t3.t2.t40 t3.t2.t41))
% 0.20/0.69  (step t3.t2.t43 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule refl)
% 0.20/0.69  (step t3.t2.t44 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule cong :premises (t3.t2.t42 t3.t2.t43))
% 0.20/0.69  (step t3.t2.t45 (cl (= (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) :rule symm :premises (t3.t2.a10))
% 0.20/0.69  (step t3.t2.t46 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule trans :premises (t3.t2.t39 t3.t2.t44 t3.t2.t45 t3.t2.t17 t3.t2.t18))
% 0.20/0.69  (step t3.t2.t47 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule cong :premises (t3.t2.t19 t3.t2.t46))
% 0.20/0.69  (step t3.t2.t48 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule symm :premises (t3.t2.a4))
% 0.20/0.69  (step t3.t2.t49 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt))) :rule symm :premises (t3.t2.a2))
% 0.20/0.69  (step t3.t2.t50 (cl (= (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))) :rule trans :premises (t3.t2.t37 t3.t2.t47 t3.t2.t48 t3.t2.t8 t3.t2.t49 t3.t2.t3))
% 0.20/0.69  (step t3.t2.t51 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule cong :premises (t3.t2.t36 t3.t2.t50))
% 0.20/0.69  (step t3.t2.t52 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule trans :premises (t3.t2.t4 t3.t2.a2 t3.t2.t9 t3.t2.a4 t3.t2.t22 t3.t2.t24 t3.t2.t33 t3.t2.t35 t3.t2.t51))
% 0.20/0.69  (step t3.t2 (cl (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4 t3.t2.a5 t3.t2.a6 t3.t2.a7 t3.t2.a8 t3.t2.a9 t3.t2.a10 t3.t2.a11 t3.t2.a12 t3.t2.a13 t3.t2.a14 t3.t2.a15))
% 0.20/0.69  (step t3.t3 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t3.t4 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) :rule and_pos)
% 0.20/0.69  (step t3.t5 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t3.t6 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t3.t7 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t3.t8 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t3.t9 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t3.t10 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t3.t11 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t3.t12 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t3.t13 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t3.t14 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t3.t15 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule and_pos)
% 0.20/0.69  (step t3.t16 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t3.t17 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t3.t18 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t3.t19 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7 t3.t8 t3.t9 t3.t10 t3.t11 t3.t12 t3.t13 t3.t14 t3.t15 t3.t16 t3.t17 t3.t18))
% 0.20/0.69  (step t3.t20 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule reordering :premises (t3.t19))
% 0.20/0.69  (step t3.t21 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule contraction :premises (t3.t20))
% 0.20/0.69  (step t3.t22 (cl (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule resolution :premises (t3.t1 t3.t21))
% 0.20/0.69  (step t3.t23 (cl (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (not (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule implies_neg2)
% 0.20/0.69  (step t3.t24 (cl (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule resolution :premises (t3.t22 t3.t23))
% 0.20/0.69  (step t3.t25 (cl (=> (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule contraction :premises (t3.t24))
% 0.20/0.69  (step t3.t26 (cl (not (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule implies :premises (t3.t25))
% 0.20/0.69  (step t3.t27 (cl (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule and_neg)
% 0.20/0.69  (step t3.t28 (cl (and (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t3.t27 t3.a15 t3.a0 t3.a1 t3.a3 t3.a4 t3.a8 t3.a10 t3.a2 t3.a6 t3.a7 t3.a14 t3.a12 t3.a13 t3.a9 t3.a5 t3.a11))
% 0.20/0.69  (step t3.t29 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule resolution :premises (t3.t26 t3.t28))
% 0.20/0.69  (step t3 (cl (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4 t3.a5 t3.a6 t3.a7 t3.a8 t3.a9 t3.a10 t3.a11 t3.a12 t3.a13 t3.a14 t3.a15))
% 0.20/0.69  (step t4 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) :rule and_pos)
% 0.20/0.69  (step t5 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t6 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t7 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t8 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t9 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule and_pos)
% 0.20/0.69  (step t10 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t11 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t12 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t13 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule and_pos)
% 0.20/0.69  (step t14 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule and_pos)
% 0.20/0.69  (step t15 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t16 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t17 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule and_pos)
% 0.20/0.69  (step t18 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t19 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule and_pos)
% 0.20/0.69  (step t20 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19))
% 0.20/0.69  (step t21 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule reordering :premises (t20))
% 0.20/0.69  (step t22 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule contraction :premises (t21))
% 0.20/0.69  (step t23 (cl (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule resolution :premises (t2 t22))
% 0.20/0.69  (step t24 (cl (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (not (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule implies_neg2)
% 0.20/0.69  (step t25 (cl (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule resolution :premises (t23 t24))
% 0.20/0.70  (step t26 (cl (=> (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))))) :rule contraction :premises (t25))
% 0.20/0.70  (step t27 (cl (not (and (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule implies :premises (t26))
% 0.20/0.70  (step t28 (cl (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt)))) :rule resolution :premises (t1 t27))
% 0.20/0.70  (step t29 (cl (= (tptp.apply tptp.strong_fixed_point tptp.fixed_pt) (tptp.apply tptp.fixed_pt (tptp.apply tptp.strong_fixed_point tptp.fixed_pt))) (not (= tptp.strong_fixed_point (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule reordering :premises (t28))
% 0.20/0.70  (step t30 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t31)
% 0.20/0.70  (assume t31.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t31.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule forall_inst :args ((:= X tptp.fixed_pt) (:= Y (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.70  (step t31.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule or :premises (t31.t1))
% 0.20/0.70  (step t31.t3 (cl (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t31.t2 t31.a0))
% 0.20/0.70  (step t31 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule subproof :discharge (t31.a0))
% 0.20/0.70  (step t32 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t30 t31))
% 0.20/0.70  (step t33 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg2)
% 0.20/0.70  (step t34 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t32 t33))
% 0.20/0.70  (step t35 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule contraction :premises (t34))
% 0.20/0.70  (step t36 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies :premises (t35))
% 0.20/0.70  (step t37 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.apply tptp.k X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.apply tptp.k X) Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule equiv_pos2)
% 0.20/0.70  (anchor :step t38 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 0.20/0.70  (step t38.t1 (cl (= X X)) :rule refl)
% 0.20/0.70  (step t38.t2 (cl (= Y Y)) :rule refl)
% 0.20/0.70  (step t38.t3 (cl (= (= (tptp.apply (tptp.apply tptp.k X) Y) X) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule all_simplify)
% 0.20/0.70  (step t38 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.apply tptp.k X) Y) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))) :rule bind)
% 0.20/0.70  (step t39 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule resolution :premises (t37 t38 a1))
% 0.20/0.70  (step t40 (cl (= tptp.fixed_pt (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t36 t39))
% 0.20/0.70  (step t41 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t42)
% 0.20/0.70  (assume t42.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t42.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (:= Y (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.70  (step t42.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule or :premises (t42.t1))
% 0.20/0.70  (step t42.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t42.t2 t42.a0))
% 0.20/0.70  (step t42 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule subproof :discharge (t42.a0))
% 0.20/0.70  (step t43 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t41 t42))
% 0.20/0.70  (step t44 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg2)
% 0.20/0.70  (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t43 t44))
% 0.20/0.70  (step t46 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule contraction :premises (t45))
% 0.20/0.70  (step t47 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies :premises (t46))
% 0.20/0.70  (step t48 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t47 t39))
% 0.20/0.70  (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t50)
% 0.20/0.70  (assume t50.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t50.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule forall_inst :args ((:= X (tptp.apply tptp.k tptp.fixed_pt)) (:= Y (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))
% 0.20/0.70  (step t50.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule or :premises (t50.t1))
% 0.20/0.70  (step t50.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t50.t2 t50.a0))
% 0.20/0.70  (step t50 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule subproof :discharge (t50.a0))
% 0.20/0.70  (step t51 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t49 t50))
% 0.20/0.70  (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule implies_neg2)
% 0.20/0.70  (step t53 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule resolution :premises (t51 t52))
% 0.20/0.70  (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))))) :rule contraction :premises (t53))
% 0.20/0.70  (step t55 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies :premises (t54))
% 0.20/0.70  (step t56 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t55 a0))
% 0.20/0.70  (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t58)
% 0.20/0.70  (assume t58.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t58.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule forall_inst :args ((:= X tptp.k) (:= Y (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.70  (step t58.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule or :premises (t58.t1))
% 0.20/0.70  (step t58.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t58.t2 t58.a0))
% 0.20/0.70  (step t58 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule subproof :discharge (t58.a0))
% 0.20/0.70  (step t59 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t57 t58))
% 0.20/0.70  (step t60 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg2)
% 0.20/0.70  (step t61 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t59 t60))
% 0.20/0.70  (step t62 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule contraction :premises (t61))
% 0.20/0.70  (step t63 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies :premises (t62))
% 0.20/0.70  (step t64 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t63 a0))
% 0.20/0.70  (step t65 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t66)
% 0.20/0.70  (assume t66.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t66.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (:= Y (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.70  (step t66.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule or :premises (t66.t1))
% 0.20/0.70  (step t66.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t66.t2 t66.a0))
% 0.20/0.70  (step t66 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule subproof :discharge (t66.a0))
% 0.20/0.70  (step t67 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t65 t66))
% 0.20/0.70  (step t68 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule implies_neg2)
% 0.20/0.70  (step t69 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule resolution :premises (t67 t68))
% 0.20/0.70  (step t70 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))))) :rule contraction :premises (t69))
% 0.20/0.70  (step t71 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies :premises (t70))
% 0.20/0.70  (step t72 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t71 a0))
% 0.20/0.70  (step t73 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t74)
% 0.20/0.70  (assume t74.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t74.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (:= Y (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))
% 0.20/0.70  (step t74.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule or :premises (t74.t1))
% 0.20/0.70  (step t74.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t74.t2 t74.a0))
% 0.20/0.70  (step t74 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule subproof :discharge (t74.a0))
% 0.20/0.70  (step t75 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t73 t74))
% 0.20/0.70  (step t76 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies_neg2)
% 0.20/0.70  (step t77 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t75 t76))
% 0.20/0.70  (step t78 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule contraction :premises (t77))
% 0.20/0.70  (step t79 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule implies :premises (t78))
% 0.20/0.70  (step t80 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t79 t39))
% 0.20/0.70  (step t81 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t82)
% 0.20/0.70  (assume t82.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t82.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))) :rule forall_inst :args ((:= X tptp.s) (:= Y tptp.fixed_pt)))
% 0.20/0.70  (step t82.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule or :premises (t82.t1))
% 0.20/0.70  (step t82.t3 (cl (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule resolution :premises (t82.t2 t82.a0))
% 0.20/0.70  (step t82 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule subproof :discharge (t82.a0))
% 0.20/0.70  (step t83 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule resolution :premises (t81 t82))
% 0.20/0.70  (step t84 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (not (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))) :rule implies_neg2)
% 0.20/0.70  (step t85 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))) :rule resolution :premises (t83 t84))
% 0.20/0.70  (step t86 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt)))) :rule contraction :premises (t85))
% 0.20/0.70  (step t87 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule implies :premises (t86))
% 0.20/0.70  (step t88 (cl (= tptp.s (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt))) :rule resolution :premises (t87 t39))
% 0.20/0.70  (step t89 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t90)
% 0.20/0.70  (assume t90.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t90.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule forall_inst :args ((:= X tptp.k) (:= Y tptp.k) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))
% 0.20/0.70  (step t90.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule or :premises (t90.t1))
% 0.20/0.70  (step t90.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t90.t2 t90.a0))
% 0.20/0.70  (step t90 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule subproof :discharge (t90.a0))
% 0.20/0.70  (step t91 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t89 t90))
% 0.20/0.70  (step t92 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies_neg2)
% 0.20/0.70  (step t93 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t91 t92))
% 0.20/0.70  (step t94 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule contraction :premises (t93))
% 0.20/0.70  (step t95 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule implies :premises (t94))
% 0.20/0.70  (step t96 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply tptp.k (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t95 a0))
% 0.20/0.70  (step t97 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t98)
% 0.20/0.70  (assume t98.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t98.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))) :rule forall_inst :args ((:= X tptp.s) (:= Y (tptp.apply tptp.s tptp.k)) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))
% 0.20/0.70  (step t98.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule or :premises (t98.t1))
% 0.20/0.70  (step t98.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule resolution :premises (t98.t2 t98.a0))
% 0.20/0.70  (step t98 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule subproof :discharge (t98.a0))
% 0.20/0.70  (step t99 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule resolution :premises (t97 t98))
% 0.20/0.70  (step t100 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))) :rule implies_neg2)
% 0.20/0.70  (step t101 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))) :rule resolution :premises (t99 t100))
% 0.20/0.70  (step t102 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))))) :rule contraction :premises (t101))
% 0.20/0.70  (step t103 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule implies :premises (t102))
% 0.20/0.70  (step t104 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)) (tptp.apply (tptp.apply tptp.s tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule resolution :premises (t103 a0))
% 0.20/0.70  (step t105 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t106)
% 0.20/0.70  (assume t106.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t106.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) (:= Y tptp.fixed_pt)))
% 0.20/0.70  (step t106.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule or :premises (t106.t1))
% 0.20/0.70  (step t106.t3 (cl (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t106.t2 t106.a0))
% 0.20/0.70  (step t106 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule subproof :discharge (t106.a0))
% 0.20/0.70  (step t107 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t105 t106))
% 0.20/0.70  (step t108 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))) :rule implies_neg2)
% 0.20/0.70  (step t109 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))) :rule resolution :premises (t107 t108))
% 0.20/0.70  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt)))) :rule contraction :premises (t109))
% 0.20/0.70  (step t111 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule implies :premises (t110))
% 0.20/0.70  (step t112 (cl (= (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t111 t39))
% 0.20/0.70  (step t113 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t114)
% 0.20/0.70  (assume t114.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t114.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))) :rule forall_inst :args ((:= X (tptp.apply tptp.k tptp.s)) (:= Y tptp.k) (:= Z tptp.fixed_pt)))
% 0.20/0.70  (step t114.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule or :premises (t114.t1))
% 0.20/0.70  (step t114.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule resolution :premises (t114.t2 t114.a0))
% 0.20/0.70  (step t114 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule subproof :discharge (t114.a0))
% 0.20/0.70  (step t115 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule resolution :premises (t113 t114))
% 0.20/0.70  (step t116 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))) :rule implies_neg2)
% 0.20/0.70  (step t117 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))) :rule resolution :premises (t115 t116))
% 0.20/0.70  (step t118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt))))) :rule contraction :premises (t117))
% 0.20/0.70  (step t119 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule implies :premises (t118))
% 0.20/0.70  (step t120 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k tptp.s) tptp.fixed_pt) (tptp.apply tptp.k tptp.fixed_pt)))) :rule resolution :premises (t119 a0))
% 0.20/0.70  (step t121 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t122)
% 0.20/0.70  (assume t122.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t122.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (:= Y (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (:= Z (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))
% 0.20/0.70  (step t122.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule or :premises (t122.t1))
% 0.20/0.70  (step t122.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t122.t2 t122.a0))
% 0.20/0.70  (step t122 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule subproof :discharge (t122.a0))
% 0.20/0.70  (step t123 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t121 t122))
% 0.20/0.70  (step t124 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule implies_neg2)
% 0.20/0.70  (step t125 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule resolution :premises (t123 t124))
% 0.20/0.70  (step t126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))))) :rule contraction :premises (t125))
% 0.20/0.70  (step t127 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule implies :premises (t126))
% 0.20/0.70  (step t128 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)) (tptp.apply (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t127 a0))
% 0.20/0.70  (step t129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t130)
% 0.20/0.70  (assume t130.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))))
% 0.20/0.70  (step t130.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))) :rule forall_inst :args ((:= X (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) (:= Y tptp.fixed_pt)))
% 0.20/0.70  (step t130.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule or :premises (t130.t1))
% 0.20/0.70  (step t130.t3 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t130.t2 t130.a0))
% 0.20/0.70  (step t130 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule subproof :discharge (t130.a0))
% 0.20/0.70  (step t131 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t129 t130))
% 0.20/0.70  (step t132 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (not (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))) :rule implies_neg2)
% 0.20/0.70  (step t133 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))) :rule resolution :premises (t131 t132))
% 0.20/0.70  (step t134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt)))) :rule contraction :premises (t133))
% 0.20/0.70  (step t135 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.apply (tptp.apply tptp.k X) Y)))) (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule implies :premises (t134))
% 0.20/0.70  (step t136 (cl (= (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt))) :rule resolution :premises (t135 t39))
% 0.20/0.70  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t138)
% 0.20/0.70  (assume t138.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t138.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule forall_inst :args ((:= X (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (:= Y (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) (:= Z tptp.fixed_pt)))
% 0.20/0.70  (step t138.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule or :premises (t138.t1))
% 0.20/0.70  (step t138.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule resolution :premises (t138.t2 t138.a0))
% 0.20/0.70  (step t138 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule subproof :discharge (t138.a0))
% 0.20/0.70  (step t139 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule resolution :premises (t137 t138))
% 0.20/0.70  (step t140 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule implies_neg2)
% 0.20/0.70  (step t141 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule resolution :premises (t139 t140))
% 0.20/0.70  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt))))) :rule contraction :premises (t141))
% 0.20/0.70  (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule implies :premises (t142))
% 0.20/0.70  (step t144 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k) tptp.fixed_pt)))) :rule resolution :premises (t143 a0))
% 0.20/0.70  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) :rule implies_neg1)
% 0.20/0.70  (anchor :step t146)
% 0.20/0.70  (assume t146.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))))
% 0.20/0.70  (step t146.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule forall_inst :args ((:= X (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (:= Y (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) (:= Z tptp.fixed_pt)))
% 0.20/0.70  (step t146.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule or :premises (t146.t1))
% 0.20/0.70  (step t146.t3 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule resolution :premises (t146.t2 t146.a0))
% 0.20/0.70  (step t146 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule subproof :discharge (t146.a0))
% 0.20/0.70  (step t147 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule resolution :premises (t145 t146))
% 0.20/0.70  (step t148 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (not (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule implies_neg2)
% 0.20/0.70  (step t149 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule resolution :premises (t147 t148))
% 0.20/0.70  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z)))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt))))) :rule contraction :premises (t149))
% 0.20/0.70  (step t151 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.apply (tptp.apply (tptp.apply tptp.s X) Y) Z) (tptp.apply (tptp.apply X Z) (tptp.apply Y Z))))) (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule implies :premises (t150))
% 0.20/0.70  (step t152 (cl (= (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k)) (tptp.apply (tptp.apply tptp.s tptp.k) tptp.k))) tptp.fixed_pt) (tptp.apply (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k (tptp.apply (tptp.apply tptp.s tptp.s) (tptp.apply tptp.s tptp.k)))) (tptp.apply (tptp.apply tptp.s (tptp.apply tptp.k tptp.s)) tptp.k)) tptp.fixed_pt)))) :rule resolution :premises (t151 a0))
% 0.20/0.70  (step t153 (cl) :rule resolution :premises (t29 t40 t48 t56 t64 t72 t80 t88 t96 t104 t112 t120 t128 t136 t144 t152 a3 a2))
% 0.20/0.70  
% 0.20/0.70  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.elC5qQnQMX/cvc5---1.0.5_12314.smt2
% 0.20/0.70  % cvc5---1.0.5 exiting
% 0.20/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------